TSTP Solution File: GEO172+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : GEO172+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 : n011.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 06:30:35 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO172+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n011.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 01:21:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 (* PROOF-FOUND *)
% 0.19/0.43 (* BEGIN-PROOF *)
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 1. (distinct_points T_0 (intersection_point T_1 T_2)) (-. (distinct_points T_0 (intersection_point T_1 T_2))) ### Axiom
% 0.19/0.43 2. (distinct_points T_0 T_0) (-. (distinct_points T_0 T_0)) ### Axiom
% 0.19/0.43 3. (All X, (-. (distinct_points X X))) (distinct_points T_0 T_0) ### All 2
% 0.19/0.43 4. (convergent_lines T_1 T_2) (-. (convergent_lines T_1 T_2)) ### Axiom
% 0.19/0.43 5. (distinct_points (intersection_point T_1 T_2) T_0) (-. (distinct_points (intersection_point T_1 T_2) T_0)) ### Axiom
% 0.19/0.43 6. (distinct_lines T_2 T_1) (-. (distinct_lines T_2 T_1)) ### Axiom
% 0.19/0.43 7. (convergent_lines T_1 T_2) (-. (convergent_lines T_1 T_2)) ### Axiom
% 0.19/0.43 8. (apart_point_and_line (intersection_point T_1 T_2) T_2) (-. (apart_point_and_line (intersection_point T_1 T_2) T_2)) ### Axiom
% 0.19/0.43 9. ((convergent_lines T_1 T_2) => (-. (apart_point_and_line (intersection_point T_1 T_2) T_2))) (apart_point_and_line (intersection_point T_1 T_2) T_2) (convergent_lines T_1 T_2) ### Imply 7 8
% 0.19/0.43 10. (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) Y)))) (convergent_lines T_1 T_2) (apart_point_and_line (intersection_point T_1 T_2) T_2) ### All 9
% 0.19/0.43 11. (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (apart_point_and_line (intersection_point T_1 T_2) T_2) (convergent_lines T_1 T_2) ### All 10
% 0.19/0.43 12. (convergent_lines T_1 T_2) (-. (convergent_lines T_1 T_2)) ### Axiom
% 0.19/0.43 13. (apart_point_and_line (intersection_point T_1 T_2) T_1) (-. (apart_point_and_line (intersection_point T_1 T_2) T_1)) ### Axiom
% 0.19/0.43 14. ((convergent_lines T_1 T_2) => (-. (apart_point_and_line (intersection_point T_1 T_2) T_1))) (apart_point_and_line (intersection_point T_1 T_2) T_1) (convergent_lines T_1 T_2) ### Imply 12 13
% 0.19/0.43 15. (All Y, ((convergent_lines T_1 Y) => (-. (apart_point_and_line (intersection_point T_1 Y) T_1)))) (convergent_lines T_1 T_2) (apart_point_and_line (intersection_point T_1 T_2) T_1) ### All 14
% 0.19/0.43 16. (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (apart_point_and_line (intersection_point T_1 T_2) T_1) (convergent_lines T_1 T_2) ### All 15
% 0.19/0.43 17. (-. (apart_point_and_line T_0 T_2)) (apart_point_and_line T_0 T_2) ### Axiom
% 0.19/0.43 18. (-. (apart_point_and_line T_0 T_1)) (apart_point_and_line T_0 T_1) ### Axiom
% 0.19/0.43 19. (((distinct_points (intersection_point T_1 T_2) T_0) /\ (distinct_lines T_2 T_1)) => ((apart_point_and_line (intersection_point T_1 T_2) T_2) \/ ((apart_point_and_line (intersection_point T_1 T_2) T_1) \/ ((apart_point_and_line T_0 T_2) \/ (apart_point_and_line T_0 T_1))))) (-. (apart_point_and_line T_0 T_1)) (-. (apart_point_and_line T_0 T_2)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (convergent_lines T_1 T_2) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (distinct_lines T_2 T_1) (distinct_points (intersection_point T_1 T_2) T_0) ### DisjTree 5 6 11 16 17 18
% 0.19/0.43 20. (All V, (((distinct_points (intersection_point T_1 T_2) T_0) /\ (distinct_lines T_2 V)) => ((apart_point_and_line (intersection_point T_1 T_2) T_2) \/ ((apart_point_and_line (intersection_point T_1 T_2) V) \/ ((apart_point_and_line T_0 T_2) \/ (apart_point_and_line T_0 V)))))) (distinct_points (intersection_point T_1 T_2) T_0) (distinct_lines T_2 T_1) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (convergent_lines T_1 T_2) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (-. (apart_point_and_line T_0 T_2)) (-. (apart_point_and_line T_0 T_1)) ### All 19
