TSTP Solution File: GEO189+3 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : GEO189+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 : n006.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 06:30:51 EDT 2022
% Result : Theorem 4.45s 4.61s
% Output : Proof 4.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO189+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n006.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 03:45:40 EDT 2022
% 0.21/0.34 % CPUTime :
% 4.45/4.61 % SZS status Theorem
% 4.45/4.61 (* PROOF-FOUND *)
% 4.45/4.61 (* BEGIN-PROOF *)
% 4.45/4.61 % SZS output start Proof
% 4.45/4.61 1. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom
% 4.45/4.61 2. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom
% 4.45/4.61 3. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom
% 4.45/4.61 4. (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_0) ### Axiom
% 4.45/4.61 5. (-. (distinct_points T_1 T_0)) (distinct_points T_1 T_0) ### Axiom
% 4.45/4.61 6. ((distinct_points T_0 T_1) => ((distinct_points T_0 T_0) \/ (distinct_points T_1 T_0))) (-. (distinct_points T_1 T_0)) (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_1) ### DisjTree 3 4 5
% 4.45/4.61 7. (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_0)) (-. (distinct_points T_1 T_0)) ### All 6
% 4.45/4.61 8. (distinct_points T_0 T_2) (-. (distinct_points T_0 T_2)) ### Axiom
% 4.45/4.61 9. (distinct_points T_0 T_2) (-. (distinct_points T_0 T_2)) ### Axiom
% 4.45/4.61 10. (apart_point_and_line T_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_2 (line_connecting T_0 T_1))) ### Axiom
% 4.45/4.61 11. (distinct_points T_1 T_0) (-. (distinct_points T_1 T_0)) ### Axiom
% 4.45/4.61 12. (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
% 4.45/4.61 13. (-. (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
% 4.45/4.61 14. (-. (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
% 4.45/4.61 15. (-. (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
% 4.45/4.61 16. (-. (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
% 4.45/4.61 17. (((distinct_points T_1 T_0) /\ (distinct_lines (line_connecting T_0 T_1) (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)) \/ ((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_0 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (distinct_points T_1 T_0) ### DisjTree 11 12 13 14 15 16
% 4.45/4.61 18. (All V, (((distinct_points T_1 T_0) /\ (distinct_lines (line_connecting T_0 T_1) V)) => ((apart_point_and_line T_1 (line_connecting T_0 T_1)) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 (line_connecting T_0 T_1)) \/ (apart_point_and_line T_0 V)))))) (distinct_points T_1 T_0) (distinct_lines (line_connecting T_0 T_1) (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))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_2))) ### All 17
% 4.45/4.61 19. (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 T_2)) (distinct_points T_1 T_0) ### All 18
% 4.45/4.61 20. (-. (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
% 4.45/4.61 21. ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) (line_connecting T_0 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_0) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line 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))) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) ### DisjTree 10 19 20
% 4.45/4.61 22. (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) ### All 21
% 4.45/4.61 23. ((distinct_points T_0 T_2) => (-. (apart_point_and_line T_0 (line_connecting T_0 T_2)))) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (distinct_points T_0 T_2) ### Imply 9 22
% 4.45/4.61 24. (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_2 (line_connecting T_0 T_2))) ### All 23
% 4.45/4.61 25. ((distinct_points T_0 T_2) => (-. (apart_point_and_line T_2 (line_connecting T_0 T_2)))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points T_0 T_2) ### Imply 8 24
% 4.45/4.61 26. (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (All Z, ((apart_point_and_line T_2 (line_connecting T_0 T_1)) => ((distinct_lines (line_connecting T_0 T_1) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_points T_1 T_0) ### All 25
% 4.64/4.84 27. (All Y, (All Z, ((apart_point_and_line T_2 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_2 Z))))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) ### All 26
% 4.64/4.84 28. (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (distinct_points T_1 T_0) ### All 27
% 4.64/4.84 29. (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_0) ### Axiom
% 4.64/4.84 30. ((distinct_points T_1 T_0) => ((distinct_points T_1 T_0) \/ (distinct_points T_0 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (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 T_0)) (distinct_points T_0 T_1) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) ### DisjTree 7 28 29
