%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : GEO182+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 : n012.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 06:30:44 EDT 2022 % Result : Theorem 1.09s 1.27s % Output : Proof 1.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO182+2 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n012.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 01:04:08 EDT 2022 % 0.12/0.33 % CPUTime : % 1.09/1.27 % SZS status Theorem % 1.09/1.27 (* PROOF-FOUND *) % 1.09/1.27 (* BEGIN-PROOF *) % 1.09/1.27 % SZS output start Proof % 1.09/1.27 1. (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (apart_point_and_line T_0 (line_connecting T_1 T_2))) ### Axiom % 1.09/1.27 2. (distinct_points T_1 T_2) (-. (distinct_points T_1 T_2)) ### Axiom % 1.09/1.27 3. (distinct_points T_1 T_1) ### Extension/test/apart1 % 1.09/1.27 4. (distinct_points T_2 T_1) (-. (distinct_points T_2 T_1)) ### Axiom % 1.09/1.27 5. (distinct_points T_1 T_2) (-. (distinct_points T_1 T_2)) ### Axiom % 1.09/1.27 6. (distinct_points T_1 T_2) (-. (distinct_points T_1 T_2)) ### Axiom % 1.09/1.27 7. (distinct_points T_2 T_1) (-. (distinct_points T_2 T_1)) ### Axiom % 1.09/1.27 8. (distinct_points T_2 T_1) (-. (distinct_points T_2 T_1)) ### Axiom % 1.09/1.27 9. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1))) ### Axiom % 1.09/1.27 10. (-. (apart_point_and_line T_2 (line_connecting T_1 T_2))) (apart_point_and_line T_2 (line_connecting T_1 T_2)) ### Axiom % 1.09/1.27 11. (-. (apart_point_and_line T_2 (line_connecting T_2 T_1))) (apart_point_and_line T_2 (line_connecting T_2 T_1)) ### Axiom % 1.09/1.27 12. (-. (apart_point_and_line T_1 (line_connecting T_1 T_2))) (apart_point_and_line T_1 (line_connecting T_1 T_2)) ### Axiom % 1.09/1.27 13. (-. (apart_point_and_line T_1 (line_connecting T_2 T_1))) (apart_point_and_line T_1 (line_connecting T_2 T_1)) ### Axiom % 1.09/1.27 14. (((distinct_points T_2 T_1) /\ (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1))) => ((apart_point_and_line T_2 (line_connecting T_1 T_2)) \/ ((apart_point_and_line T_2 (line_connecting T_2 T_1)) \/ ((apart_point_and_line T_1 (line_connecting T_1 T_2)) \/ (apart_point_and_line T_1 (line_connecting T_2 T_1)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_2))) (-. (apart_point_and_line T_2 (line_connecting T_2 T_1))) (-. (apart_point_and_line T_2 (line_connecting T_1 T_2))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) (distinct_points T_2 T_1) ### DisjTree 8 9 10 11 12 13 % 1.09/1.27 15. (All V, (((distinct_points T_2 T_1) /\ (distinct_lines (line_connecting T_1 T_2) V)) => ((apart_point_and_line T_2 (line_connecting T_1 T_2)) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line T_1 (line_connecting T_1 T_2)) \/ (apart_point_and_line T_1 V)))))) (distinct_points T_2 T_1) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) (-. (apart_point_and_line T_2 (line_connecting T_1 T_2))) (-. (apart_point_and_line T_2 (line_connecting T_2 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_1))) ### All 14 % 1.09/1.27 16. (All U, (All V, (((distinct_points T_2 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_2))) (-. (apart_point_and_line T_2 (line_connecting T_2 T_1))) (-. (apart_point_and_line T_2 (line_connecting T_1 T_2))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) (distinct_points T_2 T_1) ### All 15 % 1.09/1.27 17. ((distinct_points T_1 T_2) /\ (distinct_points T_1 T_1)) ### And 3 % 1.09/1.27 18. ((distinct_points T_2 T_1) => ((apart_point_and_line T_1 (line_connecting T_2 T_1)) => ((distinct_points T_1 T_2) /\ (distinct_points T_1 T_1)))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) (-. (apart_point_and_line T_2 (line_connecting T_1 T_2))) (-. (apart_point_and_line T_2 (line_connecting T_2 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_2))) (All U, (All V, (((distinct_points T_2 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (distinct_points T_2 T_1) ### DisjTree 7 16 17 % 1.09/1.27 19. (All Z, ((distinct_points T_2 T_1) => ((apart_point_and_line