%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO215+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 : n003.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 06:31:12 EDT 2022 % Result : Theorem 12.33s 12.51s % Output : Proof 12.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO215+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n003.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 00:37:57 EDT 2022 % 0.12/0.33 % CPUTime : % 12.33/12.51 % SZS status Theorem % 12.33/12.51 (* PROOF-FOUND *) % 12.33/12.51 (* BEGIN-PROOF *) % 12.33/12.51 % SZS output start Proof % 12.33/12.51 1. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom % 12.33/12.51 2. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom % 12.33/12.51 3. (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Axiom % 12.33/12.51 4. (convergent_lines T_1 T_0) (-. (convergent_lines T_1 T_0)) ### Axiom % 12.33/12.51 5. (distinct_lines T_1 T_0) (-. (distinct_lines T_1 T_0)) ### Axiom % 12.33/12.51 6. (-. (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 % 12.33/12.51 7. (convergent_lines T_1 T_0) (-. (convergent_lines T_1 T_0)) ### Axiom % 12.33/12.51 8. (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 % 12.33/12.51 9. ((convergent_lines T_1 T_0) => (-. (apart_point_and_line (intersection_point T_1 T_0) T_0))) (apart_point_and_line (intersection_point T_1 T_0) T_0) (convergent_lines T_1 T_0) ### Imply 7 8 % 12.33/12.51 10. (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) Y)))) (convergent_lines T_1 T_0) (apart_point_and_line (intersection_point T_1 T_0) T_0) ### All 9 % 12.33/12.51 11. (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (apart_point_and_line (intersection_point T_1 T_0) T_0) (convergent_lines T_1 T_0) ### All 10 % 12.33/12.51 12. (-. (unorthogonal_lines T_1 T_2)) (unorthogonal_lines T_1 T_2) ### Axiom % 12.33/12.51 13. (-. (unorthogonal_lines T_0 T_2)) (unorthogonal_lines T_0 T_2) ### Axiom % 12.33/12.51 14. ((distinct_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) \/ ((unorthogonal_lines T_1 T_2) \/ (unorthogonal_lines T_0 T_2))))) (-. (unorthogonal_lines T_0 T_2)) (-. (unorthogonal_lines T_1 T_2)) (convergent_lines T_1 T_0) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (apart_point_and_line (intersection_point T_1 T_0) T_1)) (distinct_lines T_1 T_0) ### DisjTree 5 6 11 12 13 % 12.33/12.51 15. (All N, ((distinct_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) \/ ((unorthogonal_lines T_1 N) \/ (unorthogonal_lines T_0 N)))))) (distinct_lines T_1 T_0) (-. (apart_point_and_line (intersection_point T_1 T_0) T_1)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (convergent_lines T_1 T_0) (-. (unorthogonal_lines T_1 T_2)) (-. (unorthogonal_lines T_0 T_2)) ### All 14 % 12.33/12.51 16. (All M, (All N, ((distinct_lines T_1 M) => ((apart_point_and_line (intersection_point T_1 T_0) T_1) \/ ((apart_point_and_line (intersection_point T_1 T_0) M) \/ ((unorthogonal_lines T_1 N) \/ (unorthogonal_lines M N))))))) (-. (unorthogonal_lines T_0 T_2)) (-. (unorthogonal_lines T_1 T_2)) (convergent_lines T_1 T_0) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (apart_point_and_line (intersection_point T_1 T_0) T_1)) (distinct_lines T_1 T_0) ### All 15 % 12.33/12.51 17. (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line (intersection_point T_1 T_0) L) \/ ((apart_point_and_line (intersection_point T_1 T_0) M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N)))))))) (distinct_lines T_1 T_0) (-. (apart_point_and_line (intersection_point T_1 T_0) T_1)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (convergent_lines T_1 T_0) (-. (unorthogonal_lines T_1 T_2)) (-. (unorthogonal_lines T_0 T_2)) ### All 16 % 12.33/12.51 18. (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (-. (unorthogonal_lines T_0 T_2)) (-. (unorthogonal_lines T_1 T_2)) (convergent_lines T_1 T_0) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (apart_point_and_line (intersection_point T_1 T_0) T_1)) (distinct_lines T_1 T_0) ### All 17 % 12.33/12.51 19. ((convergent_lines T_1 T_0) => (-. (apart_point_and_line (intersection_point T_1 T_0) T_1))) (distinct_lines T_1 T_0) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (unorthogonal_lines T_1 T_2)) (-. (unorthogonal_lines T_0 T_2)) (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (convergent_lines T_1 T_0) ### Imply 4 18 % 12.33/12.51 20. (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (convergent_lines T_1 T_0) (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (-. (unorthogonal_lines T_0 T_2)) (-. (unorthogonal_lines T_1 T_2)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (distinct_lines T_1 T_0) ### All 19 % 12.33/12.51 21. ((convergent_lines T_0 