%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO200+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Sat Jul 16 06:31:00 EDT 2022 % Result : Theorem 27.63s 27.79s % Output : Proof 27.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : GEO200+2 : TPTP v8.1.0. Released v3.3.0. % 0.12/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.34 % Computer : n008.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat Jun 18 08:54:07 EDT 2022 % 0.13/0.34 % CPUTime : % 27.63/27.79 % SZS status Theorem % 27.63/27.79 (* PROOF-FOUND *) % 27.63/27.79 (* BEGIN-PROOF *) % 27.63/27.79 % SZS output start Proof % 27.63/27.79 1. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 27.63/27.79 2. (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_0) ### Axiom % 27.63/27.79 3. (distinct_points T_1 T_0) (-. (distinct_points T_1 T_0)) ### Axiom % 27.63/27.79 4. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 27.63/27.79 5. (distinct_points T_1 T_0) (-. (distinct_points T_1 T_0)) ### Axiom % 27.63/27.79 6. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 27.63/27.79 7. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 27.63/27.79 8. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (-. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0))) ### Axiom % 27.63/27.79 9. (-. (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 % 27.63/27.79 10. (-. (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 % 27.63/27.79 11. (-. (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 % 27.63/27.79 12. (-. (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 % 27.63/27.79 13. (((distinct_points T_0 T_1) /\ (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0))) => ((apart_point_and_line T_0 (line_connecting T_0 T_1)) \/ ((apart_point_and_line T_0 (line_connecting 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_1 T_0)))))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (distinct_points T_0 T_1) ### DisjTree 7 8 9 10 11 12 % 27.63/27.79 14. (All V, (((distinct_points T_0 T_1) /\ (distinct_lines (line_connecting T_0 T_1) V)) => ((apart_point_and_line T_0 (line_connecting T_0 T_1)) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 (line_connecting T_0 T_1)) \/ (apart_point_and_line T_1 V)))))) (distinct_points T_0 T_1) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting 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_1 T_0))) ### All 13 % 27.63/27.79 15. (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (distinct_points T_0 T_1) ### All 14 % 27.63/27.79 16. (-. (distinct_points T_1 T_1)) (distinct_points T_1 T_1) ### Axiom % 27.63/27.79 17. ((distinct_points T_1 T_0) /\ (distinct_points T_1 T_1)) (-. (distinct_points T_1 T_1)) ### And 16 % 27.63/27.79 18. ((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)))) (-. (distinct_points T_1 T_1)) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (distinct_points T_0 T_1) ### DisjTree 6 15 17 % 27.63/27.79 19. (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 U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (-. (distinct_points T_1 T_1)) ### All 18 % 27.63/27.79 20. (-. (distinct_points T_1 T_1)) (distinct_points T_1 T_1) ### Axiom % 27.63/27.79 21. ((distinct_points T_1 T_1) /\ (distinct_points T_1 T_0)) (-. (distinct_points T_1 T_1)) ### And 20 % 27.63/27.79 22. ((distinct_points T_1 T_0) => ((apart_point_and_line T_1 (line_connecting T_1 T_0)) => ((distinct_points T_1 T_1) /\ (distinct_points T_1 T_0)))) (-. (distinct_points T_1 T_1)) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (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))))) (distinct_points T_1 T_0) ### DisjTree 5 19 21 % 27.63/27.79 23. (All Z, ((distinct_points T_1 T_0) => ((apart_point_and_line Z (line_connecting T_1 T_0)) => ((distinct_points Z T_1) /\ (distinct_points Z T_0))))) (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))))) (distinct_points T_0 T_1) (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (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 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (-. (distinct_points T_1 T_1)) ### All 22 % 27.63/27.79 24. (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_0) ### Axiom % 27.63/27.79 25. ((distinct_points T_0 T_0) /\ (distinct_points T_0 T_1)) (-. (distinct_points T_0 T_0)) ### And 24 % 27.63/27.79 26. ((distinct_points T_0 T_1) => ((apart_point_and_line T_0 (line_connecting T_0 T_1)) => ((distinct_points T_0 T_0) /\ (distinct_points T_0 T_1)))) (-. (distinct_points T_0 T_0)) (-. (distinct_points T_1 T_1)) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (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) (All Z, ((distinct_points T_1 T_0) => ((apart_point_and_line Z (line_connecting T_1 T_0)) => ((distinct_points Z T_1) /\ (distinct_points Z T_0))))) (distinct_points T_0 T_1) ### DisjTree 4 23 25 % 27.63/27.79 27. (distinct_points T_0 T_1) (All Z, ((distinct_points T_1 T_0) => ((apart_point_and_line Z (line_connecting T_1 T_0)) => ((distinct_points Z T_1) /\ (distinct_points Z T_0))))) (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 U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (-. (distinct_points T_1 T_1)) (-. (distinct_points T_0 T_0)) ### All 26 % 27.68/27.87 28. (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_0) ### Axiom % 27.68/27.87 29. ((distinct_points T_0 T_1) /\ (distinct_points T_0 T_0)) (-. (distinct_points T_0 T_0)) ### And 28 % 27.68/27.87 30. ((distinct_points T_1 T_0) => ((apart_point_and_line T_0 (line_connecting T_1 T_0)) => ((distinct_points T_0 T_1) /\ (distinct_points T_0 T_0)))) (-. (distinct_points T_0 T_0)) (-. (distinct_points T_1 T_1)) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (All Z, ((distinct_points T_1 T_0) => ((apart_point_and_line Z (line_connecting T_1 T_0)) => ((distinct_points Z T_1) /\ (distinct_points Z T_0))))) (distinct_points T_0 T_1) (distinct_points T_1 T_0) ### DisjTree 3 27 29 % 27.68/27.87 31. (distinct_points T_1 T_0) (distinct_points T_0 T_1) (All Z, ((distinct_points T_1 T_0) => ((apart_point_and_line Z (line_connecting T_1 T_0)) => ((distinct_points Z T_1) /\ (distinct_points Z 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 