Z (line_connecting T_2 T_1)) => ((distinct_points Z T_2) /\ (distinct_points Z T_1))))) (distinct_points T_2 T_1) (All U, (All V, (((distinct_points T_2 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_2))) (-. (apart_point_and_line T_2 (line_connecting T_2 T_1))) (-. (apart_point_and_line T_2 (line_connecting T_1 T_2))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) ### All 18 % 1.09/1.27 20. (distinct_points T_2 T_2) ### Extension/test/apart1 % 1.09/1.27 21. ((distinct_points T_2 T_1) /\ (distinct_points T_2 T_2)) ### And 20 % 1.09/1.27 22. ((distinct_points T_1 T_2) => ((apart_point_and_line T_2 (line_connecting T_1 T_2)) => ((distinct_points T_2 T_1) /\ (distinct_points T_2 T_2)))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) (-. (apart_point_and_line T_2 (line_connecting T_2 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_2))) (All U, (All V, (((distinct_points T_2 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (distinct_points T_2 T_1) (All Z, ((distinct_points T_2 T_1) => ((apart_point_and_line Z (line_connecting T_2 T_1)) => ((distinct_points Z T_2) /\ (distinct_points Z T_1))))) (distinct_points T_1 T_2) ### DisjTree 6 19 21 % 1.09/1.27 23. (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) (All Z, ((distinct_points T_2 T_1) => ((apart_point_and_line Z (line_connecting T_2 T_1)) => ((distinct_points Z T_2) /\ (distinct_points Z T_1))))) (distinct_points T_2 T_1) (All U, (All V, (((distinct_points T_2 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_2))) (-. (apart_point_and_line T_2 (line_connecting T_2 T_1))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) ### All 22 % 1.09/1.27 24. ((distinct_points T_1 T_1) /\ (distinct_points T_1 T_2)) ### And 3 % 1.09/1.27 25. ((distinct_points T_1 T_2) => ((apart_point_and_line T_1 (line_connecting T_1 T_2)) => ((distinct_points T_1 T_1) /\ (distinct_points T_1 T_2)))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) (-. (apart_point_and_line T_2 (line_connecting T_2 T_1))) (All U, (All V, (((distinct_points T_2 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (distinct_points T_2 T_1) (All Z, ((distinct_points T_2 T_1) => ((apart_point_and_line Z (line_connecting T_2 T_1)) => ((distinct_points Z T_2) /\ (distinct_points Z T_1))))) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) ### DisjTree 5 23 24 % 1.09/1.27 26. (distinct_points T_1 T_2) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (All Z, ((distinct_points T_2 T_1) => ((apart_point_and_line Z (line_connecting T_2 T_1)) => ((distinct_points Z T_2) /\ (distinct_points Z T_1))))) (distinct_points T_2 T_1) (All U, (All V, (((distinct_points T_2 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (-. (apart_point_and_line T_2 (line_connecting T_2 T_1))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) ### All 25 % 1.09/1.27 27. ((distinct_points T_2 T_2) /\ (distinct_points T_2 T_1)) ### And 20 % 1.09/1.27 28. ((distinct_points T_2 T_1) => ((apart_point_and_line T_2 (line_connecting T_2 T_1)) => ((distinct_points T_2 T_2) /\ (distinct_points T_2 T_1)))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) (All U, (All V, (((distinct_points T_2 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (All Z, ((distinct_points T_2 T_1) => ((apart_point_and_line Z (line_connecting T_2 T_1)) => ((distinct_points Z T_2) /\ (distinct_points Z T_1))))) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) (distinct_points T_2 T_1) ### DisjTree 4 26 27 % 1.09/1.32 29. (distinct_points T_2 T_1) (distinct_points T_1 T_2) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (All Z, ((distinct_points T_2 T_1) => ((apart_point_and_line Z (line_connecting T_2 T_1)) => ((distinct_points Z T_2) /\ (distinct_points Z T_1))))) (All U, (All V, (((distinct_points T_2 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) ### All 28 % 1.09/1.32 30. (All Y, (All Z, ((distinct_points T_2 Y) => ((apart_point_and_line Z (line_connecting T_2 Y)) => ((distinct_points Z T_2) /\ (distinct_points Z Y)))))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) (All