%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO175+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 : n005.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 06:30:38 EDT 2022 % Result : Theorem 0.19s 0.42s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : GEO175+1 : TPTP v8.1.0. Released v3.3.0. % 0.12/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n005.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 : Sat Jun 18 01:24:38 EDT 2022 % 0.19/0.33 % CPUTime : % 0.19/0.42 % SZS status Theorem % 0.19/0.42 (* PROOF-FOUND *) % 0.19/0.42 (* BEGIN-PROOF *) % 0.19/0.42 % SZS output start Proof % 0.19/0.42 1. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom % 0.19/0.42 2. (distinct_points T_2 (intersection_point T_0 T_1)) (-. (distinct_points T_2 (intersection_point T_0 T_1))) ### Axiom % 0.19/0.42 3. (distinct_lines T_1 T_0) (-. (distinct_lines T_1 T_0)) ### Axiom % 0.19/0.42 4. (-. (apart_point_and_line T_2 T_1)) (apart_point_and_line T_2 T_1) ### Axiom % 0.19/0.42 5. (-. (apart_point_and_line T_2 T_0)) (apart_point_and_line T_2 T_0) ### Axiom % 0.19/0.42 6. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom % 0.19/0.42 7. (apart_point_and_line (intersection_point T_0 T_1) T_1) (-. (apart_point_and_line (intersection_point T_0 T_1) T_1)) ### Axiom % 0.19/0.42 8. ((convergent_lines T_0 T_1) => (-. (apart_point_and_line (intersection_point T_0 T_1) T_1))) (apart_point_and_line (intersection_point T_0 T_1) T_1) (convergent_lines T_0 T_1) ### Imply 6 7 % 0.19/0.42 9. (All Y, ((convergent_lines T_0 Y) => (-. (apart_point_and_line (intersection_point T_0 Y) Y)))) (convergent_lines T_0 T_1) (apart_point_and_line (intersection_point T_0 T_1) T_1) ### All 8 % 0.19/0.42 10. (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (apart_point_and_line (intersection_point T_0 T_1) T_1) (convergent_lines T_0 T_1) ### All 9 % 0.19/0.42 11. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom % 0.19/0.42 12. (apart_point_and_line (intersection_point T_0 T_1) T_0) (-. (apart_point_and_line (intersection_point T_0 T_1) T_0)) ### Axiom % 0.19/0.42 13. ((convergent_lines T_0 T_1) => (-. (apart_point_and_line (intersection_point T_0 T_1) T_0))) (apart_point_and_line (intersection_point T_0 T_1) T_0) (convergent_lines T_0 T_1) ### Imply 11 12 % 0.19/0.42 14. (All Y, ((convergent_lines T_0 Y) => (-. (apart_point_and_line (intersection_point T_0 Y) T_0)))) (convergent_lines T_0 T_1) (apart_point_and_line (intersection_point T_0 T_1) T_0) ### All 13 % 0.19/0.42 15. (((distinct_points T_2 (intersection_point T_0 T_1)) /\ (distinct_lines T_1 T_0)) => ((apart_point_and_line T_2 T_1) \/ ((apart_point_and_line T_2 T_0) \/ ((apart_point_and_line (intersection_point T_0 T_1) T_1) \/ (apart_point_and_line (intersection_point T_0 T_1) T_0))))) (All Y, ((convergent_lines T_0 Y) => (-. (apart_point_and_line (intersection_point T_0 Y) T_0)))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 T_1)) (distinct_lines T_1 T_0) (distinct_points T_2 (intersection_point T_0 T_1)) ### DisjTree 2 3 4 5 10 14 % 0.19/0.42 16. (All V, (((distinct_points T_2 (intersection_point T_0 T_1)) /\ (distinct_lines T_1 V)) => ((apart_point_and_line T_2 T_1) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line (intersection_point T_0 T_1) T_1) \/ (apart_point_and_line (intersection_point T_0 T_1) V)))))) (distinct_points T_2 (intersection_point T_0 T_1)) (distinct_lines T_1 T_0) (-. (apart_point_and_line T_2 T_1)) (-. (apart_point_and_line T_2 T_0)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (convergent_lines T_0 T_1) (All Y, ((convergent_lines T_0 Y) => (-. (apart_point_and_line (intersection_point T_0 Y) T_0)))) ### All 15 % 0.19/0.42 17. (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 T_1)) (distinct_lines T_1 T_0) (distinct_points T_2 (intersection_point T_0 T_1)) (All V, (((distinct_points T_2 (intersection_point T_0 T_1)) /\ (distinct_lines T_1 V)) => ((apart_point_and_line T_2 T_1) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line (intersection_point T_0 T_1) T_1) \/ (apart_point_and_line (intersection_point T_0 T_1) V)))))) ### All 16 % 0.19/0.42 18. (All U, (All V, (((distinct_points T_2 (intersection_point T_0 T_1)) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line (intersection_point T_0 T_1) U) \/ (apart_point_and_line (intersection_point T_0 T_1) V))))))) (distinct_points T_2 (intersection_point T_0 T_1)) (distinct_lines T_1 T_0) (-. (apart_point_and_line T_2 