%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO184+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 : n024.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 06:30:46 EDT 2022 % Result : Theorem 10.46s 10.64s % Output : Proof 10.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : GEO184+2 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.31 % Computer : n024.cluster.edu % 0.12/0.31 % Model : x86_64 x86_64 % 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.31 % Memory : 8042.1875MB % 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 600 % 0.12/0.32 % DateTime : Fri Jun 17 21:42:02 EDT 2022 % 0.12/0.32 % CPUTime : % 10.46/10.64 % SZS status Theorem % 10.46/10.64 (* PROOF-FOUND *) % 10.46/10.64 (* BEGIN-PROOF *) % 10.46/10.64 % SZS output start Proof % 10.46/10.64 1. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 10.46/10.64 2. (distinct_points T_0 T_0) ### Extension/test/apart1 % 10.46/10.64 3. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 10.46/10.64 4. (distinct_lines T_2 (line_connecting T_0 T_1)) (-. (distinct_lines T_2 (line_connecting T_0 T_1))) ### Axiom % 10.46/10.64 5. (-. (distinct_lines T_2 T_2)) (distinct_lines T_2 T_2) ### Axiom % 10.46/10.64 6. (-. (distinct_lines (line_connecting T_0 T_1) T_2)) (distinct_lines (line_connecting T_0 T_1) T_2) ### Axiom % 10.46/10.64 7. ((distinct_lines T_2 (line_connecting T_0 T_1)) => ((distinct_lines T_2 T_2) \/ (distinct_lines (line_connecting T_0 T_1) T_2))) (-. (distinct_lines (line_connecting T_0 T_1) T_2)) (-. (distinct_lines T_2 T_2)) (distinct_lines T_2 (line_connecting T_0 T_1)) ### DisjTree 4 5 6 % 10.46/10.64 8. (All Z, ((distinct_lines T_2 (line_connecting T_0 T_1)) => ((distinct_lines T_2 Z) \/ (distinct_lines (line_connecting T_0 T_1) Z)))) (distinct_lines T_2 (line_connecting T_0 T_1)) (-. (distinct_lines T_2 T_2)) (-. (distinct_lines (line_connecting T_0 T_1) T_2)) ### All 7 % 10.46/10.64 9. (All Y, (All Z, ((distinct_lines T_2 Y) => ((distinct_lines T_2 Z) \/ (distinct_lines Y Z))))) (-. (distinct_lines (line_connecting T_0 T_1) T_2)) (-. (distinct_lines T_2 T_2)) (distinct_lines T_2 (line_connecting T_0 T_1)) ### All 8 % 10.46/10.64 10. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 10.46/10.64 11. (distinct_points T_1 T_0) (-. (distinct_points T_1 T_0)) ### Axiom % 10.46/10.64 12. (distinct_lines (line_connecting T_0 T_1) T_2) (-. (distinct_lines (line_connecting T_0 T_1) T_2)) ### Axiom % 10.46/10.64 13. (-. (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 % 10.46/10.64 14. (-. (apart_point_and_line T_1 T_2)) (apart_point_and_line T_1 T_2) ### Axiom % 10.46/10.64 15. (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (apart_point_and_line T_0 (line_connecting T_0 T_1)) ### Axiom % 10.46/10.64 16. (-. (apart_point_and_line T_0 T_2)) (apart_point_and_line T_0 T_2) ### Axiom % 10.46/10.64 17. (((distinct_points T_1 T_0) /\ (distinct_lines (line_connecting T_0 T_1) T_2)) => ((apart_point_and_line T_1 (line_connecting T_0 T_1)) \/ ((apart_point_and_line T_1 T_2) \/ ((apart_point_and_line T_0 (line_connecting T_0 T_1)) \/ (apart_point_and_line T_0 T_2))))) (-. (apart_point_and_line T_0 T_2)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 T_2)) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) T_2) (distinct_points T_1 T_0) ### DisjTree 11 12 13 14 15 16 % 10.46/10.64 18. (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) T_2) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 T_2)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 T_2)) ### All 17 % 10.46/10.64 19. ((distinct_points T_0 T_0) /\ (distinct_points T_0 T_1)) ### And 2 % 10.46/10.64 20. ((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 T_2)) (-. (apart_point_and_line T_1 T_2)) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) T_2) (distinct_points T_1 T_0) (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_0 T_1) ### DisjTree 10 18 19 % 10.46/10.64 21. (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) (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) T_2) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 T_2)) (-. (apart_point_and_line T_0 T_2)) ### All 20 % 10.46/10.64 22. (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 T_2)) (-. (apart_point_and_line T_1 T_2)) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) T_2) (distinct_points T_1 T_0) (distinct_points T_0 T_1) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) ### All 21 % 10.46/10.64 23. (-. (distinct_lines T_2 T_2)) (distinct_lines T_2 T_2) ### Axiom % 10.46/10.64 24. ((distinct_lines (line_connecting T_0 T_1) T_2) => ((distinct_lines (line_connecting T_0 T_1) T_2) \/ (distinct_lines T_2 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))))) (distinct_points T_0 T_1) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 T_2)) (-. (apart_point_and_line 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))))))) (distinct_lines