T_1) => ((convergent_lines T_0 T_0) \/ (convergent_lines T_1 T_0))) (distinct_lines T_1 T_0) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (unorthogonal_lines T_1 T_2)) (-. (unorthogonal_lines T_0 T_2)) (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_1) ### DisjTree 2 3 20 % 12.33/12.51 22. (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_0)) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (-. (unorthogonal_lines T_0 T_2)) (-. (unorthogonal_lines T_1 T_2)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (distinct_lines T_1 T_0) ### All 21 % 12.33/12.51 23. (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Axiom % 12.33/12.51 24. ((convergent_lines T_0 T_1) => ((distinct_lines T_1 T_0) \/ (convergent_lines T_0 T_0))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (unorthogonal_lines T_1 T_2)) (-. (unorthogonal_lines T_0 T_2)) (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (-. (convergent_lines T_0 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) ### DisjTree 1 22 23 % 12.33/12.51 25. (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 Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (-. (convergent_lines T_0 T_0)) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (-. (unorthogonal_lines T_0 T_2)) (-. (unorthogonal_lines T_1 T_2)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) ### All 24 % 12.33/12.51 26. (All X, (-. (convergent_lines X X))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (unorthogonal_lines T_1 T_2)) (-. (unorthogonal_lines T_0 T_2)) (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (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 Z, ((convergent_lines T_0 T_1) => ((distinct_lines T_1 Z) \/ (convergent_lines T_0 Z)))) ### All 25 % 12.33/12.52 27. (All Y, (All Z, ((convergent_lines T_0 Y) => ((distinct_lines Y Z) \/ (convergent_lines T_0 Z))))) (convergent_lines T_0 T_1) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (-. (unorthogonal_lines T_0 T_2)) (-. (unorthogonal_lines T_1 T_2)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (-. (convergent_lines X X))) ### All 26 % 12.33/12.52 28. (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (unorthogonal_lines T_1 T_2)) (-. (unorthogonal_lines T_0 T_2)) (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (convergent_lines T_0 T_1) (All Y, (All Z, ((convergent_lines T_0 Y) => ((distinct_lines Y Z) \/ (convergent_lines T_0 Z))))) ### All 27 % 12.33/12.52 29. (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All Y, (All Z, ((convergent_lines T_0 Y) => ((distinct_lines Y Z) \/ (convergent_lines T_0 Z))))) (convergent_lines T_0 T_1) (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (-. (unorthogonal_lines T_0 T_2)) (-. (unorthogonal_lines T_1 T_2)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (-. (convergent_lines X X))) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) ### All 28 % 12.33/12.52 30. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (unorthogonal_lines T_1 T_2)) (-. (unorthogonal_lines T_0 T_2)) (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) ### All 29 % 12.33/12.52 31. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (convergent_lines T_0 T_1) (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (-. (unorthogonal_lines T_0 T_2)) (-. (unorthogonal_lines T_1 T_2)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (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 30 % 12.33/12.52 32. (-. ((convergent_lines T_0 T_1) => ((unorthogonal_lines T_0 T_2) \/ (unorthogonal_lines T_1 T_2)))) (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) Y))))) (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### ConjTree 31 % 12.33/12.52 33. (-. (All N, ((convergent_lines T_0 T_1) => ((unorthogonal_lines T_0 N) \/ (unorthogonal_lines T_1 N))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (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 32 % 12.33/12.52 34. (-. (All M, (All N, ((convergent_lines T_0 M) => ((unorthogonal_lines T_0 N) \/ (unorthogonal_lines M N)))))) (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) Y))))) (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### NotAllEx 33 % 12.33/12.52 35. (-. (All L, (All M, (All N, ((convergent_lines L M) => ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All A, (All L, (All M, (All N, ((distinct_lines L M) => ((apart_point_and_line A L) \/ ((apart_point_and_line A M) \/ ((unorthogonal_lines L N) \/ (unorthogonal_lines M N))))))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (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 34 % 12.33/12.52 % SZS output end Proof % 12.33/12.52 (* END-PROOF *) %------------------------------------------------------------------------------