%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO177+1 : 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 : n017.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 06:30:40 EDT 2022 % Result : Theorem 0.18s 0.41s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : GEO177+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n017.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Fri Jun 17 22:49:57 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.41 % SZS status Theorem % 0.18/0.41 (* PROOF-FOUND *) % 0.18/0.41 (* BEGIN-PROOF *) % 0.18/0.41 % SZS output start Proof % 0.18/0.41 1. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 0.18/0.41 2. (distinct_points T_2 T_3) (-. (distinct_points T_2 T_3)) ### Axiom % 0.18/0.41 3. (apart_point_and_line T_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_2 (line_connecting T_0 T_1))) ### Axiom % 0.18/0.41 4. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 0.18/0.41 5. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_2 T_3)) (-. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_2 T_3))) ### Axiom % 0.18/0.41 6. (-. (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 % 0.18/0.41 7. (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (apart_point_and_line T_0 (line_connecting T_2 T_3)) ### Axiom % 0.18/0.41 8. (-. (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 % 0.18/0.41 9. (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (apart_point_and_line T_1 (line_connecting T_2 T_3)) ### Axiom % 0.18/0.41 10. (((distinct_points T_0 T_1) /\ (distinct_lines (line_connecting T_0 T_1) (line_connecting T_2 T_3))) => ((apart_point_and_line T_0 (line_connecting T_0 T_1)) \/ ((apart_point_and_line T_0 (line_connecting T_2 T_3)) \/ ((apart_point_and_line T_1 (line_connecting T_0 T_1)) \/ (apart_point_and_line T_1 (line_connecting T_2 T_3)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_2 T_3)) (distinct_points T_0 T_1) ### DisjTree 4 5 6 7 8 9 % 0.18/0.41 11. (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_2 T_3)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) ### All 10 % 0.18/0.41 12. (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_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_2 T_3)) (distinct_points T_0 T_1) ### All 11 % 0.18/0.41 13. (-. (apart_point_and_line T_2 (line_connecting T_2 T_3))) (apart_point_and_line T_2 (line_connecting T_2 T_3)) ### Axiom % 0.18/0.41 14. ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) (line_connecting T_2 T_3)) \/ (apart_point_and_line T_2 (line_connecting T_2 T_3)))) (-. (apart_point_and_line T_2 (line_connecting T_2 T_3))) (distinct_points T_0 T_1) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (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_2 (line_connecting T_0 T_1)) ### DisjTree 3 12 13 % 0.18/0.41 15. (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All U, (All V, (((distinct_points T_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_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (distinct_points T_0 T_1) (-. (apart_point_and_line T_2 (line_connecting T_2 T_3))) ### All 14 % 0.18/0.41 16. ((distinct_points T_2 T_3) => (-. (apart_point_and_line T_2 (line_connecting T_2 T_3)))) (distinct_points T_0 T_1) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (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_2 (line_connecting T_0 T_1)) (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (distinct_points T_2 T_3) ### Imply 2 15 % 0.18/0.41 17. (All Y, ((distinct_points T_2 Y) => (-. (apart_point_and_line T_2 (line_connecting T_2 Y))))) (distinct_points T_2 T_3) (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All U, (All V, (((distinct_points T_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_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (distinct_points T_0 T_1) ### All 16 % 0.18/0.41 18. (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_points T_0 T_1) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (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_2 (line_connecting T_0 T_1)) (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (distinct_points T_2 T_3) ### All 17 % 0.18/0.41 19. (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_3) (apart_point_and_line T_2 (line_connecting 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_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (distinct_points T_0 T_1) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) ### All 18 % 0.18/0.41 20. ((distinct_points T_0 T_1) => (-. (apart_point_and_line T_0 (line_connecting T_0 T_1)))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (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_2 (line_connecting T_0 T_1)) (distinct_points T_2 T_3) (All Y, (All Z, ((apart_point_and_line T_2 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_2 Z))))) (distinct_points T_0 T_1) ### Imply 1 19 % 0.18/0.43 21. (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points T_0 T_1) (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_3) (apart_point_and_line T_2 (line_connecting 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_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) ### All 20 % 0.18/0.43 22. (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_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (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_2 (line_connecting T_0 T_1)) (distinct_points T_2 T_3) (distinct_points T_0 T_1) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) ### All 21 % 0.18/0.43 23. (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 Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points T_0 T_1) (distinct_points T_2 T_3) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (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 22 % 0.18/0.43 24. (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_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (distinct_points T_2 T_3) (distinct_points T_0 T_1) (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 23 % 0.18/0.43 25. (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) (distinct_points T_2 T_3) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (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 24 % 0.18/0.43 26. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom % 0.18/0.43 27. (apart_point_and_line T_3 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_3 (line_connecting T_0 T_1))) ### Axiom % 0.18/0.43 28. (-. (apart_point_and_line T_3 (line_connecting T_2 T_3))) (apart_point_and_line T_3 (line_connecting T_2 T_3)) ### Axiom % 0.18/0.43 29. ((apart_point_and_line T_3 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) (line_connecting T_2 T_3)) \/ (apart_point_and_line T_3 (line_connecting T_2 T_3)))) (-. (apart_point_and_line T_3 (line_connecting T_2 T_3))) (distinct_points T_0 T_1) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (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_3 (line_connecting T_0 T_1)) ### DisjTree 27 12 28 % 0.18/0.43 30. (All Z, ((apart_point_and_line T_3 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_3 Z)))) (apart_point_and_line T_3 (line_connecting 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_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (distinct_points T_0 T_1) (-. (apart_point_and_line T_3 (line_connecting T_2 T_3))) ### All 29 % 0.18/0.43 31. (All Y, (All Z, ((apart_point_and_line T_3 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_3 Z))))) (-. (apart_point_and_line T_3 (line_connecting T_2 T_3))) (distinct_points T_0 T_1) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (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_3 (line_connecting T_0 T_1)) ### All 30 % 0.18/0.43 32. ((distinct_points T_0 T_1) => (-. (apart_point_and_line T_0 (line_connecting T_0 T_1)))) (apart_point_and_line T_3 (line_connecting 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_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_3 (line_connecting T_2 T_3))) (All Y, (All Z, ((apart_point_and_line T_3 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_3 Z))))) (distinct_points T_0 T_1) ### Imply 26 31 % 0.18/0.43 33. (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points T_0 T_1) (All Y, (All Z, ((apart_point_and_line T_3 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_3 Z))))) (-. (apart_point_and_line T_3 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (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_3 (line_connecting T_0 T_1)) ### All 32 % 0.18/0.43 34. (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (apart_point_and_line T_3 (line_connecting 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_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_3 (line_connecting T_2 T_3))) (distinct_points T_0 T_1) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) ### All 33 % 0.18/0.43 35. (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 Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points T_0 T_1) (-. (apart_point_and_line T_3 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (apart_point_and_line T_3 (line_connecting T_0 T_1)) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) ### All 34 % 0.18/0.43 36. (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)))))) (apart_point_and_line T_3 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_3 (line_connecting T_2 T_3))) (distinct_points T_0 T_1) (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 35 % 0.18/0.43 37. (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) (-. (apart_point_and_line T_3 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (apart_point_and_line T_3 (line_connecting T_0 T_1)) (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 36 % 0.18/0.43 38. ((apart_point_and_line T_2 (line_connecting T_0 T_1)) \/ (apart_point_and_line T_3 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_3 (line_connecting T_2 T_3))) (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_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (distinct_points T_2 T_3) (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))))))))) ### Or 25 37 % 0.18/0.43 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))))))))) (distinct_points T_0 T_1) (distinct_points T_2 T_3) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_3))) (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)))))) (-. (apart_point_and_line T_3 (line_connecting T_2 T_3))) ((apart_point_and_line T_2 (line_connecting T_0 T_1)) \/ (apart_point_and_line T_3 (line_connecting T_0 T_1))) ### Extension/test/ci2 38 % 0.18/0.43 40. ((apart_point_and_line T_2 (line_connecting T_0 T_1)) \/ (apart_point_and_line T_3 (line_connecting T_0 T_1))) (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_0 (line_connecting T_2 T_3))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_3))) (distinct_points T_2 T_3) (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))))))))) ### Extension/test/ci2 39 % 0.18/0.43 41. (-. (((distinct_points T_2 T_3) /\ (distinct_points T_0 T_1)) => (((apart_point_and_line T_2 (line_connecting T_0 T_1)) \/ (apart_point_and_line T_3 (line_connecting T_0 T_1))) => ((apart_point_and_line T_0 (line_connecting T_2 T_3)) \/ (apart_point_and_line T_1 (line_connecting T_2 T_3)))))) (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 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)))))) ### ConjTree 40 % 0.18/0.43 42. (-. (All V, (((distinct_points T_2 T_3) /\ (distinct_points T_0 V)) => (((apart_point_and_line T_2 (line_connecting T_0 V)) \/ (apart_point_and_line T_3 (line_connecting T_0 V))) => ((apart_point_and_line T_0 (line_connecting T_2 T_3)) \/ (apart_point_and_line V (line_connecting T_2 T_3))))))) (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, (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 41 % 0.18/0.43 43. (-. (All U, (All V, (((distinct_points T_2 T_3) /\ (distinct_points U V)) => (((apart_point_and_line T_2 (line_connecting U V)) \/ (apart_point_and_line T_3 (line_connecting U V))) => ((apart_point_and_line U (line_connecting T_2 T_3)) \/ (apart_point_and_line V (line_connecting T_2 T_3)))))))) (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 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)))))) ### NotAllEx 42 % 0.18/0.43 44. (-. (All Y, (All U, (All V, (((distinct_points T_2 Y) /\ (distinct_points U V)) => (((apart_point_and_line T_2 (line_connecting U V)) \/ (apart_point_and_line Y (line_connecting U V))) => ((apart_point_and_line U (line_connecting T_2 Y)) \/ (apart_point_and_line V (line_connecting T_2 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)))))) (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 43 % 0.18/0.43 45. (-. (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_points U V)) => (((apart_point_and_line X (line_connecting U V)) \/ (apart_point_and_line Y (line_connecting U V))) => ((apart_point_and_line U (line_connecting X Y)) \/ (apart_point_and_line V (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, ((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)))))) ### NotAllEx 44 % 0.18/0.43 % SZS output end Proof % 0.18/0.43 (* END-PROOF *) %------------------------------------------------------------------------------