% 4.64/4.84 31. (All Z, ((distinct_points T_1 T_0) => ((distinct_points T_1 Z) \/ (distinct_points T_0 Z)))) (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_0)) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) ### All 30
% 4.64/4.84 32. (All Y, (All Z, ((distinct_points T_1 Y) => ((distinct_points T_1 Z) \/ (distinct_points Y Z))))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (All U, (All V, (((distinct_points T_1 T_0) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (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 T_0)) (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 31
% 4.64/4.84 33. (All Y, (All U, (All V, (((distinct_points T_1 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) (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_0)) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (All Y, (All Z, ((distinct_points T_1 Y) => ((distinct_points T_1 Z) \/ (distinct_points Y Z))))) ### All 32
% 4.64/4.84 34. (All X, (-. (distinct_points X X))) (All Y, (All Z, ((distinct_points T_1 Y) => ((distinct_points T_1 Z) \/ (distinct_points Y Z))))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_1))) (-. (apart_point_and_line 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_2 (line_connecting T_0 T_1)) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (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 T_1) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) (All Y, (All U, (All V, (((distinct_points T_1 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) ### All 33
% 4.64/4.84 35. ((distinct_points T_0 T_1) => (-. (apart_point_and_line T_1 (line_connecting T_0 T_1)))) (All Y, (All U, (All V, (((distinct_points T_1 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (All Y, (All Z, ((distinct_points T_1 Y) => ((distinct_points T_1 Z) \/ (distinct_points Y Z))))) (All X, (-. (distinct_points X X))) (distinct_points T_0 T_1) ### Imply 2 34
% 4.64/4.85 36. (distinct_points T_0 T_1) (All X, (-. (distinct_points X X))) (All Y, (All Z, ((distinct_points T_1 Y) => ((distinct_points T_1 Z) \/ (distinct_points Y Z))))) (-. (apart_point_and_line 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_2 (line_connecting T_0 T_1)) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) (All Y, (All U, (All V, (((distinct_points T_1 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) ### All 35
% 4.64/4.85 37. ((distinct_points T_0 T_1) => (-. (apart_point_and_line T_0 (line_connecting T_0 T_1)))) (All Y, (All U, (All V, (((distinct_points T_1 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (All Y, (All Z, ((distinct_points T_1 Y) => ((distinct_points T_1 Z) \/ (distinct_points Y Z))))) (All X, (-. (distinct_points X X))) (distinct_points T_0 T_1) ### Imply 1 36
% 4.64/4.85 38. (distinct_points T_0 T_1) (All X, (-. (distinct_points X X))) (All Y, (All Z, ((distinct_points T_1 Y) => ((distinct_points T_1 Z) \/ (distinct_points Y Z))))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points T_0 T_2) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line Y (line_connecting T_0 Y))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) (All Y, (All U, (All V, (((distinct_points T_1 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) ### All 37
% 4.64/4.85 39. (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (All Y, (All U, (All V, (((distinct_points T_1 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) (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 T_2) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (All Y, (All Z, ((distinct_points T_1 Y) => ((distinct_points T_1 Z) \/ (distinct_points Y Z))))) (All X, (-. (distinct_points X X))) (distinct_points T_0 T_1) ### All 38
% 4.64/4.85 40. (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, (-. (distinct_points X X))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points 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 Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) (All Y, (All U, (All V, (((distinct_points T_1 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_1 U) \/ ((apart_point_and_line T_1 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 Y (line_connecting X Y)))))) ### All 39
% 4.64/4.85 41. (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 Y (line_connecting X Y)))))) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) (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 T_2) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (All X, (-. (distinct_points X X))) (distinct_points T_0 T_1) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### All 40
