%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO188+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 : n011.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 06:30:50 EDT 2022 % Result : Theorem 4.46s 4.63s % Output : Proof 4.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO188+3 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.34 % Computer : n011.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sat Jun 18 03:55:07 EDT 2022 % 0.12/0.34 % CPUTime : % 4.46/4.63 % SZS status Theorem % 4.46/4.63 (* PROOF-FOUND *) % 4.46/4.63 (* BEGIN-PROOF *) % 4.46/4.63 % SZS output start Proof % 4.46/4.63 1. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 4.46/4.63 2. (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_0) ### Axiom % 4.46/4.63 3. (distinct_points T_1 T_0) (-. (distinct_points T_1 T_0)) ### Axiom % 4.46/4.63 4. (distinct_points T_1 T_0) (-. (distinct_points T_1 T_0)) ### Axiom % 4.46/4.63 5. (distinct_points T_2 T_0) (-. (distinct_points T_2 T_0)) ### Axiom % 4.46/4.63 6. (distinct_points T_2 T_0) (-. (distinct_points T_2 T_0)) ### Axiom % 4.46/4.63 7. (apart_point_and_line T_2 (line_connecting T_1 T_0)) (-. (apart_point_and_line T_2 (line_connecting T_1 T_0))) ### Axiom % 4.46/4.63 8. (distinct_points T_1 T_0) (-. (distinct_points T_1 T_0)) ### Axiom % 4.46/4.63 9. (distinct_lines (line_connecting T_1 T_0) (line_connecting T_2 T_0)) (-. (distinct_lines (line_connecting T_1 T_0) (line_connecting T_2 T_0))) ### Axiom % 4.46/4.63 10. (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (apart_point_and_line T_1 (line_connecting T_1 T_0)) ### Axiom % 4.46/4.63 11. (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (apart_point_and_line T_1 (line_connecting T_2 T_0)) ### Axiom % 4.46/4.63 12. (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (apart_point_and_line T_0 (line_connecting T_1 T_0)) ### Axiom % 4.46/4.63 13. (-. (apart_point_and_line T_0 (line_connecting T_2 T_0))) (apart_point_and_line T_0 (line_connecting T_2 T_0)) ### Axiom % 4.46/4.63 14. (((distinct_points T_1 T_0) /\ (distinct_lines (line_connecting T_1 T_0) (line_connecting T_2 T_0))) => ((apart_point_and_line T_1 (line_connecting T_1 T_0)) \/ ((apart_point_and_line T_1 (line_connecting T_2 T_0)) \/ ((apart_point_and_line T_0 (line_connecting T_1 T_0)) \/ (apart_point_and_line T_0 (line_connecting T_2 T_0)))))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (distinct_lines (line_connecting T_1 T_0) (line_connecting T_2 T_0)) (distinct_points T_1 T_0) ### DisjTree 8 9 10 11 12 13 % 4.46/4.63 15. (All V, (((distinct_points T_1 T_0) /\ (distinct_lines (line_connecting T_1 T_0) V)) => ((apart_point_and_line T_1 (line_connecting T_1 T_0)) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 (line_connecting T_1 T_0)) \/ (apart_point_and_line T_0 V)))))) (distinct_points T_1 T_0) (distinct_lines (line_connecting T_1 T_0) (line_connecting T_2 T_0)) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_0))) ### All 14 % 4.46/4.63 16. (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_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (distinct_lines (line_connecting T_1 T_0) (line_connecting T_2 T_0)) (distinct_points T_1 T_0) ### All 15 % 4.46/4.63 17. (-. (apart_point_and_line T_2 (line_connecting T_2 T_0))) (apart_point_and_line T_2 (line_connecting T_2 T_0)) ### Axiom % 4.46/4.63 18. ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) (line_connecting T_2 T_0)) \/ (apart_point_and_line T_2 (line_connecting T_2 T_0)))) (-. (apart_point_and_line T_2 (line_connecting T_2 T_0))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_0))) (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_1 T_0)) ### DisjTree 7 16 17 % 4.46/4.63 19. (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_2 (line_connecting T_2 T_0))) ### All 18 % 4.46/4.63 20. ((distinct_points T_2 T_0) => (-. (apart_point_and_line T_0 (line_connecting T_2 T_0)))) (-. (apart_point_and_line T_2 (line_connecting T_2 T_0))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (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_1 T_0)) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (distinct_points T_2 T_0) ### Imply 6 19 % 4.46/4.63 21. (All Y, ((distinct_points T_2 Y) => (-. (apart_point_and_line Y (line_connecting T_2 Y))))) (distinct_points T_2 T_0) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_2 (line_connecting T_2 T_0))) ### All 20 % 4.46/4.63 22. (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (apart_point_and_line T_2 (line_connecting T_2 T_0))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (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_1 T_0)) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (distinct_points T_2 T_0) ### All 21 % 4.46/4.63 23. ((distinct_points T_2 T_0) => (-. (apart_point_and_line T_2 (line_connecting T_2 T_0)))) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (distinct_points T_1 T_0) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_2 T_0) ### Imply 5 22 % 4.46/4.63 24. (All Y, ((distinct_points T_2 Y) => (-. (apart_point_and_line T_2 (line_connecting T_2 Y))))) (distinct_points T_2 T_0) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (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_1 T_0)) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) ### All 23 % 4.47/4.66 25. (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (distinct_points T_1 T_0) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_2 T_0) ### All 24 % 4.47/4.66 26. (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_2 T_0) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (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_1 T_0)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) ### All 25 % 4.47/4.66 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, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (distinct_points T_1 T_0) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_2 T_0) ### All 26 % 4.47/4.66 28. ((distinct_points T_1 T_0) => (-. (apart_point_and_line T_0 (line_connecting T_1 T_0)))) (distinct_points T_2 T_0) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (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_1 T_0)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (distinct_points T_1 T_0) ### Imply 4 27 % 4.47/4.66 29. (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line