TSTP Solution File: GEO188+2 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : GEO188+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 06:30:49 EDT 2022
% Result : Theorem 1.42s 1.65s
% Output : Proof 1.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO188+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n012.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 14:03:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.42/1.65 % SZS status Theorem
% 1.42/1.65 (* PROOF-FOUND *)
% 1.42/1.65 (* BEGIN-PROOF *)
% 1.42/1.65 % SZS output start Proof
% 1.42/1.65 1. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom
% 1.42/1.65 2. (distinct_points T_0 T_0) ### Extension/test/apart1
% 1.42/1.65 3. (distinct_points T_1 T_0) (-. (distinct_points T_1 T_0)) ### Axiom
% 1.42/1.65 4. (distinct_points T_2 T_0) (-. (distinct_points T_2 T_0)) ### Axiom
% 1.42/1.65 5. (distinct_points T_1 T_0) (-. (distinct_points T_1 T_0)) ### Axiom
% 1.42/1.65 6. (distinct_points T_2 T_0) (-. (distinct_points T_2 T_0)) ### Axiom
% 1.42/1.65 7. (apart_point_and_line T_2 (line_connecting T_1 T_0)) (-. (apart_point_and_line T_2 (line_connecting T_1 T_0))) ### Axiom
% 1.42/1.65 8. (distinct_points T_1 T_0) (-. (distinct_points T_1 T_0)) ### Axiom
% 1.42/1.65 9. (distinct_lines (line_connecting T_1 T_0) (line_connecting T_2 T_0)) (-. (distinct_lines (line_connecting T_1 T_0) (line_connecting T_2 T_0))) ### Axiom
% 1.42/1.65 10. (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (apart_point_and_line T_1 (line_connecting T_1 T_0)) ### Axiom
% 1.42/1.65 11. (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (apart_point_and_line T_1 (line_connecting T_2 T_0)) ### Axiom
% 1.42/1.65 12. (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (apart_point_and_line T_0 (line_connecting T_1 T_0)) ### Axiom
% 1.42/1.65 13. (-. (apart_point_and_line T_0 (line_connecting T_2 T_0))) (apart_point_and_line T_0 (line_connecting T_2 T_0)) ### Axiom
% 1.42/1.65 14. (((distinct_points T_1 T_0) /\ (distinct_lines (line_connecting T_1 T_0) (line_connecting T_2 T_0))) => ((apart_point_and_line T_1 (line_connecting T_1 T_0)) \/ ((apart_point_and_line T_1 (line_connecting T_2 T_0)) \/ ((apart_point_and_line T_0 (line_connecting T_1 T_0)) \/ (apart_point_and_line T_0 (line_connecting T_2 T_0)))))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (distinct_lines (line_connecting T_1 T_0) (line_connecting T_2 T_0)) (distinct_points T_1 T_0) ### DisjTree 8 9 10 11 12 13
% 1.42/1.65 15. (All V, (((distinct_points T_1 T_0) /\ (distinct_lines (line_connecting T_1 T_0) V)) => ((apart_point_and_line T_1 (line_connecting T_1 T_0)) \/ ((apart_point_and_line T_1 V) \/ ((apart_point_and_line T_0 (line_connecting T_1 T_0)) \/ (apart_point_and_line T_0 V)))))) (distinct_points T_1 T_0) (distinct_lines (line_connecting T_1 T_0) (line_connecting T_2 T_0)) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_0))) ### All 14
% 1.42/1.65 16. (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_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (distinct_lines (line_connecting T_1 T_0) (line_connecting T_2 T_0)) (distinct_points T_1 T_0) ### All 15
% 1.42/1.65 17. (-. (apart_point_and_line T_2 (line_connecting T_2 T_0))) (apart_point_and_line T_2 (line_connecting T_2 T_0)) ### Axiom
% 1.42/1.65 18. ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) (line_connecting T_2 T_0)) \/ (apart_point_and_line T_2 (line_connecting T_2 T_0)))) (-. (apart_point_and_line T_2 (line_connecting T_2 T_0))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_0))) (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_1 T_0)) ### DisjTree 7 16 17
% 1.42/1.65 19. (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_2 (line_connecting T_2 T_0))) ### All 18
% 1.42/1.65 20. (distinct_points T_2 T_2) ### Extension/test/apart1
% 1.42/1.65 21. ((distinct_points T_2 T_2) /\ (distinct_points T_2 T_0)) ### And 20
% 1.42/1.65 22. ((distinct_points T_2 T_0) => ((apart_point_and_line T_2 (line_connecting T_2 T_0)) => ((distinct_points T_2 T_2) /\ (distinct_points T_2 T_0)))) (distinct_points T_1 T_0) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_0))) (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_1 T_0)) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (distinct_points T_2 T_0) ### DisjTree 6 19 21
% 1.42/1.65 23. (All Z, ((distinct_points T_2 T_0) => ((apart_point_and_line Z (line_connecting T_2 T_0)) => ((distinct_points Z T_2) /\ (distinct_points Z T_0))))) (distinct_points T_2 T_0) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (distinct_points T_1 T_0) ### All 22
% 1.42/1.65 24. ((distinct_points T_0 T_1) /\ (distinct_points T_0 T_0)) ### And 2
