TSTP Solution File: GEO204+3 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : GEO204+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 : n014.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 06:31:03 EDT 2022
% Result : Theorem 15.19s 15.40s
% Output : Proof 15.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO204+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n014.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 14:16:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 15.19/15.40 % SZS status Theorem
% 15.19/15.40 (* PROOF-FOUND *)
% 15.19/15.40 (* BEGIN-PROOF *)
% 15.19/15.40 % SZS output start Proof
% 15.19/15.40 1. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom
% 15.19/15.40 2. (-. (distinct_points T_0 T_2)) (distinct_points T_0 T_2) ### Axiom
% 15.19/15.40 3. (-. (distinct_points T_1 T_2)) (distinct_points T_1 T_2) ### Axiom
% 15.19/15.40 4. ((distinct_points T_0 T_1) => ((distinct_points T_0 T_2) \/ (distinct_points T_1 T_2))) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_0 T_2)) (distinct_points T_0 T_1) ### DisjTree 1 2 3
% 15.19/15.40 5. (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) (distinct_points T_0 T_1) (-. (distinct_points T_0 T_2)) (-. (distinct_points T_1 T_2)) ### All 4
% 15.19/15.40 6. (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) (-. (distinct_points T_1 T_2)) (-. (distinct_points T_0 T_2)) (distinct_points T_0 T_1) ### All 5
% 15.19/15.40 7. (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (distinct_points T_0 T_1) (-. (distinct_points T_0 T_2)) (-. (distinct_points T_1 T_2)) ### All 6
% 15.19/15.40 8. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom
% 15.19/15.40 9. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom
% 15.19/15.40 10. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (-. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2))) ### Axiom
% 15.19/15.40 11. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom
% 15.19/15.40 12. (apart_point_and_line T_0 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) ### Axiom
% 15.19/15.40 13. ((distinct_points T_0 T_1) => (-. (apart_point_and_line T_0 (line_connecting T_0 T_1)))) (apart_point_and_line T_0 (line_connecting T_0 T_1)) (distinct_points T_0 T_1) ### Imply 11 12
% 15.19/15.40 14. (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points T_0 T_1) (apart_point_and_line T_0 (line_connecting T_0 T_1)) ### All 13
% 15.19/15.40 15. (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (apart_point_and_line T_0 (line_connecting T_0 T_1)) (distinct_points T_0 T_1) ### All 14
% 15.19/15.40 16. (distinct_points T_0 T_2) (-. (distinct_points T_0 T_2)) ### Axiom
% 15.19/15.40 17. (apart_point_and_line T_0 (line_connecting T_0 T_2)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_2))) ### Axiom
% 15.19/15.40 18. ((distinct_points T_0 T_2) => (-. (apart_point_and_line T_0 (line_connecting T_0 T_2)))) (apart_point_and_line T_0 (line_connecting T_0 T_2)) (distinct_points T_0 T_2) ### Imply 16 17
% 15.19/15.40 19. (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (apart_point_and_line T_0 (line_connecting T_0 T_2)) ### All 18
% 15.19/15.40 20. (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (apart_point_and_line T_0 (line_connecting T_0 T_2)) (distinct_points T_0 T_2) ### All 19
% 15.19/15.40 21. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom
% 15.19/15.40 22. (apart_point_and_line T_1 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) ### Axiom
% 15.19/15.40 23. ((distinct_points T_0 T_1) => (-. (apart_point_and_line T_1 (line_connecting T_0 T_1)))) (apart_point_and_line T_1 (line_connecting T_0 T_1)) (distinct_points T_0 T_1) ### Imply 21 22
% 15.19/15.40 24. (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (distinct_points T_0 T_1) (apart_point_and_line T_1 (line_connecting T_0 T_1)) ### All 23
% 15.19/15.40 25. (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (apart_point_and_line T_1 (line_connecting T_0 T_1)) (distinct_points T_0 T_1) ### All 24
% 15.19/15.40 26. (distinct_points T_0 T_2) (-. (distinct_points T_0 T_2)) ### Axiom
% 15.19/15.40 27. (apart_point_and_line T_1 (line_connecting T_0 T_2)) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) ### Axiom
% 15.19/15.40 28. (-. (distinct_points T_1 T_2)) (distinct_points T_1 T_2) ### Axiom
% 15.19/15.40 29. (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) (apart_point_and_line T_2 (line_connecting T_0 T_2)) ### Axiom
% 15.19/15.40 30. ((apart_point_and_line T_1 (line_connecting T_0 T_2)) => ((distinct_points T_1 T_2) \/ (apart_point_and_line T_2 (line_connecting T_0 T_2)))) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) (-. (distinct_points T_1 T_2)) (apart_point_and_line T_1 (line_connecting T_0 T_2)) ### DisjTree 27 28 29
% 15.19/15.40 31. (All Z, ((apart_point_and_line T_1 (line_connecting T_0 T_2)) => ((distinct_points T_1 Z) \/ (apart_point_and_line Z (line_connecting T_0 T_2))))) (apart_point_and_line T_1 (line_connecting T_0 T_2)) (-. (distinct_points T_1 T_2)) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) ### All 30
% 15.19/15.40 32. (All Y, (All Z, ((apart_point_and_line T_1 Y) => ((distinct_points T_1 Z) \/ (apart_point_and_line Z Y))))) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) (-. (distinct_points T_1 T_2)) (apart_point_and_line T_1 (line_connecting T_0 T_2)) ### All 31
% 15.19/15.40 33. (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_1 (line_connecting T_0 T_2)) (-. (distinct_points T_1 T_2)) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) ### All 32
% 15.19/15.40 34. ((distinct_points T_0 T_2) => (-. (apart_point_and_line T_2 (line_connecting T_0 T_2)))) (-. (distinct_points T_1 T_2)) (apart_point_and_line T_1 (line_connecting T_0 T_2)) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (distinct_points T_0 T_2) ### Imply 26 33
% 15.19/15.40 35. (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (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_1 (line_connecting T_0 T_2)) (-. (distinct_points T_1 T_2)) ### All 34
% 15.19/15.40 36. (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (distinct_points T_1 T_2)) (apart_point_and_line T_1 (line_connecting T_0 T_2)) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (distinct_points T_0 T_2) ### All 35