U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (-. (distinct_points T_1 T_1)) (-. (distinct_points T_0 T_0)) ### All 30 % 27.68/27.87 32. (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_0)) (-. (distinct_points T_1 T_1)) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (All Z, ((distinct_points T_1 T_0) => ((apart_point_and_line Z (line_connecting T_1 T_0)) => ((distinct_points Z T_1) /\ (distinct_points Z T_0))))) (distinct_points T_0 T_1) (distinct_points T_1 T_0) ### All 31 % 27.68/27.87 33. ((distinct_points T_0 T_1) => ((distinct_points T_0 T_0) \/ (distinct_points T_1 T_0))) (All Z, ((distinct_points T_1 T_0) => ((apart_point_and_line Z (line_connecting T_1 T_0)) => ((distinct_points Z T_1) /\ (distinct_points Z T_0))))) (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (-. (distinct_points T_1 T_1)) (All Y, (All Z, ((distinct_points T_0 Y) => ((apart_point_and_line Z (line_connecting T_0 Y)) => ((distinct_points Z T_0) /\ (distinct_points Z Y)))))) (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_1) ### DisjTree 1 2 32 % 27.68/27.87 34. (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 Y, (All Z, ((distinct_points T_0 Y) => ((apart_point_and_line Z (line_connecting T_0 Y)) => ((distinct_points Z T_0) /\ (distinct_points Z Y)))))) (-. (distinct_points T_1 T_1)) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (All Z, ((distinct_points T_1 T_0) => ((apart_point_and_line Z (line_connecting T_1 T_0)) => ((distinct_points Z T_1) /\ (distinct_points Z T_0))))) ### All 33 % 27.68/27.87 35. (All Y, (All Z, ((distinct_points T_1 Y) => ((apart_point_and_line Z (line_connecting T_1 Y)) => ((distinct_points Z T_1) /\ (distinct_points Z Y)))))) (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (-. (distinct_points T_1 T_1)) (All Y, (All Z, ((distinct_points T_0 Y) => ((apart_point_and_line Z (line_connecting T_0 Y)) => ((distinct_points Z T_0) /\ (distinct_points Z Y)))))) (-. (distinct_points T_0 T_0)) (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 34 % 27.68/27.87 36. (All X, (-. (distinct_points X X))) (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)))))) (-. (distinct_points T_1 T_1)) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (All Y, (All Z, ((distinct_points T_1 Y) => ((apart_point_and_line Z (line_connecting T_1 Y)) => ((distinct_points Z T_1) /\ (distinct_points Z Y)))))) ### All 35 % 27.68/27.87 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 Y, (All Z, ((distinct_points T_1 Y) => ((apart_point_and_line Z (line_connecting T_1 Y)) => ((distinct_points Z T_1) /\ (distinct_points Z Y)))))) (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (-. (distinct_points T_1 T_1)) (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, (-. (distinct_points X X))) ### All 36 % 27.68/27.87 38. (All Y, (All U, (All V, (((distinct_points T_0 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) (All X, (-. (distinct_points X X))) (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_1 T_1)) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (All Y, (All Z, ((distinct_points T_1 Y) => ((apart_point_and_line Z (line_connecting T_1 Y)) => ((distinct_points Z T_1) /\ (distinct_points Z Y)))))) (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 % 27.68/27.87 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))))))) (All Y, (All Z, ((distinct_points T_1 Y) => ((apart_point_and_line Z (line_connecting T_1 Y)) => ((distinct_points Z T_1) /\ (distinct_points Z Y)))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (-. (distinct_points T_1 T_1)) (distinct_points T_0 T_1) (All X, (-. (distinct_points X X))) (All Y, (All U, (All V, (((distinct_points T_0 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) ### All 38 % 27.68/27.87 40. (All Y, (All U, (All V, (((distinct_points T_0 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) (All X, (-. (distinct_points X X))) (distinct_points T_0 T_1) (-. (distinct_points T_1 T_1)) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (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 % 27.92/28.10 41. (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 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_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (-. (distinct_points T_1 T_1)) (distinct_points T_0 T_1) (All X, (-. (distinct_points X X))) ### All 40 % 27.92/28.10 42. (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (All X, (-. (distinct_points X X))) (distinct_points T_0 T_1) (-. (distinct_points T_1 T_1)) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) ### All 41 % 27.92/28.10 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, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (distinct_points T_0 T_1) (All X, (-. (distinct_points X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### All 42 % 27.92/28.10 44. (-. (-. (distinct_lines (line_connecting T_0 T_1) (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, (-. (distinct_points 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 X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) ### NotNot 43 % 27.92/28.10 45. (-. ((distinct_points T_0 T_1) => (-. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 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, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (-. (distinct_points X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotImply 44 % 27.92/28.10 46. (-. (All Y, ((distinct_points T_0 Y) => (-. (distinct_lines (line_connecting T_0 Y) (line_connecting Y T_0)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (All X, (-. (distinct_points X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) ### NotAllEx 45 % 27.92/28.10 47. (-. (All X, (All Y, ((distinct_points X Y) => (-. (distinct_lines (line_connecting X Y) (line_connecting Y 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, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (-. (distinct_points X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotAllEx 46 % 27.92/28.10 % SZS output end Proof % 27.92/28.10 (* END-PROOF *) %------------------------------------------------------------------------------