%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO201+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 06:31:01 EDT 2022 % Result : Theorem 0.20s 0.55s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : GEO201+2 : TPTP v8.1.0. Released v3.3.0. % 0.13/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.35 % Computer : n008.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Fri Jun 17 17:08:37 EDT 2022 % 0.13/0.35 % CPUTime : % 0.20/0.55 % SZS status Theorem % 0.20/0.55 (* PROOF-FOUND *) % 0.20/0.55 (* BEGIN-PROOF *) % 0.20/0.55 % SZS output start Proof % 0.20/0.55 1. (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) (-. (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0))) ### Axiom % 0.20/0.55 2. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom % 0.20/0.55 3. (-. (distinct_lines T_0 T_1)) (convergent_lines T_0 T_1) ### Extension/test/ceq3ctrp 2 % 0.20/0.55 4. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom % 0.20/0.55 5. (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 % 0.20/0.55 6. (-. ((apart_point_and_line (intersection_point T_0 T_1) 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) ### NotOr 5 % 0.20/0.55 7. (distinct_points (intersection_point T_0 T_1) (intersection_point T_0 T_1)) ### Extension/test/apart1 % 0.20/0.55 8. ((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_1)) => (distinct_points (intersection_point T_0 T_1) (intersection_point T_0 T_1)))) (apart_point_and_line (intersection_point T_0 T_1) T_0) (convergent_lines T_0 T_1) ### DisjTree 4 6 7 % 0.20/0.55 9. (All Z, ((convergent_lines T_0 T_1) => (((apart_point_and_line Z T_0) \/ (apart_point_and_line Z T_1)) => (distinct_points Z (intersection_point T_0 T_1))))) (convergent_lines T_0 T_1) (apart_point_and_line (intersection_point T_0 T_1) T_0) ### All 8 % 0.20/0.55 10. (All Y, (All Z, ((convergent_lines T_0 Y) => (((apart_point_and_line Z T_0) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point T_0 Y)))))) (apart_point_and_line (intersection_point T_0 T_1) T_0) (convergent_lines T_0 T_1) ### All 9 % 0.20/0.55 11. (All X, (All Y, (All Z, ((convergent_lines X Y) => (((apart_point_and_line Z X) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point X Y))))))) (convergent_lines T_0 T_1) (apart_point_and_line (intersection_point T_0 T_1) T_0) ### All 10 % 0.20/0.55 12. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom % 0.20/0.55 13. (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 % 0.20/0.55 14. (-. ((apart_point_and_line (intersection_point T_0 T_1) 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_1) ### NotOr 13 % 0.20/0.55 15. ((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_1)) => (distinct_points (intersection_point T_0 T_1) (intersection_point T_0 T_1)))) (apart_point_and_line (intersection_point T_0 T_1) T_1) (convergent_lines T_0 T_1) ### DisjTree 12 14 7 % 0.20/0.55 16. (All Z, ((convergent_lines T_0 T_1) => (((apart_point_and_line Z T_0) \/ (apart_point_and_line Z T_1)) => (distinct_points Z (intersection_point T_0 T_1))))) (convergent_lines T_0 T_1) (apart_point_and_line (intersection_point T_0 T_1) T_1) ### All 15 % 0.20/0.55 17. (All Y, (All Z, ((convergent_lines T_0 Y) => (((apart_point_and_line Z T_0) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point T_0 Y)))))) (apart_point_and_line (intersection_point T_0 T_1) T_1) (convergent_lines T_0 T_1) ### All 16 % 0.20/0.55 18. (All X, (All Y, (All Z, ((convergent_lines X Y) => (((apart_point_and_line Z X) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point X Y))))))) (convergent_lines T_0 T_1) (apart_point_and_line (intersection_point T_0 T_1) T_1) ### All 17 % 0.20/0.55 19. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom % 0.20/0.55 20. (convergent_lines T_0 T_0) (-. (convergent_lines T_0 T_0)) ### Axiom % 0.20/0.55 21. (-. (distinct_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Extension/test/ceq3ctrp 20 % 0.20/0.55 22. (All X, (-. (distinct_lines X X))) (convergent_lines T_0 T_0) ### All 21 % 0.20/0.55 23. (-. (convergent_lines T_1 T_0)) (convergent_lines T_1 T_0) ### Axiom % 0.20/0.55 24. ((convergent_lines T_0 T_1) => ((convergent_lines T_0 T_0) \/ (convergent_lines T_1 T_0))) (-. (convergent_lines T_1 T_0)) (All X, (-. (distinct_lines X X))) (convergent_lines T_0 T_1) ### DisjTree 19 22 23 % 0.20/0.55 25. (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_0 T_1) (All X, (-. (distinct_lines X X))) (-. (convergent_lines T_1 T_0)) ### All 