TSTP Solution File: GEO186+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : GEO186+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 : n019.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 06:30:47 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO186+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jun 17 17:01:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 (* PROOF-FOUND *)
% 0.20/0.43 (* BEGIN-PROOF *)
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 1. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom
% 0.20/0.43 2. (distinct_points T_2 (intersection_point T_0 T_1)) (-. (distinct_points T_2 (intersection_point T_0 T_1))) ### Axiom
% 0.20/0.43 3. (distinct_lines T_1 T_0) (-. (distinct_lines T_1 T_0)) ### Axiom
% 0.20/0.43 4. (-. (apart_point_and_line T_2 T_1)) (apart_point_and_line T_2 T_1) ### Axiom
% 0.20/0.43 5. (-. (apart_point_and_line T_2 T_0)) (apart_point_and_line T_2 T_0) ### Axiom
% 0.20/0.43 6. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom
% 0.20/0.43 7. (apart_point_and_line (intersection_point T_0 T_1) T_1) (-. (apart_point_and_line (intersection_point T_0 T_1) T_1)) ### Axiom
% 0.20/0.43 8. ((convergent_lines T_0 T_1) => (-. (apart_point_and_line (intersection_point T_0 T_1) T_1))) (apart_point_and_line (intersection_point T_0 T_1) T_1) (convergent_lines T_0 T_1) ### Imply 6 7
% 0.20/0.43 9. (All Y, ((convergent_lines T_0 Y) => (-. (apart_point_and_line (intersection_point T_0 Y) Y)))) (convergent_lines T_0 T_1) (apart_point_and_line (intersection_point T_0 T_1) T_1) ### All 8
% 0.20/0.43 10. (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (apart_point_and_line (intersection_point T_0 T_1) T_1) (convergent_lines T_0 T_1) ### All 9
% 0.20/0.43 11. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom
% 0.20/0.43 12. (apart_point_and_line (intersection_point T_0 T_1) T_0) (-. (apart_point_and_line (intersection_point T_0 T_1) T_0)) ### Axiom
% 0.20/0.43 13. ((convergent_lines T_0 T_1) => (-. (apart_point_and_line (intersection_point T_0 T_1) T_0))) (apart_point_and_line (intersection_point T_0 T_1) T_0) (convergent_lines T_0 T_1) ### Imply 11 12
% 0.20/0.43 14. (All Y, ((convergent_lines T_0 Y) => (-. (apart_point_and_line (intersection_point T_0 Y) T_0)))) (convergent_lines T_0 T_1) (apart_point_and_line (intersection_point T_0 T_1) T_0) ### All 13
% 0.20/0.43 15. (((distinct_points T_2 (intersection_point T_0 T_1)) /\ (distinct_lines T_1 T_0)) => ((apart_point_and_line T_2 T_1) \/ ((apart_point_and_line T_2 T_0) \/ ((apart_point_and_line (intersection_point T_0 T_1) T_1) \/ (apart_point_and_line (intersection_point T_0 T_1) T_0))))) (All Y, ((convergent_lines T_0 Y) => (-. (apart_point_and_line (intersection_point T_0 Y) T_0)))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 T_1)) (distinct_lines T_1 T_0) (distinct_points T_2 (intersection_point T_0 T_1)) ### DisjTree 2 3 4 5 10 14
% 0.20/0.43 16. (All V, (((distinct_points T_2 (intersection_point T_0 T_1)) /\ (distinct_lines T_1 V)) => ((apart_point_and_line T_2 T_1) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line (intersection_point T_0 T_1) T_1) \/ (apart_point_and_line (intersection_point T_0 T_1) V)))))) (distinct_points T_2 (intersection_point T_0 T_1)) (distinct_lines T_1 T_0) (-. (apart_point_and_line T_2 T_1)) (-. (apart_point_and_line T_2 T_0)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (convergent_lines T_0 T_1) (All Y, ((convergent_lines T_0 Y) => (-. (apart_point_and_line (intersection_point T_0 Y) T_0)))) ### All 15
% 0.20/0.43 17. (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 T_1)) (distinct_lines T_1 T_0) (distinct_points T_2 (intersection_point T_0 T_1)) (All V, (((distinct_points T_2 (intersection_point T_0 T_1)) /\ (distinct_lines T_1 V)) => ((apart_point_and_line T_2 T_1) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line (intersection_point T_0 T_1) T_1) \/ (apart_point_and_line (intersection_point T_0 T_1) V)))))) ### All 16
% 0.20/0.43 18. (All U, (All V, (((distinct_points T_2 (intersection_point T_0 T_1)) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line (intersection_point T_0 T_1) U) \/ (apart_point_and_line (intersection_point T_0 T_1) V))))))) (distinct_points T_2 (intersection_point T_0 T_1)) (distinct_lines T_1 T_0) (-. (apart_point_and_line T_2 T_1)) (-. (apart_point_and_line T_2 T_0)) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) X))))) ### All 17
% 0.20/0.43 19. (convergent_lines T_0 T_0) (-. (convergent_lines T_0 T_0)) ### Axiom
% 0.20/0.43 20. (All X, (-. (convergent_lines X X))) (convergent_lines T_0 T_0) ### All 19