T_2 (line_connecting T_0 T_1)) (-. (distinct_lines T_2 T_2)) (All Y, (All Z, ((distinct_lines T_2 Y) => ((distinct_lines T_2 Z) \/ (distinct_lines Y Z))))) ### DisjTree 9 22 23 % 10.46/10.64 25. (All Z, ((distinct_lines (line_connecting T_0 T_1) T_2) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (distinct_lines T_2 Z)))) (All Y, (All Z, ((distinct_lines T_2 Y) => ((distinct_lines T_2 Z) \/ (distinct_lines Y Z))))) (-. (distinct_lines T_2 T_2)) (distinct_lines 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 T_2)) (-. (apart_point_and_line T_1 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_1) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) ### All 24 % 10.46/10.64 26. (All Y, (All Z, ((distinct_lines (line_connecting T_0 T_1) Y) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (distinct_lines Y Z))))) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (distinct_points T_0 T_1) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 T_2)) (-. (apart_point_and_line 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))))))) (distinct_lines T_2 (line_connecting T_0 T_1)) (-. (distinct_lines T_2 T_2)) (All Y, (All Z, ((distinct_lines T_2 Y) => ((distinct_lines T_2 Z) \/ (distinct_lines Y Z))))) ### All 25 % 10.46/10.64 27. (All X, (-. (distinct_lines X X))) (All Y, (All Z, ((distinct_lines T_2 Y) => ((distinct_lines T_2 Z) \/ (distinct_lines Y Z))))) (distinct_lines 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 T_2)) (-. (apart_point_and_line T_1 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_1) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (All Y, (All Z, ((distinct_lines (line_connecting T_0 T_1) Y) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (distinct_lines Y Z))))) ### All 26 % 10.62/10.85 28. (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (distinct_points T_0 T_1) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 T_2)) (-. (apart_point_and_line 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))))))) (distinct_lines T_2 (line_connecting T_0 T_1)) (All Y, (All Z, ((distinct_lines T_2 Y) => ((distinct_lines T_2 Z) \/ (distinct_lines Y Z))))) (All X, (-. (distinct_lines X X))) ### All 27 % 10.62/10.85 29. (distinct_points T_1 T_1) ### Extension/test/apart1 % 10.62/10.85 30. ((distinct_points T_1 T_0) /\ (distinct_points T_1 T_1)) ### And 29 % 10.62/10.85 31. ((distinct_points T_0 T_1) => ((apart_point_and_line T_1 (line_connecting T_0 T_1)) => ((distinct_points T_1 T_0) /\ (distinct_points T_1 T_1)))) (All X, (-. (distinct_lines X X))) (All Y, (All Z, ((distinct_lines T_2 Y) => ((distinct_lines T_2 Z) \/ (distinct_lines Y Z))))) (distinct_lines 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 T_2)) (-. (apart_point_and_line T_1 T_2)) (distinct_points T_1 T_0) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (distinct_points T_0 T_1) ### DisjTree 3 28 30 % 10.62/10.85 32. (distinct_points T_0 T_1) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 T_2)) (-. (apart_point_and_line 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))))))) (distinct_lines T_2 (line_connecting T_0 T_1)) (All Y, (All Z, ((distinct_lines T_2 Y) => ((distinct_lines T_2 Z) \/ (distinct_lines Y Z))))) (All X, (-. (distinct_lines X X))) ### All 31 % 10.62/10.85 33. (All Y, (All Z, ((distinct_points T_0 Y) => ((apart_point_and_line Z (line_connecting T_0 Y)) => ((distinct_points Z T_0) /\ (distinct_points Z Y)))))) (All X, (-. (distinct_lines X X))) (All Y, (All Z, ((distinct_lines T_2 Y) => ((distinct_lines T_2 Z) \/ (distinct_lines Y Z))))) (distinct_lines 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 T_2)) (-. (apart_point_and_line T_1 T_2)) (distinct_points T_1 T_0) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (distinct_points T_0 T_1) ### All 32 % 10.62/10.85 34. ((distinct_points T_0 T_1) => ((distinct_points T_0 T_0) \/ (distinct_points T_1 T_0))) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (apart_point_and_line T_1 T_2)) (-. (apart_point_and_line 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))))))) (distinct_lines T_2 (line_connecting T_0 T_1)) (All Y, (All Z, ((distinct_lines T_2 Y) => ((distinct_lines T_2 Z) \/ (distinct_lines Y Z))))) (All X, (-. (distinct_lines X X))) (All Y, (All Z, ((distinct_points T_0 Y) => ((apart_point_and_line Z (line_connecting T_0 Y)) => ((distinct_points Z T_0) /\ (distinct_points Z Y)))))) (distinct_points T_0 T_1) ### DisjTree 1 2 33 % 10.62/10.85 35. (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) (distinct_points T_0 T_1) (All Y, (All Z, ((distinct_points T_0 Y) => ((apart_point_and_line Z (line_connecting T_0 Y)) => ((distinct_points Z T_0) /\ (distinct_points Z Y)))))) (All X, (-. (distinct_lines X X))) (All Y, (All Z, ((distinct_lines T_2 Y) => ((distinct_lines T_2 Z) \/ (distinct_lines Y Z))))) (distinct_lines 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 T_2)) (-. (apart_point_and_line