%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO188+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 : n012.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 06:30:49 EDT 2022 % Result : Theorem 1.42s 1.65s % Output : Proof 1.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GEO188+2 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.34 % Computer : n012.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 14:03:23 EDT 2022 % 0.13/0.34 % CPUTime : % 1.42/1.65 % SZS status Theorem % 1.42/1.65 (* PROOF-FOUND *) % 1.42/1.65 (* BEGIN-PROOF *) % 1.42/1.65 % SZS output start Proof % 1.42/1.65 1. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 1.42/1.65 2. (distinct_points T_0 T_0) ### Extension/test/apart1 % 1.42/1.65 3. (distinct_points T_1 T_0) (-. (distinct_points T_1 T_0)) ### Axiom % 1.42/1.65 4. (distinct_points T_2 T_0) (-. (distinct_points T_2 T_0)) ### Axiom % 1.42/1.65 5. (distinct_points T_1 T_0) (-. (distinct_points T_1 T_0)) ### Axiom % 1.42/1.65 6. (distinct_points T_2 T_0) (-. (distinct_points T_2 T_0)) ### Axiom % 1.42/1.65 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 % 1.42/1.65 8. (distinct_points T_1 T_0) (-. (distinct_points T_1 T_0)) ### Axiom % 1.42/1.65 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 % 1.42/1.65 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 % 1.42/1.65 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 % 1.42/1.65 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 % 1.42/1.65 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 % 1.42/1.65 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 % 1.42/1.65 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 % 1.42/1.65 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 % 1.42/1.65 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 % 1.42/1.65 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 % 1.42/1.65 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 % 1.42/1.65 20. (distinct_points T_2 T_2) ### Extension/test/apart1 % 1.42/1.65 21. ((distinct_points T_2 T_2) /\ (distinct_points T_2 T_0)) ### And 20 % 1.42/1.65 22. ((distinct_points T_2 T_0) => ((apart_point_and_line T_2 (line_connecting T_2 T_0)) => ((distinct_points T_2 T_2) /\ (distinct_points 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)) (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) ### DisjTree 6 19 21 % 1.42/1.65 23. (All Z, ((distinct_points T_2 T_0) => ((apart_point_and_line Z (line_connecting T_2 T_0)) => ((distinct_points Z T_2) /\ (distinct_points Z T_0))))) (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_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) ### All 22 % 1.42/1.65 24. ((distinct_points T_0 T_1) /\ (distinct_points T_0 T_0)) ### And 2 % 1.42/1.65 25. ((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)))) (-. (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_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 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 Z, ((distinct_points T_2 T_0) => ((apart_point_and_line Z (line_connecting T_2 T_0)) => ((distinct_points Z T_2) /\ (distinct_points Z T_0))))) (distinct_points T_1 T_0) ### DisjTree 5 23 24 % 1.42/1.65 26. (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_2 T_0) => ((apart_point_and_line Z (line_connecting T_2 T_0)) => ((distinct_points Z T_2) /\ (distinct_points Z T_0))))) (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_2 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))) ### All 25 % 1.52/1.72 27. ((distinct_points T_0 T_2) /\ (distinct_points T_0 T_0)) ### And 2 % 1.52/1.72 28. ((distinct_points T_2 T_0) => ((apart_point_and_line T_0 (line_connecting T_2 T_0)) => ((distinct_points T_0 T_2) /\ (distinct_points T_0 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))) (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 Z, ((distinct_points T_2 T_0) => ((apart_point_and_line Z (line_connecting T_2 T_0)) => ((distinct_points Z T_2) /\ (distinct_points Z 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))))) (distinct_points T_2 T_0) ### DisjTree 4 26 27 % 1.52/1.72 29. (distinct_points T_2 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_1 T_0) (All Z, ((distinct_points T_2 T_0) => ((apart_point_and_line Z (line_connecting T_2 T_0)) => ((distinct_points Z T_2) /\ (distinct_points Z 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_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) ### All 28 % 1.52/1.72 30. (distinct_points T_1 T_1) ### Extension/test/apart1 % 1.52/1.72 31. ((distinct_points T_1 T_1) /\ (distinct_points T_1 T_0)) ### And 30 % 1.52/1.72 32. ((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)))) (-. (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 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 Z, ((distinct_points T_2 T_0) => ((apart_point_and_line Z (line_connecting T_2 T_0)) => ((distinct_points Z T_2) /\ (distinct_points Z 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_2 T_0) (distinct_points T_1 T_0) ### DisjTree 3 29 31 % 1.52/1.72 33. (distinct_points T_1 T_0) (distinct_points T_2 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 Z, ((distinct_points T_2 T_0) => ((apart_point_and_line Z (line_connecting T_2 T_0)) => ((distinct_points Z T_2) /\ (distinct_points Z 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_1 (line_connecting T_2 T_0))) ### All 32 % 1.52/1.72 34. (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)))))) (-. (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 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 Z, ((distinct_points T_2 T_0) => ((apart_point_and_line Z (line_connecting T_2 T_0)) => ((distinct_points Z T_2) /\ (distinct_points Z T_0))))) (distinct_points T_2 T_0) (distinct_points T_1 T_0) ### All 33 % 1.52/1.72 35. (All Y, (All Z, ((distinct_points T_2 Y) => ((apart_point_and_line Z (line_connecting T_2 Y)) => ((distinct_points Z T_2) /\ (distinct_points Z Y)))))) (distinct_points T_1 T_0) (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_1 (line_connecting T_2 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 34 % 1.52/1.72 36. (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)))))) (-. (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 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) (distinct_points T_1 T_0) ### All 35 % 1.52/1.72 37. (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_1 T_0) (distinct_points T_2 T_0) (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 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 36 % 1.52/1.72 38. (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_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)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (distinct_points T_2 T_0) (distinct_points T_1 T_0) (All Y, (All Z, ((apart_point_and_line T_2 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_2 Z))))) ### All 37 % 1.52/1.73 39. (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, ((apart_point_and_line T_2 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_2 Z))))) (distinct_points T_1 T_0) (distinct_points T_2 T_0) (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 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 38 % 1.52/1.73 40. ((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_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)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (distinct_points T_2 T_0) (All Y, (All Z, ((apart_point_and_line T_2 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_2 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) ### DisjTree 1 2 39 % 1.52/1.73 41. (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, (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, ((apart_point_and_line T_2 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_2 Z))))) (distinct_points T_2 T_0) (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 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 40 % 1.52/1.73 42. (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) => ((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)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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 Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) ### All 41 % 1.52/1.73 43. (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) (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) (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 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 X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) ### All 42 % 1.52/1.73 44. (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 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)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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 43 % 1.52/1.73 45. (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) (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, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_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 44 % 1.52/1.73 46. (-. (((distinct_points T_2 T_0) /\ ((distinct_points T_2 T_1) /\ ((distinct_points T_0 T_1) /\ (-. (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, (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 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))))))))) ### ConjTree 45 % 1.52/1.73 47. (-. (All Z, (((distinct_points T_2 T_0) /\ ((distinct_points T_2 Z) /\ ((distinct_points T_0 Z) /\ (-. (apart_point_and_line Z (line_connecting T_2 T_0)))))) => (-. (apart_point_and_line T_2 (line_connecting Z 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, (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 46 % 1.52/1.73 48. (-. (All Y, (All Z, (((distinct_points T_2 Y) /\ ((distinct_points T_2 Z) /\ ((distinct_points Y Z) /\ (-. (apart_point_and_line Z (line_connecting T_2 Y)))))) => (-. (apart_point_and_line T_2 (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, (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 47 % 1.52/1.73 49. (-. (All X, (All Y, (All Z, (((distinct_points X Y) /\ ((distinct_points X Z) /\ ((distinct_points Y Z) /\ (-. (apart_point_and_line Z (line_connecting X Y)))))) => (-. (apart_point_and_line X (line_connecting 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 X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_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 48 % 1.52/1.73 % SZS output end Proof % 1.52/1.73 (* END-PROOF *) %------------------------------------------------------------------------------