% 0.20/0.43 21. ((convergent_lines T_0 T_1) => ((distinct_lines T_1 T_0) \/ (convergent_lines T_0 T_0))) (All X, (-. (convergent_lines X X))) (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))))) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 T_1)) (distinct_points T_2 (intersection_point T_0 T_1)) (All U, (All V, (((distinct_points T_2 (intersection_point T_0 T_1)) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line (intersection_point T_0 T_1) U) \/ (apart_point_and_line (intersection_point T_0 T_1) V))))))) (convergent_lines T_0 T_1) ### DisjTree 1 18 20
% 0.20/0.43 22. (All Z, ((convergent_lines T_0 T_1) => ((distinct_lines T_1 Z) \/ (convergent_lines T_0 Z)))) (convergent_lines T_0 T_1) (All U, (All V, (((distinct_points T_2 (intersection_point T_0 T_1)) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line (intersection_point T_0 T_1) U) \/ (apart_point_and_line (intersection_point T_0 T_1) V))))))) (distinct_points T_2 (intersection_point T_0 T_1)) (-. (apart_point_and_line T_2 T_1)) (-. (apart_point_and_line 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))))) (All X, (-. (convergent_lines X X))) ### All 21
% 0.20/0.43 23. (All Y, (All U, (All V, (((distinct_points T_2 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 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) X))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 T_1)) (distinct_points T_2 (intersection_point T_0 T_1)) (convergent_lines T_0 T_1) (All Z, ((convergent_lines T_0 T_1) => ((distinct_lines T_1 Z) \/ (convergent_lines T_0 Z)))) ### All 22
% 0.20/0.43 24. (All Y, (All Z, ((convergent_lines T_0 Y) => ((distinct_lines Y Z) \/ (convergent_lines T_0 Z))))) (convergent_lines T_0 T_1) (distinct_points T_2 (intersection_point T_0 T_1)) (-. (apart_point_and_line T_2 T_1)) (-. (apart_point_and_line 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))))) (All X, (-. (convergent_lines X X))) (All Y, (All U, (All V, (((distinct_points T_2 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) ### All 23
% 0.20/0.43 25. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All Y, (All U, (All V, (((distinct_points T_2 Y) /\ (distinct_lines U V)) => ((apart_point_and_line T_2 U) \/ ((apart_point_and_line T_2 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) X))))) (All X, (All Y, ((convergent_lines X Y) => (-. (apart_point_and_line (intersection_point X Y) Y))))) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 T_1)) (distinct_points T_2 (intersection_point T_0 T_1)) (convergent_lines T_0 T_1) ### All 24
% 0.20/0.43 26. (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))))))))) (convergent_lines T_0 T_1) (distinct_points T_2 (intersection_point T_0 T_1)) (-. (apart_point_and_line T_2 T_1)) (-. (apart_point_and_line 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))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) ### All 25
% 0.20/0.43 27. (-. (((distinct_points T_2 T_3) /\ ((convergent_lines T_0 T_1) /\ ((-. (apart_point_and_line T_2 T_0)) /\ (-. (apart_point_and_line T_2 T_1))))) => (-. (distinct_points T_2 (intersection_point T_0 T_1))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (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, (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 26
% 0.20/0.43 28. (-. (All V, (((distinct_points T_2 T_3) /\ ((convergent_lines T_0 V) /\ ((-. (apart_point_and_line T_2 T_0)) /\ (-. (apart_point_and_line T_2 V))))) => (-. (distinct_points T_2 (intersection_point T_0 V)))))) (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, ((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))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) ### NotAllEx 27
% 0.20/0.43 29. (-. (All U, (All V, (((distinct_points T_2 T_3) /\ ((convergent_lines U V) /\ ((-. (apart_point_and_line T_2 U)) /\ (-. (apart_point_and_line T_2 V))))) => (-. (distinct_points T_2 (intersection_point U V))))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (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, (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 28
% 0.20/0.43 30. (-. (All Y, (All U, (All V, (((distinct_points T_2 Y) /\ ((convergent_lines U V) /\ ((-. (apart_point_and_line T_2 U)) /\ (-. (apart_point_and_line T_2 V))))) => (-. (distinct_points T_2 (intersection_point U V)))))))) (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, ((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))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) ### NotAllEx 29
% 0.20/0.43 31. (-. (All X, (All Y, (All U, (All V, (((distinct_points X Y) /\ ((convergent_lines U V) /\ ((-. (apart_point_and_line X U)) /\ (-. (apart_point_and_line X V))))) => (-. (distinct_points X (intersection_point U V))))))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (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, (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 30
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43 (* END-PROOF *)
%------------------------------------------------------------------------------