24 % 0.20/0.55 26. (apart_point_and_line (intersection_point T_1 T_0) T_0) (-. (apart_point_and_line (intersection_point T_1 T_0) T_0)) ### Axiom % 0.20/0.55 27. (-. ((apart_point_and_line (intersection_point T_1 T_0) T_1) \/ (apart_point_and_line (intersection_point T_1 T_0) T_0))) (apart_point_and_line (intersection_point T_1 T_0) T_0) ### NotOr 26 % 0.20/0.55 28. (distinct_points (intersection_point T_1 T_0) (intersection_point T_1 T_0)) ### Extension/test/apart1 % 0.20/0.55 29. ((convergent_lines T_1 T_0) => (((apart_point_and_line (intersection_point T_1 T_0) T_1) \/ (apart_point_and_line (intersection_point T_1 T_0) T_0)) => (distinct_points (intersection_point T_1 T_0) (intersection_point T_1 T_0)))) (apart_point_and_line (intersection_point T_1 T_0) T_0) (All X, (-. (distinct_lines X X))) (convergent_lines T_0 T_1) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) ### DisjTree 25 27 28 % 0.20/0.55 30. (All Z, ((convergent_lines T_1 T_0) => (((apart_point_and_line Z T_1) \/ (apart_point_and_line Z T_0)) => (distinct_points Z (intersection_point T_1 T_0))))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_0 T_1) (All X, (-. (distinct_lines X X))) (apart_point_and_line (intersection_point T_1 T_0) T_0) ### All 29 % 0.20/0.55 31. (apart_point_and_line (intersection_point T_1 T_0) T_1) (-. (apart_point_and_line (intersection_point T_1 T_0) T_1)) ### Axiom % 0.20/0.55 32. (-. ((apart_point_and_line (intersection_point T_1 T_0) T_1) \/ (apart_point_and_line (intersection_point T_1 T_0) T_0))) (apart_point_and_line (intersection_point T_1 T_0) T_1) ### NotOr 31 % 0.20/0.55 33. ((convergent_lines T_1 T_0) => (((apart_point_and_line (intersection_point T_1 T_0) T_1) \/ (apart_point_and_line (intersection_point T_1 T_0) T_0)) => (distinct_points (intersection_point T_1 T_0) (intersection_point T_1 T_0)))) (apart_point_and_line (intersection_point T_1 T_0) T_1) (All X, (-. (distinct_lines X X))) (convergent_lines T_0 T_1) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) ### DisjTree 25 32 28 % 0.20/0.55 34. (All Z, ((convergent_lines T_1 T_0) => (((apart_point_and_line Z T_1) \/ (apart_point_and_line Z T_0)) => (distinct_points Z (intersection_point T_1 T_0))))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_0 T_1) (All X, (-. (distinct_lines X X))) (apart_point_and_line (intersection_point T_1 T_0) T_1) ### All 33 % 0.20/0.55 35. (((distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) /\ (distinct_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_1) \/ ((apart_point_and_line (intersection_point T_1 T_0) T_0) \/ (apart_point_and_line (intersection_point T_1 T_0) T_1))))) (All X, (-. (distinct_lines X X))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (All Z, ((convergent_lines T_1 T_0) => (((apart_point_and_line Z T_1) \/ (apart_point_and_line Z T_0)) => (distinct_points Z (intersection_point T_1 T_0))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => (((apart_point_and_line Z X) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point X Y))))))) (convergent_lines T_0 T_1) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) ### DisjTree 1 3 11 18 30 34 % 0.20/0.55 36. (All V, (((distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) /\ (distinct_lines T_0 V)) => ((apart_point_and_line (intersection_point T_0 T_1) T_0) \/ ((apart_point_and_line (intersection_point T_0 T_1) V) \/ ((apart_point_and_line (intersection_point T_1 T_0) T_0) \/ (apart_point_and_line (intersection_point T_1 T_0) V)))))) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => (((apart_point_and_line Z X) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point X Y))))))) (All Z, ((convergent_lines T_1 T_0) => (((apart_point_and_line Z T_1) \/ (apart_point_and_line Z T_0)) => (distinct_points Z (intersection_point T_1 T_0))))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (All X, (-. (distinct_lines X X))) ### All 35 % 0.20/0.55 37. (All U, (All V, (((distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) /\ (distinct_lines U V)) => ((apart_point_and_line (intersection_point T_0 T_1) U) \/ ((apart_point_and_line (intersection_point T_0 T_1) V) \/ ((apart_point_and_line (intersection_point T_1 T_0) U) \/ (apart_point_and_line (intersection_point T_1 T_0) V))))))) (All X, (-. (distinct_lines X X))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (All Z, ((convergent_lines T_1 T_0) => (((apart_point_and_line Z T_1) \/ (apart_point_and_line Z