% 1.42/1.65 25. ((distinct_points T_1 T_0) => ((apart_point_and_line T_0 (line_connecting T_1 T_0)) => ((distinct_points T_0 T_1) /\ (distinct_points T_0 T_0)))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_0 (line_connecting T_2 T_0))) (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_1 T_0)) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (distinct_points T_2 T_0) (All Z, ((distinct_points T_2 T_0) => ((apart_point_and_line Z (line_connecting T_2 T_0)) => ((distinct_points Z T_2) /\ (distinct_points Z T_0))))) (distinct_points T_1 T_0) ### DisjTree 5 23 24
% 1.42/1.65 26. (All Z, ((distinct_points T_1 T_0) => ((apart_point_and_line Z (line_connecting T_1 T_0)) => ((distinct_points Z T_1) /\ (distinct_points Z T_0))))) (distinct_points T_1 T_0) (All Z, ((distinct_points T_2 T_0) => ((apart_point_and_line Z (line_connecting T_2 T_0)) => ((distinct_points Z T_2) /\ (distinct_points Z T_0))))) (distinct_points T_2 T_0) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) ### All 25
% 1.52/1.72 27. ((distinct_points T_0 T_2) /\ (distinct_points T_0 T_0)) ### And 2
% 1.52/1.72 28. ((distinct_points T_2 T_0) => ((apart_point_and_line T_0 (line_connecting T_2 T_0)) => ((distinct_points T_0 T_2) /\ (distinct_points T_0 T_0)))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (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_1 T_0)) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (All Z, ((distinct_points T_2 T_0) => ((apart_point_and_line Z (line_connecting T_2 T_0)) => ((distinct_points Z T_2) /\ (distinct_points Z T_0))))) (distinct_points T_1 T_0) (All Z, ((distinct_points T_1 T_0) => ((apart_point_and_line Z (line_connecting T_1 T_0)) => ((distinct_points Z T_1) /\ (distinct_points Z T_0))))) (distinct_points T_2 T_0) ### DisjTree 4 26 27
% 1.52/1.72 29. (distinct_points T_2 T_0) (All Z, ((distinct_points T_1 T_0) => ((apart_point_and_line Z (line_connecting T_1 T_0)) => ((distinct_points Z T_1) /\ (distinct_points Z T_0))))) (distinct_points T_1 T_0) (All Z, ((distinct_points T_2 T_0) => ((apart_point_and_line Z (line_connecting T_2 T_0)) => ((distinct_points Z T_2) /\ (distinct_points Z T_0))))) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) ### All 28
% 1.52/1.72 30. (distinct_points T_1 T_1) ### Extension/test/apart1
% 1.52/1.72 31. ((distinct_points T_1 T_1) /\ (distinct_points T_1 T_0)) ### And 30
% 1.52/1.72 32. ((distinct_points T_1 T_0) => ((apart_point_and_line T_1 (line_connecting T_1 T_0)) => ((distinct_points T_1 T_1) /\ (distinct_points T_1 T_0)))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (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_1 T_0)) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (All Z, ((distinct_points T_2 T_0) => ((apart_point_and_line Z (line_connecting T_2 T_0)) => ((distinct_points Z T_2) /\ (distinct_points Z T_0))))) (All Z, ((distinct_points T_1 T_0) => ((apart_point_and_line Z (line_connecting T_1 T_0)) => ((distinct_points Z T_1) /\ (distinct_points Z T_0))))) (distinct_points T_2 T_0) (distinct_points T_1 T_0) ### DisjTree 3 29 31
% 1.52/1.72 33. (distinct_points T_1 T_0) (distinct_points T_2 T_0) (All Z, ((distinct_points T_1 T_0) => ((apart_point_and_line Z (line_connecting T_1 T_0)) => ((distinct_points Z T_1) /\ (distinct_points Z T_0))))) (All Z, ((distinct_points T_2 T_0) => ((apart_point_and_line Z (line_connecting T_2 T_0)) => ((distinct_points Z T_2) /\ (distinct_points Z T_0))))) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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_1 (line_connecting T_2 T_0))) ### All 32
% 1.52/1.72 34. (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)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (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_1 T_0)) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (All Z, ((distinct_points T_2 T_0) => ((apart_point_and_line Z (line_connecting T_2 T_0)) => ((distinct_points Z T_2) /\ (distinct_points Z T_0))))) (distinct_points T_2 T_0) (distinct_points T_1 T_0) ### All 33
% 1.52/1.72 35. (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_0) (distinct_points T_2 T_0) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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_1 (line_connecting T_2 T_0))) (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)))))) ### All 34
% 1.52/1.72 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 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)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (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_1 T_0)) (All Z, ((apart_point_and_line T_2 (line_connecting T_1 T_0)) => ((distinct_lines (line_connecting T_1 T_0) Z) \/ (apart_point_and_line T_2 Z)))) (distinct_points T_2 T_0) (distinct_points T_1 T_0) ### All 35