T_1)) (-. (apart_point_and_line T_2 T_0)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) ### All 17 % 0.19/0.42 19. (convergent_lines T_0 T_0) (-. (convergent_lines T_0 T_0)) ### Axiom % 0.19/0.42 20. (All X, (-. (convergent_lines X X))) (convergent_lines T_0 T_0) ### All 19 % 0.19/0.42 21. ((convergent_lines T_0 T_1) => ((distinct_lines T_1 T_0) \/ (convergent_lines T_0 T_0))) (All X, (-. (convergent_lines X X))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 T_1)) (distinct_points T_2 (intersection_point T_0 T_1)) (All U, (All V, (((distinct_points T_2 (intersection_point T_0 T_1)) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line (intersection_point T_0 T_1) U) \/ (apart_point_and_line (intersection_point T_0 T_1) V))))))) (convergent_lines T_0 T_1) ### DisjTree 1 18 20 % 0.19/0.42 22. (All Z, ((convergent_lines T_0 T_1) => ((distinct_lines T_1 Z) \/ (convergent_lines T_0 Z)))) (convergent_lines T_0 T_1) (All U, (All V, (((distinct_points T_2 (intersection_point T_0 T_1)) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line (intersection_point T_0 T_1) U) \/ (apart_point_and_line (intersection_point T_0 T_1) V))))))) (distinct_points T_2 (intersection_point T_0 T_1)) (-. (apart_point_and_line T_2 T_1)) (-. (apart_point_and_line T_2 T_0)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (-. (convergent_lines X X))) ### All 21 % 0.19/0.42 23. (All Y, (All U, (All V, (((distinct_points T_2 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 T_1)) (distinct_points T_2 (intersection_point T_0 T_1)) (convergent_lines T_0 T_1) (All Z, ((convergent_lines T_0 T_1) => ((distinct_lines T_1 Z) \/ (convergent_lines T_0 Z)))) ### All 22 % 0.19/0.42 24. (All Y, (All Z, ((convergent_lines T_0 Y) => ((distinct_lines Y Z) \/ (convergent_lines T_0 Z))))) (convergent_lines T_0 T_1) (distinct_points T_2 (intersection_point T_0 T_1)) (-. (apart_point_and_line T_2 T_1)) (-. (apart_point_and_line T_2 T_0)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (-. (convergent_lines X X))) (All Y, (All U, (All V, (((distinct_points T_2 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) ### All 23 % 0.19/0.42 25. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All Y, (All U, (All V, (((distinct_points T_2 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 T_1)) (distinct_points T_2 (intersection_point T_0 T_1)) (convergent_lines T_0 T_1) ### All 24 % 0.19/0.42 26. (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))))))))) (convergent_lines T_0 T_1) (distinct_points T_2 (intersection_point T_0 T_1)) (-. (apart_point_and_line T_2 T_1)) (-. (apart_point_and_line T_2 T_0)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) ### All 25 % 0.19/0.42 27. (-. (((distinct_points T_2 T_3) /\ ((convergent_lines T_0 T_1) /\ (distinct_points T_2 (intersection_point T_0 T_1)))) => ((apart_point_and_line T_2 T_0) \/ (apart_point_and_line T_2 T_1)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) 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 26 % 0.19/0.42 28. (-. (All V, (((distinct_points T_2 T_3) /\ ((convergent_lines T_0 V) /\ (distinct_points T_2 (intersection_point T_0 V)))) => ((apart_point_and_line T_2 T_0) \/ (apart_point_and_line T_2 V))))) (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, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) ### NotAllEx 27 % 0.19/0.42 29. (-. (All U, (All V, (((distinct_points T_2 T_3) /\ ((convergent_lines U V) /\ (distinct_points T_2 (intersection_point U V)))) => ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V)))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) 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 28 % 0.19/0.42 30. (-. (All Y, (All U, (All V, (((distinct_points T_2 Y) /\ ((convergent_lines U V) /\ (distinct_points T_2 (intersection_point U V)))) => ((apart_point_and_line T_2 U) \/ (apart_point_and_line T_2 V))))))) (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, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) ### NotAllEx 29 % 0.19/0.42 31. (-. (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ ((convergent_lines U V) /\ (distinct_points X (intersection_point U V)))) => ((apart_point_and_line X U) \/ (apart_point_and_line X V)))))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) 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 30 % 0.19/0.42 % SZS output end Proof % 0.19/0.42 (* END-PROOF *) %------------------------------------------------------------------------------