TSTP Solution File: GEO188+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : GEO188+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n015.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 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO188+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sat Jun 18 11:02:28 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 (* PROOF-FOUND *)
% 0.21/0.44 (* BEGIN-PROOF *)
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 1. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom
% 0.21/0.44 2. (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_0) ### Axiom
% 0.21/0.44 3. (distinct_points T_1 T_0) (-. (distinct_points T_1 T_0)) ### Axiom
% 0.21/0.44 4. (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
% 0.21/0.44 5. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom
% 0.21/0.44 6. (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
% 0.21/0.44 7. (-. (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
% 0.21/0.44 8. (-. (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
% 0.21/0.44 9. (-. (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
% 0.21/0.44 10. (-. (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
% 0.21/0.44 11. (((distinct_points T_0 T_1) /\ (distinct_lines (line_connecting T_1 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_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_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (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_1 T_0))) (distinct_lines (line_connecting T_1 T_0) (line_connecting T_2 T_0)) (distinct_points T_0 T_1) ### DisjTree 5 6 7 8 9 10
% 0.21/0.44 12. (All V, (((distinct_points T_0 T_1) /\ (distinct_lines (line_connecting T_1 T_0) V)) => ((apart_point_and_line T_0 (line_connecting T_1 T_0)) \/ ((apart_point_and_line T_0 V) \/ ((apart_point_and_line T_1 (line_connecting T_1 T_0)) \/ (apart_point_and_line T_1 V)))))) (distinct_points T_0 T_1) (distinct_lines (line_connecting T_1 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_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))) ### All 11
% 0.21/0.44 13. (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))))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (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_1 T_0))) (distinct_lines (line_connecting T_1 T_0) (line_connecting T_2 T_0)) (distinct_points T_0 T_1) ### All 12
% 0.21/0.44 14. (distinct_points T_2 T_0) (-. (distinct_points T_2 T_0)) ### Axiom
% 0.21/0.44 15. (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
% 0.21/0.44 16. ((distinct_points 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_2 T_0) ### Imply 14 15
% 0.21/0.44 17. (All Y, ((distinct_points T_2 Y) => (-. (apart_point_and_line T_2 (line_connecting T_2 Y))))) (distinct_points T_2 T_0) (apart_point_and_line T_2 (line_connecting T_2 T_0)) ### All 16
% 0.21/0.44 18. (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (apart_point_and_line T_2 (line_connecting T_2 T_0)) (distinct_points T_2 T_0) ### All 17
% 0.21/0.44 19. ((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)))) (distinct_points T_2 T_0) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_points T_0 T_1) (-. (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_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_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))))))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) ### DisjTree 4 13 18
% 0.21/0.44 20. (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_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))))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (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_1 T_0))) (distinct_points T_0 T_1) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_points T_2 T_0) ### All 19
% 0.21/0.44 21. (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) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_points T_0 T_1) (-. (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_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_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))))))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) ### All 20
% 0.21/0.44 22. (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_2 (line_connecting T_1 T_0)) (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))))))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (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_1 T_0))) (distinct_points T_0 T_1) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_points T_2 T_0) ### All 21
% 0.21/0.44 23. ((distinct_points T_1 T_0) => (-. (apart_point_and_line T_1 (line_connecting T_1 T_0)))) (distinct_points T_2 T_0) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_points T_0 T_1) (-. (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_1 (line_connecting T_2 T_0))) (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))))))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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_1 T_0) ### Imply 3 22
% 0.21/0.44 24. (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 Y))))) (distinct_points T_1 T_0) (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_2 (line_connecting T_1 T_0)) (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))))))) (-. (apart_point_and_line T_1 (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))) (distinct_points T_0 T_1) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_points T_2 T_0) ### All 23
% 0.21/0.45 25. (distinct_points T_2 T_0) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_points T_0 T_1) (-. (apart_point_and_line T_0 (line_connecting T_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (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))))))) (apart_point_and_line T_2 (line_connecting T_1 T_0)) (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_1 T_0) (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 Y))))) ### Extension/test/ci2 24
% 0.21/0.45 26. ((distinct_points T_0 T_1) => ((distinct_points T_0 T_0) \/ (distinct_points T_1 T_0))) (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 Y))))) (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_2 (line_connecting T_1 T_0)) (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))))))) (-. (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 X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_points T_2 T_0) (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_1) ### DisjTree 1 2 25
% 0.21/0.45 27. (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_2 T_0) (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_2 T_0))) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (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))))))) (apart_point_and_line T_2 (line_connecting T_1 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_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 Y))))) ### All 26
% 0.21/0.45 28. (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 Y))))) (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_2 (line_connecting T_1 T_0)) (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))))))) (-. (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 X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_points T_2 T_0) (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_1) ### All 27
% 0.21/0.45 29. (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_points T_0 T_1) (-. (distinct_points T_0 T_0)) (distinct_points T_2 T_0) (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_2 T_0))) (-. (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, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 Y))))) (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) ### All 28
% 0.21/0.45 30. (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 Y))))) (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_2 (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 X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_points T_2 T_0) (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_1) (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 29
% 0.21/0.45 31. (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_points T_0 T_1) (-. (distinct_points T_0 T_0)) (distinct_points T_2 T_0) (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_2 T_0))) (-. (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, ((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 30
% 0.21/0.45 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 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_2 (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 X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_points T_2 T_0) (-. (distinct_points T_0 T_0)) (distinct_points T_0 T_1) ### All 31
% 0.21/0.45 33. (All X, (-. (distinct_points X X))) (distinct_points T_0 T_1) (distinct_points T_2 T_0) (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_2 T_0))) (-. (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, ((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 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
% 0.21/0.45 34. (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) => ((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_2 (line_connecting T_1 T_0)) (-. (apart_point_and_line T_1 (line_connecting T_2 T_0))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (distinct_points T_2 T_0) (distinct_points T_0 T_1) (All X, (-. (distinct_points X X))) ### Extension/test/ci2 33
% 0.21/0.45 35. (-. (((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, (-. (distinct_points X X))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (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, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y 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))))))))) ### ConjTree 34
% 0.21/0.45 36. (-. (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) => ((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, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (-. (distinct_points X X))) ### NotAllEx 35
% 0.21/0.45 37. (-. (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, (-. (distinct_points X X))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line X (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, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y 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))))))))) ### NotAllEx 36
% 0.21/0.45 38. (-. (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) => ((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, ((distinct_points X Y) => (-. (apart_point_and_line X (line_connecting X Y)))))) (All X, (-. (distinct_points X X))) ### NotAllEx 37
% 0.21/0.45 % SZS output end Proof
% 0.21/0.45 (* END-PROOF *)
%------------------------------------------------------------------------------