T_1 T_2)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) ### All 34 % 10.62/10.85 36. (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 X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (apart_point_and_line T_1 T_2)) (-. (apart_point_and_line T_0 T_2)) (distinct_lines T_2 (line_connecting T_0 T_1)) (All Y, (All Z, ((distinct_lines T_2 Y) => ((distinct_lines T_2 Z) \/ (distinct_lines Y Z))))) (All X, (-. (distinct_lines X X))) (All Y, (All Z, ((distinct_points T_0 Y) => ((apart_point_and_line Z (line_connecting T_0 Y)) => ((distinct_points Z T_0) /\ (distinct_points Z Y)))))) (distinct_points T_0 T_1) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) ### All 35 % 10.62/10.85 37. (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, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) (distinct_points T_0 T_1) (All X, (-. (distinct_lines X X))) (All Y, (All Z, ((distinct_lines T_2 Y) => ((distinct_lines T_2 Z) \/ (distinct_lines Y Z))))) (distinct_lines T_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_0 T_2)) (-. (apart_point_and_line T_1 T_2)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (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 36 % 10.62/10.85 38. (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (apart_point_and_line T_1 T_2)) (-. (apart_point_and_line T_0 T_2)) (distinct_lines T_2 (line_connecting T_0 T_1)) (All Y, (All Z, ((distinct_lines T_2 Y) => ((distinct_lines T_2 Z) \/ (distinct_lines Y Z))))) (All X, (-. (distinct_lines X X))) (distinct_points T_0 T_1) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) (All 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 37 % 10.62/10.85 39. (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (distinct_points T_0 T_1) (All X, (-. (distinct_lines X X))) (All Y, (All Z, ((distinct_lines T_2 Y) => ((distinct_lines T_2 Z) \/ (distinct_lines Y Z))))) (distinct_lines T_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_0 T_2)) (-. (apart_point_and_line T_1 T_2)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) ### All 38 % 10.62/10.85 40. (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (apart_point_and_line T_1 T_2)) (-. (apart_point_and_line T_0 T_2)) (distinct_lines T_2 (line_connecting T_0 T_1)) (All X, (-. (distinct_lines X X))) (distinct_points T_0 T_1) (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 Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) ### All 39 % 10.62/10.85 41. (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (distinct_points T_0 T_1) (All X, (-. (distinct_lines X X))) (distinct_lines T_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_0 T_2)) (-. (apart_point_and_line T_1 T_2)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) ### All 40 % 10.62/10.85 42. (-. (((distinct_points T_0 T_1) /\ ((convergent_lines T_2 T_3) /\ ((-. (apart_point_and_line T_0 T_2)) /\ (-. (apart_point_and_line T_1 T_2))))) => (-. (distinct_lines T_2 (line_connecting 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))))))))) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All X, (-. (distinct_lines X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### ConjTree 41 % 10.62/10.85 43. (-. (All V, (((distinct_points T_0 T_1) /\ ((convergent_lines T_2 V) /\ ((-. (apart_point_and_line T_0 T_2)) /\ (-. (apart_point_and_line T_1 T_2))))) => (-. (distinct_lines T_2 (line_connecting T_0 T_1)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (-. (distinct_lines X X))) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) ### NotAllEx 42 % 10.62/10.85 44. (-. (All U, (All V, (((distinct_points T_0 T_1) /\ ((convergent_lines U V) /\ ((-. (apart_point_and_line T_0 U)) /\ (-. (apart_point_and_line T_1 U))))) => (-. (distinct_lines U (line_connecting 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))))))))) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All X, (-. (distinct_lines X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotAllEx 43 % 10.62/10.85 45. (-. (All Y, (All U, (All V, (((distinct_points T_0 Y) /\ ((convergent_lines U V) /\ ((-. (apart_point_and_line T_0 U)) /\ (-. (apart_point_and_line Y U))))) => (-. (distinct_lines U (line_connecting T_0 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, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (-. (distinct_lines X X))) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) ### NotAllEx 44 % 10.62/10.85 46. (-. (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ ((convergent_lines U V) /\ ((-. (apart_point_and_line X U)) /\ (-. (apart_point_and_line Y U))))) => (-. (distinct_lines U (line_connecting X Y))))))))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All X, (-. (distinct_lines X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotAllEx 45 % 10.62/10.85 % SZS output end Proof % 10.62/10.85 (* END-PROOF *) %------------------------------------------------------------------------------