U, (All V, (((distinct_points T_2 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) (distinct_points T_2 T_1) ### All 29 % 1.09/1.32 31. (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)))))))) (distinct_points T_2 T_1) (distinct_points T_1 T_2) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) (All Y, (All Z, ((distinct_points T_2 Y) => ((apart_point_and_line Z (line_connecting T_2 Y)) => ((distinct_points Z T_2) /\ (distinct_points Z Y)))))) ### All 30 % 1.09/1.32 32. (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 Y, (All Z, ((distinct_points T_2 Y) => ((apart_point_and_line Z (line_connecting T_2 Y)) => ((distinct_points Z T_2) /\ (distinct_points Z Y)))))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) (distinct_points T_2 T_1) ### All 31 % 1.09/1.32 33. (All Y, (All Z, ((distinct_points T_1 Y) => ((apart_point_and_line Z (line_connecting T_1 Y)) => ((distinct_points Z T_1) /\ (distinct_points Z Y)))))) (distinct_points T_2 T_1) (distinct_points T_1 T_2) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) (All Y, (All Z, ((distinct_points T_2 Y) => ((apart_point_and_line Z (line_connecting T_2 Y)) => ((distinct_points Z T_2) /\ (distinct_points Z 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))))))))) ### All 32 % 1.09/1.32 34. ((distinct_points T_1 T_2) => ((distinct_points T_1 T_1) \/ (distinct_points T_2 T_1))) (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 Y, (All Z, ((distinct_points T_2 Y) => ((apart_point_and_line Z (line_connecting T_2 Y)) => ((distinct_points Z T_2) /\ (distinct_points Z Y)))))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) (All Y, (All Z, ((distinct_points T_1 Y) => ((apart_point_and_line Z (line_connecting T_1 Y)) => ((distinct_points Z T_1) /\ (distinct_points Z Y)))))) (distinct_points T_1 T_2) ### DisjTree 2 3 33 % 1.09/1.32 35. (All Z, ((distinct_points T_1 T_2) => ((distinct_points T_1 Z) \/ (distinct_points T_2 Z)))) (distinct_points T_1 T_2) (All Y, (All Z, ((distinct_points T_1 Y) => ((apart_point_and_line Z (line_connecting T_1 Y)) => ((distinct_points Z T_1) /\ (distinct_points Z Y)))))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) (All Y, (All Z, ((distinct_points T_2 Y) => ((apart_point_and_line Z (line_connecting T_2 Y)) => ((distinct_points Z T_2) /\ (distinct_points Z 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))))))))) ### All 34 % 1.09/1.32 36. (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z 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))))))))) (All Y, (All Z, ((distinct_points T_2 Y) => ((apart_point_and_line Z (line_connecting T_2 Y)) => ((distinct_points Z T_2) /\ (distinct_points Z Y)))))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) (distinct_points T_1 T_2) (All Z, ((distinct_points T_1 T_2) => ((distinct_points T_1 Z) \/ (distinct_points T_2 Z)))) ### All 35 % 1.09/1.32 37. (-. (apart_point_and_line T_0 (line_connecting T_2 T_1))) (apart_point_and_line T_0 (line_connecting T_2 T_1)) ### Axiom % 1.09/1.32 38. ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) (line_connecting T_2 T_1)) \/ (apart_point_and_line T_0 (line_connecting T_2 T_1)))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_1))) (All Z, ((distinct_points T_1 T_2) => ((distinct_points T_1 Z) \/ (distinct_points T_2 Z)))) (distinct_points T_1 T_2) (All Y, (All Z, ((distinct_points T_2 Y) => ((apart_point_and_line Z (line_connecting T_2 Y)) => ((distinct_points Z T_2) /\ (distinct_points Z 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))))))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) ### DisjTree 1 36 37 % 1.09/1.32 39. (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z 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))))))))) (All Y, (All Z, ((distinct_points T_2 Y) => ((apart_point_and_line Z (line_connecting T_2 Y)) => ((distinct_points Z T_2) /\ (distinct_points Z Y)))))) (distinct_points T_1 T_2) (All Z, ((distinct_points T_1 T_2) => ((distinct_points T_1 Z) \/ (distinct_points T_2 