% 0.19/0.43 21. (All U, (All V, (((distinct_points (intersection_point T_1 T_2) T_0) /\ (distinct_lines U V)) => ((apart_point_and_line (intersection_point T_1 T_2) U) \/ ((apart_point_and_line (intersection_point T_1 T_2) V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (-. (apart_point_and_line T_0 T_1)) (-. (apart_point_and_line T_0 T_2)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (convergent_lines T_1 T_2) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (distinct_lines T_2 T_1) (distinct_points (intersection_point T_1 T_2) T_0) ### All 20
% 0.19/0.43 22. (-. (convergent_lines T_1 T_1)) (convergent_lines T_1 T_1) ### Axiom
% 0.19/0.43 23. ((convergent_lines T_1 T_2) => ((distinct_lines T_2 T_1) \/ (convergent_lines T_1 T_1))) (-. (convergent_lines T_1 T_1)) (distinct_points (intersection_point T_1 T_2) T_0) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (-. (apart_point_and_line T_0 T_2)) (-. (apart_point_and_line T_0 T_1)) (All U, (All V, (((distinct_points (intersection_point T_1 T_2) T_0) /\ (distinct_lines U V)) => ((apart_point_and_line (intersection_point T_1 T_2) U) \/ ((apart_point_and_line (intersection_point T_1 T_2) V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (convergent_lines T_1 T_2) ### DisjTree 4 21 22
% 0.19/0.43 24. (All Z, ((convergent_lines T_1 T_2) => ((distinct_lines T_2 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_1 T_2) (All U, (All V, (((distinct_points (intersection_point T_1 T_2) T_0) /\ (distinct_lines U V)) => ((apart_point_and_line (intersection_point T_1 T_2) U) \/ ((apart_point_and_line (intersection_point T_1 T_2) V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (-. (apart_point_and_line T_0 T_1)) (-. (apart_point_and_line T_0 T_2)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (distinct_points (intersection_point T_1 T_2) T_0) (-. (convergent_lines T_1 T_1)) ### All 23
% 0.19/0.43 25. (All X, (-. (convergent_lines X X))) (distinct_points (intersection_point T_1 T_2) T_0) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (-. (apart_point_and_line T_0 T_2)) (-. (apart_point_and_line T_0 T_1)) (All U, (All V, (((distinct_points (intersection_point T_1 T_2) T_0) /\ (distinct_lines U V)) => ((apart_point_and_line (intersection_point T_1 T_2) U) \/ ((apart_point_and_line (intersection_point T_1 T_2) V) \/ ((apart_point_and_line T_0 U) \/ (apart_point_and_line T_0 V))))))) (convergent_lines T_1 T_2) (All Z, ((convergent_lines T_1 T_2) => ((distinct_lines T_2 Z) \/ (convergent_lines T_1 Z)))) ### All 24
% 0.19/0.43 26. (All Y, (All U, (All V, (((distinct_points (intersection_point T_1 T_2) Y) /\ (distinct_lines U V)) => ((apart_point_and_line (intersection_point T_1 T_2) U) \/ ((apart_point_and_line (intersection_point T_1 T_2) V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) (All Z, ((convergent_lines T_1 T_2) => ((distinct_lines T_2 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_1 T_2) (-. (apart_point_and_line T_0 T_1)) (-. (apart_point_and_line T_0 T_2)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (distinct_points (intersection_point T_1 T_2) T_0) (All X, (-. (convergent_lines X X))) ### All 25
% 0.19/0.43 27. (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, (-. (convergent_lines X X))) (distinct_points (intersection_point T_1 T_2) T_0) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (-. (apart_point_and_line T_0 T_2)) (-. (apart_point_and_line T_0 T_1)) (convergent_lines T_1 T_2) (All Z, ((convergent_lines T_1 T_2) => ((distinct_lines T_2 Z) \/ (convergent_lines T_1 Z)))) ### All 26
% 0.19/0.43 28. ((distinct_points T_0 (intersection_point T_1 T_2)) => ((distinct_points T_0 T_0) \/ (distinct_points (intersection_point T_1 T_2) T_0))) (All Z, ((convergent_lines T_1 T_2) => ((distinct_lines T_2 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_1 T_2) (-. (apart_point_and_line T_0 T_1)) (-. (apart_point_and_line T_0 T_2)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (-. (convergent_lines X 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, (-. (distinct_points X X))) (distinct_points T_0 (intersection_point T_1 T_2)) ### DisjTree 1 3 27