% 1.52/1.72 37. (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) (distinct_points T_2 T_0) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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_1 (line_connecting T_2 T_0))) (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)))))) (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 36
% 1.52/1.72 38. (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, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (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)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (distinct_points T_2 T_0) (distinct_points T_1 T_0) (All Y, (All Z, ((apart_point_and_line T_2 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_2 Z))))) ### All 37
% 1.52/1.73 39. (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, ((apart_point_and_line T_2 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_2 Z))))) (distinct_points T_1 T_0) (distinct_points T_2 T_0) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (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)))))) (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 38
% 1.52/1.73 40. ((distinct_points T_0 T_1) => ((distinct_points T_0 T_0) \/ (distinct_points T_1 T_0))) (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 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)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (distinct_points T_2 T_0) (All Y, (All Z, ((apart_point_and_line T_2 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_2 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))))))))) (distinct_points T_0 T_1) ### DisjTree 1 2 39
% 1.52/1.73 41. (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 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, ((apart_point_and_line T_2 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_2 Z))))) (distinct_points T_2 T_0) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (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)))))) (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 40
% 1.52/1.73 42. (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 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)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (distinct_points T_2 T_0) (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_1) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) ### All 41
% 1.52/1.73 43. (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 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_2 T_0) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (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)))))) (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 42
% 1.52/1.73 44. (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 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)))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (distinct_points T_2 T_0) (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_1) ### All 43
% 1.52/1.73 45. (distinct_points T_0 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))))))))) (distinct_points T_2 T_0) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (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)))))) ### All 44
% 1.52/1.73 46. (-. (((distinct_points T_2 T_0) /\ ((distinct_points T_2 T_1) /\ ((distinct_points T_0 T_1) /\ (-. (apart_point_and_line T_1 (line_connecting T_2 T_0)))))) => (-. (apart_point_and_line T_2 (line_connecting T_1 T_0))))) (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 45
% 1.52/1.73 47. (-. (All Z, (((distinct_points T_2 T_0) /\ ((distinct_points T_2 Z) /\ ((distinct_points T_0 Z) /\ (-. (apart_point_and_line Z (line_connecting T_2 T_0)))))) => (-. (apart_point_and_line T_2 (line_connecting Z T_0)))))) (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 46
% 1.52/1.73 48. (-. (All Y, (All Z, (((distinct_points T_2 Y) /\ ((distinct_points T_2 Z) /\ ((distinct_points Y Z) /\ (-. (apart_point_and_line Z (line_connecting T_2 Y)))))) => (-. (apart_point_and_line T_2 (line_connecting Z Y))))))) (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 47
% 1.52/1.73 49. (-. (All X, (All Y, (All Z, (((distinct_points X Y) /\ ((distinct_points X Z) /\ ((distinct_points Y Z) /\ (-. (apart_point_and_line Z (line_connecting X Y)))))) => (-. (apart_point_and_line X (line_connecting 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))))))) (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 48
% 1.52/1.73 % SZS output end Proof
% 1.52/1.73 (* END-PROOF *)
%------------------------------------------------------------------------------