T_0)) => (distinct_points Z (intersection_point T_1 T_0))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => (((apart_point_and_line Z X) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point X Y))))))) (convergent_lines T_0 T_1) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) ### All 36 % 0.20/0.55 38. (All Y, (All U, (All V, (((distinct_points (intersection_point T_0 T_1) Y) /\ (distinct_lines U V)) => ((apart_point_and_line (intersection_point T_0 T_1) U) \/ ((apart_point_and_line (intersection_point T_0 T_1) V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => (((apart_point_and_line Z X) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point X Y))))))) (All Z, ((convergent_lines T_1 T_0) => (((apart_point_and_line Z T_1) \/ (apart_point_and_line Z T_0)) => (distinct_points Z (intersection_point T_1 T_0))))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (All X, (-. (distinct_lines X X))) ### All 37 % 0.20/0.55 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 X, (-. (distinct_lines X X))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (All Z, ((convergent_lines T_1 T_0) => (((apart_point_and_line Z T_1) \/ (apart_point_and_line Z T_0)) => (distinct_points Z (intersection_point T_1 T_0))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => (((apart_point_and_line Z X) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point X Y))))))) (convergent_lines T_0 T_1) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) ### All 38 % 0.20/0.55 40. (All Y, (All Z, ((convergent_lines T_1 Y) => (((apart_point_and_line Z T_1) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point T_1 Y)))))) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => (((apart_point_and_line Z X) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point X Y))))))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (All X, (-. (distinct_lines X 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 39 % 0.20/0.55 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 X, (-. (distinct_lines X X))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => (((apart_point_and_line Z X) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point X Y))))))) (convergent_lines T_0 T_1) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) ### All 40 % 0.20/0.55 42. (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => (((apart_point_and_line Z X) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point X Y))))))) (All X, (-. (distinct_lines X 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 41 % 0.20/0.55 43. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) (All X, (-. (distinct_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => (((apart_point_and_line Z X) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point X Y))))))) (convergent_lines T_0 T_1) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) ### All 42 % 0.20/0.55 44. (-. (-. (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => (((apart_point_and_line Z X) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point X Y))))))) (All X, (-. (distinct_lines X 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, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### NotNot 43 % 0.20/0.55 45. (-. ((convergent_lines T_0 T_1) => (-. (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) (All X, (-. (distinct_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => (((apart_point_and_line Z X) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point X Y))))))) ### NotImply 44 % 0.20/0.55 46. (-. (All Y, ((convergent_lines T_0 Y) => (-. (distinct_points (intersection_point T_0 Y) (intersection_point Y T_0)))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => (((apart_point_and_line Z X) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point X Y))))))) (All X, (-. (distinct_lines X 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, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### NotAllEx 45 % 0.20/0.55 47. (-. (All X, (All Y, ((convergent_lines X Y) => (-. (distinct_points (intersection_point X Y) (intersection_point Y X))))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) (All X, (-. (distinct_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => (((apart_point_and_line Z X) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point X Y))))))) ### NotAllEx 46 % 0.20/0.55 % SZS output end Proof % 0.20/0.55 (* END-PROOF *) %------------------------------------------------------------------------------