% 15.19/15.40 37. (((distinct_points T_0 T_1) /\ (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2))) => ((apart_point_and_line T_0 (line_connecting T_0 T_1)) \/ ((apart_point_and_line T_0 (line_connecting T_0 T_2)) \/ ((apart_point_and_line T_1 (line_connecting T_0 T_1)) \/ (apart_point_and_line T_1 (line_connecting T_0 T_2)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (-. (distinct_points T_1 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_0 T_2) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (distinct_points T_0 T_1) ### DisjTree 9 10 15 20 25 36
% 15.19/15.40 38. (All V, (((distinct_points T_0 T_1) /\ (distinct_lines (line_connecting T_0 T_1) V)) => ((apart_point_and_line T_0 (line_connecting T_0 T_1)) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 (line_connecting T_0 T_1)) \/ (apart_point_and_line T_1 V)))))) (distinct_points T_0 T_1) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_points T_0 T_2) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (distinct_points 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)))))) ### All 37
% 15.19/15.40 39. (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (-. (distinct_points T_1 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (distinct_points T_0 T_2) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (distinct_points T_0 T_1) ### All 38
% 15.19/15.43 40. (-. (distinct_points T_1 T_2)) (distinct_points T_1 T_2) ### Axiom
% 15.19/15.43 41. ((distinct_points T_0 T_1) => ((distinct_points T_0 T_2) \/ (distinct_points T_1 T_2))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (distinct_points 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)))))) (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (distinct_points T_0 T_1) ### DisjTree 8 39 40
% 15.19/15.43 42. (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) (distinct_points T_0 T_1) (All U, (All V, (((distinct_points T_0 T_1) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 U) \/ (apart_point_and_line T_1 V))))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (-. (distinct_points T_1 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) ### All 41
% 15.19/15.43 43. (All Y, (All U, (All V, (((distinct_points T_0 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (distinct_points 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)))))) (distinct_points T_0 T_1) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) ### All 42
% 15.19/15.43 44. (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) (distinct_points T_0 T_1) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (-. (distinct_points T_1 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (All Y, (All U, (All V, (((distinct_points T_0 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_0 U) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) ### All 43
% 15.19/15.43 45. (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))))))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (distinct_points 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)))))) (distinct_points T_0 T_1) (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) ### All 44
% 15.19/15.43 46. (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (distinct_points T_0 T_1) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (-. (distinct_points T_1 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 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 45
% 15.19/15.43 47. (-. (-. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 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, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (distinct_points 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)))))) (distinct_points T_0 T_1) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotNot 46
% 15.19/15.43 48. (-. (equal_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (distinct_points T_0 T_1) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (-. (distinct_points T_1 T_2)) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X 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))))))))) ### Definition-Pseudo(equal_lines) 47
% 15.19/15.43 49. (-. ((distinct_points T_0 T_2) /\ (equal_lines (line_connecting T_0 T_1) (line_connecting T_0 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, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (-. (distinct_points T_1 T_2)) (distinct_points T_0 T_1) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotAnd 7 48
% 15.19/15.43 50. (equal_points T_1 T_2) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (distinct_points T_0 T_1) (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, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X 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))))))))) (-. ((distinct_points T_0 T_2) /\ (equal_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)))) ### Definition-Pseudo(equal_points) 49
% 15.19/15.43 51. (-. (((distinct_points T_0 T_1) /\ (equal_points T_1 T_2)) => ((distinct_points T_0 T_2) /\ (equal_lines (line_connecting T_0 T_1) (line_connecting T_0 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, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (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, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### ConjTree 50
% 15.19/15.43 52. (-. (All Z, (((distinct_points T_0 T_1) /\ (equal_points T_1 Z)) => ((distinct_points T_0 Z) /\ (equal_lines (line_connecting T_0 T_1) (line_connecting T_0 Z)))))) (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_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X 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 51
% 15.19/15.43 53. (-. (All Y, (All Z, (((distinct_points T_0 Y) /\ (equal_points Y Z)) => ((distinct_points T_0 Z) /\ (equal_lines (line_connecting T_0 Y) (line_connecting T_0 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, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (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, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotAllEx 52
% 15.19/15.43 54. (-. (All X, (All Y, (All Z, (((distinct_points X Y) /\ (equal_points Y Z)) => ((distinct_points X Z) /\ (equal_lines (line_connecting X Y) (line_connecting X Z)))))))) (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_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X 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 53
% 15.19/15.43 % SZS output end Proof
% 15.19/15.43 (* END-PROOF *)
%------------------------------------------------------------------------------