% 0.19/0.43 29. (All Z, ((distinct_points T_0 (intersection_point T_1 T_2)) => ((distinct_points T_0 Z) \/ (distinct_points (intersection_point T_1 T_2) Z)))) (distinct_points T_0 (intersection_point T_1 T_2)) (All X, (-. (distinct_points X 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, (-. (convergent_lines X X))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (-. (apart_point_and_line T_0 T_2)) (-. (apart_point_and_line T_0 T_1)) (convergent_lines T_1 T_2) (All Z, ((convergent_lines T_1 T_2) => ((distinct_lines T_2 Z) \/ (convergent_lines T_1 Z)))) ### All 28
% 0.19/0.43 30. (All Y, (All Z, ((distinct_points T_0 Y) => ((distinct_points T_0 Z) \/ (distinct_points Y Z))))) (All Z, ((convergent_lines T_1 T_2) => ((distinct_lines T_2 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_1 T_2) (-. (apart_point_and_line T_0 T_1)) (-. (apart_point_and_line T_0 T_2)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (-. (convergent_lines X 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, (-. (distinct_points X X))) (distinct_points T_0 (intersection_point T_1 T_2)) ### All 29
% 0.19/0.43 31. (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (distinct_points T_0 (intersection_point T_1 T_2)) (All X, (-. (distinct_points X 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, (-. (convergent_lines X X))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (-. (apart_point_and_line T_0 T_2)) (-. (apart_point_and_line T_0 T_1)) (convergent_lines T_1 T_2) (All Z, ((convergent_lines T_1 T_2) => ((distinct_lines T_2 Z) \/ (convergent_lines T_1 Z)))) ### All 30
% 0.19/0.43 32. (All Y, (All Z, ((convergent_lines T_1 Y) => ((distinct_lines Y Z) \/ (convergent_lines T_1 Z))))) (convergent_lines T_1 T_2) (-. (apart_point_and_line T_0 T_1)) (-. (apart_point_and_line T_0 T_2)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (-. (convergent_lines X 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, (-. (distinct_points X X))) (distinct_points T_0 (intersection_point T_1 T_2)) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) ### All 31
% 0.19/0.43 33. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (distinct_points T_0 (intersection_point T_1 T_2)) (All X, (-. (distinct_points X 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, (-. (convergent_lines X X))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (-. (apart_point_and_line T_0 T_2)) (-. (apart_point_and_line T_0 T_1)) (convergent_lines T_1 T_2) ### All 32
% 0.19/0.43 34. (-. (((convergent_lines T_1 T_2) /\ ((-. (apart_point_and_line T_0 T_1)) /\ (-. (apart_point_and_line T_0 T_2)))) => (-. (distinct_points T_0 (intersection_point T_1 T_2))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (-. (convergent_lines X 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, (-. (distinct_points X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) ### ConjTree 33
% 0.19/0.43 35. (-. (All Z, (((convergent_lines T_1 T_2) /\ ((-. (apart_point_and_line Z T_1)) /\ (-. (apart_point_and_line Z T_2)))) => (-. (distinct_points Z (intersection_point T_1 T_2)))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X 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 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, (-. (convergent_lines X X))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) ### NotAllEx 34
% 0.19/0.43 36. (-. (All Y, (All Z, (((convergent_lines T_1 Y) /\ ((-. (apart_point_and_line Z T_1)) /\ (-. (apart_point_and_line Z Y)))) => (-. (distinct_points Z (intersection_point T_1 Y))))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (-. (convergent_lines X 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, (-. (distinct_points X X))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((distinct_points X Z) \/ (distinct_points Y Z)))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) ### NotAllEx 35
% 0.19/0.43 37. (-. (All X, (All Y, (All Z, (((convergent_lines X Y) /\ ((-. (apart_point_and_line Z X)) /\ (-. (apart_point_and_line Z Y)))) => (-. (distinct_points Z (intersection_point X Y)))))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X 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 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, (-. (convergent_lines X X))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) ### NotAllEx 36
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 (* END-PROOF *)
%------------------------------------------------------------------------------