%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO206+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 : n027.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 06:31:05 EDT 2022 % Result : Theorem 43.95s 44.17s % Output : Proof 43.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : GEO206+1 : TPTP v8.1.0. Released v3.3.0. % 0.12/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.34 % Computer : n027.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 02:22:37 EDT 2022 % 0.13/0.34 % CPUTime : % 43.95/44.17 % SZS status Theorem % 43.95/44.17 (* PROOF-FOUND *) % 43.95/44.17 (* BEGIN-PROOF *) % 43.95/44.17 % SZS output start Proof % 43.95/44.17 1. (distinct_lines T_0 (parallel_through_point T_1 T_2)) (-. (distinct_lines T_0 (parallel_through_point T_1 T_2))) ### Axiom % 43.95/44.17 2. (-. (apart_point_and_line T_2 T_0)) (apart_point_and_line T_2 T_0) ### Axiom % 43.95/44.17 3. (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (apart_point_and_line T_2 (parallel_through_point T_1 T_2)) ### Axiom % 43.95/44.17 4. (-. (convergent_lines T_0 (parallel_through_point T_1 T_2))) (convergent_lines T_0 (parallel_through_point T_1 T_2)) ### Axiom % 43.95/44.17 5. ((distinct_lines T_0 (parallel_through_point T_1 T_2)) => ((apart_point_and_line T_2 T_0) \/ ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ (convergent_lines T_0 (parallel_through_point T_1 T_2))))) (-. (convergent_lines T_0 (parallel_through_point T_1 T_2))) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (-. (apart_point_and_line T_2 T_0)) (distinct_lines T_0 (parallel_through_point T_1 T_2)) ### DisjTree 1 2 3 4 % 43.95/44.17 6. (All Z, ((distinct_lines T_0 Z) => ((apart_point_and_line T_2 T_0) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines T_0 Z))))) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (-. (convergent_lines T_0 (parallel_through_point T_1 T_2))) ### All 5 % 43.95/44.17 7. (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 (parallel_through_point T_1 T_2))) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (-. (apart_point_and_line T_2 T_0)) (distinct_lines T_0 (parallel_through_point T_1 T_2)) ### All 6 % 43.95/44.17 8. (distinct_lines (parallel_through_point T_1 T_2) T_0) (-. (distinct_lines (parallel_through_point T_1 T_2) T_0)) ### Axiom % 43.95/44.17 9. (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (apart_point_and_line T_2 (parallel_through_point T_1 T_2)) ### Axiom % 43.95/44.17 10. (-. (apart_point_and_line T_2 T_0)) (apart_point_and_line T_2 T_0) ### Axiom % 43.95/44.17 11. (convergent_lines (parallel_through_point T_1 T_2) T_0) (-. (convergent_lines (parallel_through_point T_1 T_2) T_0)) ### Axiom % 43.95/44.17 12. (-. (convergent_lines (parallel_through_point T_1 T_2) T_1)) (convergent_lines (parallel_through_point T_1 T_2) T_1) ### Axiom % 43.95/44.17 13. (-. (convergent_lines T_0 T_1)) (convergent_lines T_0 T_1) ### Axiom % 43.95/44.17 14. ((convergent_lines (parallel_through_point T_1 T_2) T_0) => ((convergent_lines (parallel_through_point T_1 T_2) T_1) \/ (convergent_lines T_0 T_1))) (-. (convergent_lines T_0 T_1)) (-. (convergent_lines (parallel_through_point T_1 T_2) T_1)) (convergent_lines (parallel_through_point T_1 T_2) T_0) ### DisjTree 11 12 13 % 43.95/44.17 15. (All Z, ((convergent_lines (parallel_through_point T_1 T_2) T_0) => ((convergent_lines (parallel_through_point T_1 T_2) Z) \/ (convergent_lines T_0 Z)))) (convergent_lines (parallel_through_point T_1 T_2) T_0) (-. (convergent_lines (parallel_through_point T_1 T_2) T_1)) (-. (convergent_lines T_0 T_1)) ### All 14 % 43.95/44.17 16. (All Y, (All Z, ((convergent_lines (parallel_through_point T_1 T_2) Y) => ((convergent_lines (parallel_through_point T_1 T_2) Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_0 T_1)) (-. (convergent_lines (parallel_through_point T_1 T_2) T_1)) (convergent_lines (parallel_through_point T_1 T_2) T_0) ### All 15 % 43.95/44.17 17. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines (parallel_through_point T_1 T_2) T_0) (-. (convergent_lines (parallel_through_point T_1 T_2) T_1)) (-. (convergent_lines T_0 T_1)) ### All 16 % 43.95/44.17 18. (All Y, (-. (convergent_lines (parallel_through_point Y T_2) Y))) (-. (convergent_lines T_0 T_1)) (convergent_lines (parallel_through_point T_1 T_2) T_0) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### All 17 % 43.95/44.17 19. (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines (parallel_through_point T_1 T_2) T_0) (-. (convergent_lines T_0 T_1)) ### All 18 % 43.95/44.17 20. ((distinct_lines (parallel_through_point T_1 T_2) T_0) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 T_0) \/ (convergent_lines (parallel_through_point T_1 T_2) T_0)))) (-. (convergent_lines T_0 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (distinct_lines (parallel_through_point T_1 T_2) T_0) ### DisjTree 8 9 10 19 % 43.95/44.17 21. (All Z, ((distinct_lines (parallel_through_point T_1 T_2) Z) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines (parallel_through_point T_1 T_2) Z))))) (distinct_lines (parallel_through_point T_1 T_2) T_0) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (-. (apart_point_and_line T_2 T_0)) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_1)) ### All 20 % 43.95/44.17 22. (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Axiom % 43.95/44.17 23. ((convergent_lines T_0 (parallel_through_point T_1 T_2)) => ((distinct_lines (parallel_through_point T_1 T_2) T_0) \/ (convergent_lines T_0 T_0))) (-. (convergent_lines T_0 T_0)) (-. (convergent_lines T_0 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All Z, ((distinct_lines (parallel_through_point T_1 T_2) Z) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines (parallel_through_point T_1 T_2) Z))))) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) ### DisjTree 7 21 22 % 