%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO185+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n028.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 06:30:47 EDT 2022 % Result : Theorem 0.18s 0.46s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO185+3 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n028.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 17:22:29 EDT 2022 % 0.12/0.34 % CPUTime : % 0.18/0.46 % SZS status Theorem % 0.18/0.46 (* PROOF-FOUND *) % 0.18/0.46 (* BEGIN-PROOF *) % 0.18/0.46 % SZS output start Proof % 0.18/0.46 1. (apart_point_and_line T_0 T_1) (-. (apart_point_and_line T_0 T_1)) ### Axiom % 0.18/0.46 2. (apart_point_and_line T_0 T_1) (-. (apart_point_and_line T_0 T_1)) ### Axiom % 0.18/0.46 3. (-. (distinct_points T_0 (intersection_point T_1 T_2))) (distinct_points T_0 (intersection_point T_1 T_2)) ### Axiom % 0.18/0.46 4. (distinct_lines T_1 T_2) (-. (distinct_lines T_1 T_2)) ### Axiom % 0.18/0.46 5. (-. (convergent_lines T_1 T_2)) (distinct_lines T_1 T_2) ### Extension/test/p1ctrp 4 % 0.18/0.46 6. (apart_point_and_line (intersection_point T_1 T_2) T_1) (-. (apart_point_and_line (intersection_point T_1 T_2) T_1)) ### Axiom % 0.18/0.46 7. ((convergent_lines T_1 T_2) => (-. (apart_point_and_line (intersection_point T_1 T_2) T_1))) (apart_point_and_line (intersection_point T_1 T_2) T_1) (distinct_lines T_1 T_2) ### Imply 5 6 % 0.18/0.46 8. (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (distinct_lines T_1 T_2) (apart_point_and_line (intersection_point T_1 T_2) T_1) ### All 7 % 0.18/0.46 9. ((apart_point_and_line T_0 T_1) => ((distinct_points T_0 (intersection_point T_1 T_2)) \/ (apart_point_and_line (intersection_point T_1 T_2) T_1))) (distinct_lines T_1 T_2) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (apart_point_and_line T_0 T_1) ### DisjTree 2 3 8 % 0.18/0.46 10. (All Z, ((apart_point_and_line T_0 T_1) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z T_1)))) (apart_point_and_line T_0 T_1) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (distinct_lines T_1 T_2) ### All 9 % 0.18/0.46 11. (-. (apart_point_and_line T_0 T_2)) (apart_point_and_line T_0 T_2) ### Axiom % 0.18/0.46 12. ((apart_point_and_line T_0 T_1) => ((distinct_lines T_1 T_2) \/ (apart_point_and_line T_0 T_2))) (-. (apart_point_and_line T_0 T_2)) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (All Z, ((apart_point_and_line T_0 T_1) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z T_1)))) (apart_point_and_line T_0 T_1) ### DisjTree 1 10 11 % 0.18/0.46 13. (All Z, ((apart_point_and_line T_0 T_1) => ((distinct_lines T_1 Z) \/ (apart_point_and_line T_0 Z)))) (apart_point_and_line T_0 T_1) (All Z, ((apart_point_and_line T_0 T_1) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z T_1)))) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (-. (apart_point_and_line T_0 T_2)) ### All 12 % 0.18/0.46 14. (-. (distinct_points T_0 (intersection_point T_1 T_2))) (distinct_points T_0 (intersection_point T_1 T_2)) ### Axiom % 0.18/0.46 15. (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) (apart_point_and_line (intersection_point T_1 T_2) T_2) ### Axiom % 0.18/0.46 16. ((apart_point_and_line T_0 T_2) => ((distinct_points T_0 (intersection_point T_1 T_2)) \/ (apart_point_and_line (intersection_point T_1 T_2) T_2))) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (All Z, ((apart_point_and_line T_0 T_1) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z T_1)))) (apart_point_and_line T_0 T_1) (All Z, ((apart_point_and_line T_0 T_1) => ((distinct_lines T_1 Z) \/ (apart_point_and_line T_0 Z)))) ### DisjTree 13 14 15 % 0.18/0.46 17. (All Z, ((apart_point_and_line T_0 T_2) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z T_2)))) (All Z, ((apart_point_and_line T_0 T_1) => ((distinct_lines T_1 Z) \/ (apart_point_and_line T_0 Z)))) (apart_point_and_line T_0 T_1) (All Z, ((apart_point_and_line T_0 T_1) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z T_1)))) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) ### All 16 % 0.18/0.46 18. (All Y, (All Z, ((apart_point_and_line T_0 Y) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z Y))))) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (All Z, ((apart_point_and_line T_0 T_1) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z T_1)))) (apart_point_and_line T_0 T_1) (All Z, ((apart_point_and_line T_0 T_1) => ((distinct_lines T_1 Z) \/ (apart_point_and_line T_0 Z)))) ### All 17 % 0.18/0.46 19. (All Z, ((apart_point_and_line T_0 T_1) => ((distinct_lines T_1 Z) \/ (apart_point_and_line T_0 Z)))) (apart_point_and_line T_0 T_1) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) (All Y, (All Z, ((apart_point_and_line T_0 Y) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z