% 4.64/4.85 42. (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) (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, (-. (distinct_points X X))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (All Y, ((distinct_points T_0 Y) => (-. (apart_point_and_line T_0 (line_connecting T_0 Y))))) (distinct_points 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, ((distinct_points X Y) => (-. (apart_point_and_line Y (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))))))))) ### All 41
% 4.64/4.85 43. (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))))))))) (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_lines Y Z) \/ (apart_point_and_line X Z)))))) (distinct_points T_0 T_2) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (All X, (-. (distinct_points X X))) (distinct_points T_0 T_1) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) ### All 42
% 4.64/4.85 44. (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, (-. (distinct_points X X))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (apart_point_and_line T_2 (line_connecting T_0 T_1)) (distinct_points 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, ((distinct_points X Y) => (-. (apart_point_and_line Y (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))))))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) ### All 43
% 4.64/4.85 45. (-. (-. (apart_point_and_line T_2 (line_connecting T_0 T_1)))) (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))))))))) (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_lines Y Z) \/ (apart_point_and_line X Z)))))) (distinct_points T_0 T_2) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (All X, (-. (distinct_points X X))) (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 44
% 4.64/4.85 46. (-. (incident_point_and_line T_2 (line_connecting T_0 T_1))) (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, (-. (distinct_points X X))) (-. (apart_point_and_line T_1 (line_connecting T_0 T_2))) (distinct_points 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, ((distinct_points X Y) => (-. (apart_point_and_line Y (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))))))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) ### Definition-Pseudo(incident_point_and_line) 45
% 4.64/4.85 47. (incident_point_and_line 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, (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 Y (line_connecting X Y)))))) (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 T_2) (All X, (-. (distinct_points X X))) (distinct_points T_0 T_1) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (-. (incident_point_and_line T_2 (line_connecting T_0 T_1))) ### Definition-Pseudo(incident_point_and_line) 46
% 4.64/4.85 48. (-. (((distinct_points T_0 T_2) /\ ((distinct_points T_0 T_1) /\ ((distinct_points T_2 T_1) /\ (incident_point_and_line T_1 (line_connecting T_0 T_2))))) => (incident_point_and_line T_2 (line_connecting T_0 T_1)))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (All X, (-. (distinct_points X X))) (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, ((distinct_points X Y) => (-. (apart_point_and_line Y (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))))))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) ### ConjTree 47
% 4.64/4.85 49. (-. (All Z, (((distinct_points T_0 T_2) /\ ((distinct_points T_0 Z) /\ ((distinct_points T_2 Z) /\ (incident_point_and_line Z (line_connecting T_0 T_2))))) => (incident_point_and_line T_2 (line_connecting T_0 Z))))) (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))))))))) (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_lines Y Z) \/ (apart_point_and_line X Z)))))) (All X, (-. (distinct_points X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotAllEx 48
% 4.64/4.85 50. (-. (All Y, (All Z, (((distinct_points T_0 Y) /\ ((distinct_points T_0 Z) /\ ((distinct_points Y Z) /\ (incident_point_and_line Z (line_connecting T_0 Y))))) => (incident_point_and_line Y (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, (-. (distinct_points X X))) (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, ((distinct_points X Y) => (-. (apart_point_and_line Y (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))))))))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) ### NotAllEx 49
% 4.64/4.85 51. (-. (All X, (All Y, (All Z, (((distinct_points X Y) /\ ((distinct_points X Z) /\ ((distinct_points Y Z) /\ (incident_point_and_line Z (line_connecting X Y))))) => (incident_point_and_line Y (line_connecting X Z))))))) (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))))))))) (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_lines Y Z) \/ (apart_point_and_line X Z)))))) (All X, (-. (distinct_points X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotAllEx 50
% 4.64/4.85 % SZS output end Proof
% 4.64/4.85 (* END-PROOF *)
%------------------------------------------------------------------------------