43.95/44.17 24. (All Z, ((convergent_lines T_0 (parallel_through_point T_1 T_2)) => ((distinct_lines (parallel_through_point T_1 T_2) Z) \/ (convergent_lines T_0 Z)))) (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (-. (apart_point_and_line T_2 T_0)) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (All Z, ((distinct_lines (parallel_through_point T_1 T_2) Z) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines (parallel_through_point T_1 T_2) Z))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_1)) (-. (convergent_lines T_0 T_0)) ### All 23 % 43.95/44.17 25. (All X, (-. (convergent_lines X X))) (-. (convergent_lines T_0 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All Z, ((distinct_lines (parallel_through_point T_1 T_2) Z) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines (parallel_through_point T_1 T_2) Z))))) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) (All Z, ((convergent_lines T_0 (parallel_through_point T_1 T_2)) => ((distinct_lines (parallel_through_point T_1 T_2) Z) \/ (convergent_lines T_0 Z)))) ### All 24 % 43.95/44.19 26. (All Y, (All Z, ((convergent_lines T_0 Y) => ((distinct_lines Y Z) \/ (convergent_lines T_0 Z))))) (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (-. (apart_point_and_line T_2 T_0)) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (All Z, ((distinct_lines (parallel_through_point T_1 T_2) Z) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines (parallel_through_point T_1 T_2) Z))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_1)) (All X, (-. (convergent_lines X X))) ### All 25 % 43.95/44.19 27. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (-. (convergent_lines T_0 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All Z, ((distinct_lines (parallel_through_point T_1 T_2) Z) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines (parallel_through_point T_1 T_2) Z))))) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) ### All 26 % 43.95/44.19 28. (All Y, (-. (apart_point_and_line T_2 (parallel_through_point Y T_2)))) (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) (-. (apart_point_and_line T_2 T_0)) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (All Z, ((distinct_lines (parallel_through_point T_1 T_2) Z) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines (parallel_through_point T_1 T_2) Z))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_1)) (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 27 % 43.95/44.19 29. (All X, (All Y, (-. (apart_point_and_line X (parallel_through_point Y X))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (-. (convergent_lines T_0 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All Z, ((distinct_lines (parallel_through_point T_1 T_2) Z) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines (parallel_through_point T_1 T_2) Z))))) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (-. (apart_point_and_line T_2 T_0)) (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) ### All 28 % 43.95/44.19 30. (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) (-. (apart_point_and_line T_2 T_0)) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_1)) (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 X, (All Y, (-. (apart_point_and_line X (parallel_through_point Y X))))) ### All 29 % 43.95/44.19 31. (All X, (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line X Y) \/ ((apart_point_and_line X Z) \/ (convergent_lines Y Z))))))) (All X, (All Y, (-. (apart_point_and_line X (parallel_through_point Y X))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (-. (convergent_lines T_0 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (-. (apart_point_and_line T_2 T_0)) ### All 30 % 43.95/44.19 32. (-. (((-. (apart_point_and_line T_2 T_0)) /\ (-. (convergent_lines T_0 T_1))) => (-. (distinct_lines T_0 (parallel_through_point T_1 T_2))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (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 X, (All Y, (-. (apart_point_and_line X (parallel_through_point Y X))))) (All X, (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line X Y) \/ ((apart_point_and_line X Z) \/ (convergent_lines Y Z))))))) ### ConjTree 31 % 43.95/44.19 33. (-. (All Z, (((-. (apart_point_and_line T_2 T_0)) /\ (-. (convergent_lines T_0 Z))) => (-. (distinct_lines T_0 (parallel_through_point Z T_2)))))) (All X, (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line X Y) \/ ((apart_point_and_line X Z) \/ (convergent_lines Y Z))))))) (All X, (All Y, (-. (apart_point_and_line X (parallel_through_point Y X))))) (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, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) ### NotAllEx 32 % 43.95/44.19 34. (-. (All Y, (All Z, (((-. (apart_point_and_line T_2 Y)) /\ (-. (convergent_lines Y Z))) => (-. (distinct_lines Y (parallel_through_point Z T_2))))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (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 X, (All Y, (-. (apart_point_and_line X (parallel_through_point Y X))))) (All X, (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line X Y) \/ ((apart_point_and_line X Z) \/ (convergent_lines Y Z))))))) ### NotAllEx 33 % 43.95/44.19 35. (-. (All X, (All Y, (All Z, (((-. (apart_point_and_line X Y)) /\ (-. (convergent_lines Y Z))) => (-. (distinct_lines Y (parallel_through_point Z X)))))))) (All X, (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line X Y) \/ ((apart_point_and_line X Z) \/ (convergent_lines Y Z))))))) (All X, (All Y, (-. (apart_point_and_line X (parallel_through_point Y X))))) (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, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) ### NotAllEx 34 % 43.95/44.19 % SZS output end Proof % 43.95/44.19 (* END-PROOF *) %------------------------------------------------------------------------------