TSTP Solution File: GEO200+3 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : GEO200+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 : n021.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 06:31:00 EDT 2022
% Result : Theorem 35.04s 35.24s
% Output : Proof 35.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO200+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n021.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 : Fri Jun 17 23:15:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 35.04/35.24 % SZS status Theorem
% 35.04/35.24 (* PROOF-FOUND *)
% 35.04/35.24 (* BEGIN-PROOF *)
% 35.04/35.24 % SZS output start Proof
% 35.04/35.24 1. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom
% 35.04/35.24 2. (distinct_points T_0 T_0) (-. (distinct_points T_0 T_0)) ### Axiom
% 35.04/35.24 3. (All X, (-. (distinct_points X X))) (distinct_points T_0 T_0) ### All 2
% 35.04/35.24 4. (-. (distinct_points T_1 T_0)) (distinct_points T_1 T_0) ### Axiom
% 35.04/35.24 5. ((distinct_points T_0 T_1) => ((distinct_points T_0 T_0) \/ (distinct_points T_1 T_0))) (-. (distinct_points T_1 T_0)) (All X, (-. (distinct_points X X))) (distinct_points T_0 T_1) ### DisjTree 1 3 4
% 35.04/35.24 6. (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, (-. (distinct_points X X))) (-. (distinct_points T_1 T_0)) ### All 5
% 35.04/35.24 7. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom
% 35.04/35.24 8. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (-. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0))) ### Axiom
% 35.04/35.24 9. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom
% 35.04/35.24 10. (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
% 35.04/35.24 11. ((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 9 10
% 35.04/35.24 12. (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 11
% 35.04/35.24 13. (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 12
% 35.04/35.24 14. (-. (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
% 35.04/35.24 15. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom
% 35.04/35.24 16. (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
% 35.04/35.24 17. ((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 15 16
% 35.04/35.24 18. (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 17
% 35.04/35.24 19. (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 18
% 35.04/35.24 20. (-. (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
% 35.04/35.24 21. (((distinct_points T_0 T_1) /\ (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0))) => ((apart_point_and_line T_0 (line_connecting T_0 T_1)) \/ ((apart_point_and_line T_0 (line_connecting 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_1 T_0)))))) (-. (apart_point_and_line T_1 (line_connecting T_1 T_0))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (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_1 T_0)) (distinct_points T_0 T_1) ### DisjTree 7 8 13 14 19 20
% 35.04/35.24 22. (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_1 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_1 T_0))) (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_1 T_0))) ### All 21
% 35.04/35.24 23. (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_1 T_0))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (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_1 T_0)) (distinct_points T_0 T_1) ### All 22
% 35.04/35.24 24. ((distinct_points T_1 T_0) => (-. (apart_point_and_line T_1 (line_connecting T_1 T_0)))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 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_1 T_0))) (All X, (All Y, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X 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))))))) (All X, (-. (distinct_points X X))) (distinct_points T_0 T_1) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) ### Imply 6 23
% 35.04/35.24 25. (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 Y))))) (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, (-. (distinct_points X X))) (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, ((distinct_points X Y) => (-. (apart_point_and_line Y (line_connecting X Y)))))) (-. (apart_point_and_line T_0 (line_connecting T_1 T_0))) (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_1 T_0)) ### All 24
% 35.04/35.24 26. ((distinct_points T_1 T_0) => (-. (apart_point_and_line T_0 (line_connecting T_1 T_0)))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (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 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 Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 Y))))) (All X, (-. (distinct_points X X))) (distinct_points T_0 T_1) (All Z, ((distinct_points T_0 T_1) => ((distinct_points T_0 Z) \/ (distinct_points T_1 Z)))) ### Imply 6 25
% 35.04/35.24 27. (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line Y (line_connecting T_1 Y))))) (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, (-. (distinct_points X X))) (All Y, ((distinct_points T_1 Y) => (-. (apart_point_and_line T_1 (line_connecting T_1 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))))))) (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_1 T_0)) ### All 26
% 35.04/35.24 28. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (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 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, (-. (distinct_points X X))) (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, ((distinct_points T_1 Y) => (-. (apart_point_and_line Y (line_connecting T_1 Y))))) ### All 27
% 35.04/35.25 29. (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, (-. (distinct_points X X))) (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, ((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_1 T_0)) ### All 28
% 35.04/35.25 30. (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_1 T_0)) (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, (-. (distinct_points X X))) (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 29
% 35.04/35.25 31. (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, (-. (distinct_points X X))) (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_1 T_0)) (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 30
% 35.04/35.25 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))))))))) (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0)) (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, (-. (distinct_points X X))) (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 31
% 35.04/35.25 33. (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))) (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_1 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 32
% 35.04/35.25 34. (-. (-. (distinct_lines (line_connecting T_0 T_1) (line_connecting T_1 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, ((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, (-. (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 33
% 35.04/35.25 35. (-. (equal_lines (line_connecting T_0 T_1) (line_connecting T_1 T_0))) (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))) (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) 34
% 35.04/35.25 36. (-. ((distinct_points T_0 T_1) => (equal_lines (line_connecting T_0 T_1) (line_connecting T_1 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, ((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, (-. (distinct_points X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotImply 35
% 35.04/35.25 37. (-. (All Y, ((distinct_points T_0 Y) => (equal_lines (line_connecting T_0 Y) (line_connecting Y T_0))))) (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, ((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 36
% 35.04/35.25 38. (-. (All X, (All Y, ((distinct_points X Y) => (equal_lines (line_connecting X Y) (line_connecting Y X)))))) (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ (distinct_lines U V)) => ((apart_point_and_line X U) \/ ((apart_point_and_line X V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V))))))))) (All X, (All Y, ((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, (-. (distinct_points X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### NotAllEx 37
% 35.04/35.25 % SZS output end Proof
% 35.04/35.25 (* END-PROOF *)
%------------------------------------------------------------------------------