Z)))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_1))) ### All 38 % 1.09/1.32 40. (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 (line_connecting T_2 T_1))) (All Z, ((distinct_points T_1 T_2) => ((distinct_points T_1 Z) \/ (distinct_points T_2 Z)))) (distinct_points T_1 T_2) (All Y, (All Z, ((distinct_points T_2 Y) => ((apart_point_and_line Z (line_connecting T_2 Y)) => ((distinct_points Z T_2) /\ (distinct_points Z 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))))))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) ### All 39 % 1.09/1.33 41. (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 (line_connecting T_1 T_2)) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z 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))))))))) (All Y, (All Z, ((distinct_points T_2 Y) => ((apart_point_and_line Z (line_connecting T_2 Y)) => ((distinct_points Z T_2) /\ (distinct_points Z Y)))))) (distinct_points T_1 T_2) (All Z, ((distinct_points T_1 T_2) => ((distinct_points T_1 Z) \/ (distinct_points T_2 Z)))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_1))) ### All 40 % 1.09/1.33 42. (All Y, (All Z, ((distinct_points T_1 Y) => ((distinct_points T_1 Z) \/ (distinct_points Y Z))))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_1))) (distinct_points T_1 T_2) (All Y, (All Z, ((distinct_points T_2 Y) => ((apart_point_and_line Z (line_connecting T_2 Y)) => ((distinct_points Z T_2) /\ (distinct_points Z 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))))))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (apart_point_and_line T_0 (line_connecting 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)))))) ### All 41 % 1.09/1.33 43. (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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 (line_connecting T_1 T_2)) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z 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))))))))) (All Y, (All Z, ((distinct_points T_2 Y) => ((apart_point_and_line Z (line_connecting T_2 Y)) => ((distinct_points Z T_2) /\ (distinct_points Z Y)))))) (distinct_points T_1 T_2) (-. (apart_point_and_line T_0 (line_connecting T_2 T_1))) ### All 42 % 1.09/1.33 44. (-. (apart_point_and_line T_0 (line_connecting T_2 T_1))) (distinct_points T_1 T_2) (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, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (apart_point_and_line T_0 (line_connecting 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)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### All 43 % 1.09/1.33 45. (-. ((distinct_points T_1 T_2) => ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => (apart_point_and_line T_0 (line_connecting T_2 T_1))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z 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 44 % 1.09/1.33 46. (-. (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => (apart_point_and_line Z (line_connecting T_2 T_1)))))) (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, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (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, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotAllEx 45 % 1.09/1.33 47. (-. (All Y, (All Z, ((distinct_points T_1 Y) => ((apart_point_and_line Z (line_connecting T_1 Y)) => (apart_point_and_line Z (line_connecting Y T_1))))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (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, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z 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 46 % 1.09/1.33 48. (-. (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => (apart_point_and_line Z (line_connecting Y 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, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (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, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotAllEx 47 % 1.09/1.33 % SZS output end Proof % 1.09/1.33 (* END-PROOF *) %------------------------------------------------------------------------------