Y))))) ### All 18 % 0.18/0.46 20. (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (apart_point_and_line T_0 T_1) (All Z, ((apart_point_and_line T_0 T_1) => ((distinct_lines T_1 Z) \/ (apart_point_and_line T_0 Z)))) ### All 19 % 0.18/0.46 21. (All Y, (All Z, ((apart_point_and_line T_0 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_0 Z))))) (apart_point_and_line T_0 T_1) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) ### All 20 % 0.18/0.46 22. (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (apart_point_and_line T_0 T_1) (All Y, (All Z, ((apart_point_and_line T_0 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_0 Z))))) ### All 21 % 0.18/0.46 23. (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_0 T_1) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) ### All 22 % 0.18/0.46 24. (-. (incident_point_and_line T_0 T_1)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) ### Extension/test/not_a4 23 % 0.18/0.46 25. (apart_point_and_line T_0 T_2) (-. (apart_point_and_line T_0 T_2)) ### Axiom % 0.18/0.46 26. (-. (distinct_points T_0 (intersection_point T_1 T_2))) (distinct_points T_0 (intersection_point T_1 T_2)) ### Axiom % 0.18/0.46 27. (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) (apart_point_and_line (intersection_point T_1 T_2) T_2) ### Axiom % 0.18/0.46 28. ((apart_point_and_line T_0 T_2) => ((distinct_points T_0 (intersection_point T_1 T_2)) \/ (apart_point_and_line (intersection_point T_1 T_2) T_2))) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (apart_point_and_line T_0 T_2) ### DisjTree 25 26 27 % 0.18/0.46 29. (All Z, ((apart_point_and_line T_0 T_2) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z T_2)))) (apart_point_and_line T_0 T_2) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) ### All 28 % 0.18/0.46 30. (All Y, (All Z, ((apart_point_and_line T_0 Y) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z Y))))) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (apart_point_and_line T_0 T_2) ### All 29 % 0.18/0.46 31. (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (apart_point_and_line T_0 T_2) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) ### All 30 % 0.18/0.46 32. (-. (incident_point_and_line T_0 T_2)) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) ### Extension/test/not_a4 31 % 0.18/0.46 33. (-. ((incident_point_and_line T_0 T_1) /\ (incident_point_and_line T_0 T_2))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (-. (distinct_points T_0 (intersection_point T_1 T_2))) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) ### NotAnd 24 32 % 0.18/0.46 34. (equal_points T_0 (intersection_point T_1 T_2)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (-. ((incident_point_and_line T_0 T_1) /\ (incident_point_and_line T_0 T_2))) ### Extension/test/ax1 33 % 0.18/0.46 35. (convergent_lines T_1 T_2) (-. ((incident_point_and_line T_0 T_1) /\ (incident_point_and_line T_0 T_2))) (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, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (equal_points T_0 (intersection_point T_1 T_2)) ### Extension/test/ci4 34 % 0.18/0.46 36. (-. (((distinct_points T_0 T_3) /\ ((convergent_lines T_1 T_2) /\ (equal_points T_0 (intersection_point T_1 T_2)))) => ((incident_point_and_line T_0 T_1) /\ (incident_point_and_line T_0 T_2)))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) ### ConjTree 35 % 0.18/0.46 37. (-. (All V, (((distinct_points T_0 T_3) /\ ((convergent_lines T_1 V) /\ (equal_points T_0 (intersection_point T_1 V)))) => ((incident_point_and_line T_0 T_1) /\ (incident_point_and_line T_0 V))))) (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, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) ### NotAllEx 36 % 0.18/0.46 38. (-. (All U, (All V, (((distinct_points T_0 T_3) /\ ((convergent_lines U V) /\ (equal_points T_0 (intersection_point U V)))) => ((incident_point_and_line T_0 U) /\ (incident_point_and_line T_0 V)))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) ### NotAllEx 37 % 0.18/0.46 39. (-. (All Y, (All U, (All V, (((distinct_points T_0 Y) /\ ((convergent_lines U V) /\ (equal_points T_0 (intersection_point U V)))) => ((incident_point_and_line T_0 U) /\ (incident_point_and_line T_0 V))))))) (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, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) ### NotAllEx 38 % 0.18/0.46 40. (-. (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ ((convergent_lines U V) /\ (equal_points X (intersection_point U V)))) => ((incident_point_and_line X U) /\ (incident_point_and_line X V)))))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) ### NotAllEx 39 % 0.18/0.46 % SZS output end Proof % 0.18/0.46 (* END-PROOF *) %------------------------------------------------------------------------------