Y (line_connecting T_1 Y))))) (distinct_points T_1 T_0) (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, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_2 T_0) ### All 28 % 4.47/4.66 30. ((distinct_points T_1 T_0) => (-. (apart_point_and_line T_1 (line_connecting T_1 T_0)))) (distinct_points T_2 T_0) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (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_1 T_0)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line Y (line_connecting T_1 Y))))) (distinct_points T_1 T_0) ### Imply 3 29 % 4.47/4.66 31. (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 Y))))) (distinct_points T_1 T_0) (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line Y (line_connecting T_1 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, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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_2 T_0))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_2 T_0) ### All 30 % 4.47/4.66 32. (distinct_points T_2 T_0) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (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_1 T_0)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (distinct_points T_1 T_0) (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 Y))))) ### All 31 % 4.47/4.66 33. (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)))))))) (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 Y))))) (distinct_points T_1 T_0) (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, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_2 T_0) ### All 32 % 4.47/4.71 34. (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_2 T_0) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (distinct_points T_1 T_0) (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 Y))))) ### All 33 % 4.47/4.71 35. ((distinct_points T_0 T_1) => ((distinct_points T_0 T_0) \/ (distinct_points T_1 T_0))) (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 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, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_2 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))))))))) (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_1) ### DisjTree 1 2 34 % 4.47/4.71 36. (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))))))))) (distinct_points T_2 T_0) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 Y))))) ### All 35 % 4.47/4.71 37. (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 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, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_2 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))))))))) (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_1) ### All 36 % 4.47/4.71 38. (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))))))))) (distinct_points T_2 T_0) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) ### All 37 % 4.47/4.71 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_lines Y Z) \/ (apart_point_and_line X Z)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_2 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))))))))) (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_1) ### All 38 % 4.47/4.71 40. (All X, (-. (distinct_points X X))) (distinct_points T_0 T_1) (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_2 T_0) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X 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, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### All 39 % 4.47/4.71 41. (-. (-. (apart_point_and_line T_2 (line_connecting T_1 T_0)))) (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, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_2 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))))))))) (distinct_points T_0 T_1) (All X, (-. (distinct_points X X))) ### NotNot 40 % 4.47/4.71 42. (-. (incident_point_and_line T_2 (line_connecting T_1 T_0))) (All X, (-. (distinct_points X X))) (distinct_points T_0 T_1) (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_2 T_0) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X 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, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### Definition-Pseudo(incident_point_and_line) 41 % 4.47/4.71 43. (incident_point_and_line T_1 (line_connecting T_2 T_0)) (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, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_2 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))))))))) (distinct_points T_0 T_1) (All X, (-. (distinct_points X X))) (-. (incident_point_and_line T_2 (line_connecting T_1 T_0))) ### Definition-Pseudo(incident_point_and_line) 42 % 4.54/4.72 44. (-. (((distinct_points T_2 T_0) /\ ((distinct_points T_2 T_1) /\ ((distinct_points T_0 T_1) /\ (incident_point_and_line T_1 (line_connecting T_2 T_0))))) => (incident_point_and_line T_2 (line_connecting T_1 T_0)))) (All X, (-. (distinct_points X X))) (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 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)))))) ### ConjTree 43 % 4.54/4.72 45. (-. (All Z, (((distinct_points T_2 T_0) /\ ((distinct_points T_2 Z) /\ ((distinct_points T_0 Z) /\ (incident_point_and_line Z (line_connecting T_2 T_0))))) => (incident_point_and_line T_2 (line_connecting Z T_0))))) (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, ((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, (-. (distinct_points X X))) ### NotAllEx 44 % 4.54/4.72 46. (-. (All Y, (All Z, (((distinct_points T_2 Y) /\ ((distinct_points T_2 Z) /\ ((distinct_points Y Z) /\ (incident_point_and_line Z (line_connecting T_2 Y))))) => (incident_point_and_line T_2 (line_connecting Z Y)))))) (All X, (-. (distinct_points X X))) (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 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)))))) ### NotAllEx 45 % 4.54/4.72 47. (-. (All X, (All Y, (All Z, (((distinct_points X Y) /\ ((distinct_points X Z) /\ ((distinct_points Y Z) /\ (incident_point_and_line Z (line_connecting X Y))))) => (incident_point_and_line X (line_connecting 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, ((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, (-. (distinct_points X X))) ### NotAllEx 46 % 4.54/4.72 % SZS output end Proof % 4.54/4.72 (* END-PROOF *) %------------------------------------------------------------------------------