TSTP Solution File: GEO201+2 by SuperZenon---0.0.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SuperZenon---0.0.1
% Problem  : GEO201+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 : n008.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 06:31:01 EDT 2022

% Result   : Theorem 0.20s 0.55s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : GEO201+2 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13  % Command  : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.35  % Computer : n008.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Fri Jun 17 17:08:37 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.55  % SZS status Theorem
% 0.20/0.55  (* PROOF-FOUND *)
% 0.20/0.55  (* BEGIN-PROOF *)
% 0.20/0.55  % SZS output start Proof
% 0.20/0.55  1. (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) (-. (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)))   ### Axiom
% 0.20/0.55  2. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1))   ### Axiom
% 0.20/0.55  3. (-. (distinct_lines T_0 T_1)) (convergent_lines T_0 T_1)   ### Extension/test/ceq3ctrp 2
% 0.20/0.55  4. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1))   ### Axiom
% 0.20/0.55  5. (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
% 0.20/0.55  6. (-. ((apart_point_and_line (intersection_point T_0 T_1) 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)   ### NotOr 5
% 0.20/0.55  7. (distinct_points (intersection_point T_0 T_1) (intersection_point T_0 T_1))   ### Extension/test/apart1
% 0.20/0.55  8. ((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_1)) => (distinct_points (intersection_point T_0 T_1) (intersection_point T_0 T_1)))) (apart_point_and_line (intersection_point T_0 T_1) T_0) (convergent_lines T_0 T_1)   ### DisjTree 4 6 7
% 0.20/0.55  9. (All Z, ((convergent_lines T_0 T_1) => (((apart_point_and_line Z T_0) \/ (apart_point_and_line Z T_1)) => (distinct_points Z (intersection_point T_0 T_1))))) (convergent_lines T_0 T_1) (apart_point_and_line (intersection_point T_0 T_1) T_0)   ### All 8
% 0.20/0.55  10. (All Y, (All Z, ((convergent_lines T_0 Y) => (((apart_point_and_line Z T_0) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point T_0 Y)))))) (apart_point_and_line (intersection_point T_0 T_1) T_0) (convergent_lines T_0 T_1)   ### All 9
% 0.20/0.55  11. (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))))))) (convergent_lines T_0 T_1) (apart_point_and_line (intersection_point T_0 T_1) T_0)   ### All 10
% 0.20/0.55  12. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1))   ### Axiom
% 0.20/0.55  13. (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
% 0.20/0.55  14. (-. ((apart_point_and_line (intersection_point T_0 T_1) 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_1)   ### NotOr 13
% 0.20/0.55  15. ((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_1)) => (distinct_points (intersection_point T_0 T_1) (intersection_point T_0 T_1)))) (apart_point_and_line (intersection_point T_0 T_1) T_1) (convergent_lines T_0 T_1)   ### DisjTree 12 14 7
% 0.20/0.55  16. (All Z, ((convergent_lines T_0 T_1) => (((apart_point_and_line Z T_0) \/ (apart_point_and_line Z T_1)) => (distinct_points Z (intersection_point T_0 T_1))))) (convergent_lines T_0 T_1) (apart_point_and_line (intersection_point T_0 T_1) T_1)   ### All 15
% 0.20/0.55  17. (All Y, (All Z, ((convergent_lines T_0 Y) => (((apart_point_and_line Z T_0) \/ (apart_point_and_line Z Y)) => (distinct_points Z (intersection_point T_0 Y)))))) (apart_point_and_line (intersection_point T_0 T_1) T_1) (convergent_lines T_0 T_1)   ### All 16
% 0.20/0.55  18. (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))))))) (convergent_lines T_0 T_1) (apart_point_and_line (intersection_point T_0 T_1) T_1)   ### All 17
% 0.20/0.55  19. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1))   ### Axiom
% 0.20/0.55  20. (convergent_lines T_0 T_0) (-. (convergent_lines T_0 T_0))   ### Axiom
% 0.20/0.55  21. (-. (distinct_lines T_0 T_0)) (convergent_lines T_0 T_0)   ### Extension/test/ceq3ctrp 20
% 0.20/0.55  22. (All X, (-. (distinct_lines X X))) (convergent_lines T_0 T_0)   ### All 21
% 0.20/0.55  23. (-. (convergent_lines T_1 T_0)) (convergent_lines T_1 T_0)   ### Axiom
% 0.20/0.55  24. ((convergent_lines T_0 T_1) => ((convergent_lines T_0 T_0) \/ (convergent_lines T_1 T_0))) (-. (convergent_lines T_1 T_0)) (All X, (-. (distinct_lines X X))) (convergent_lines T_0 T_1)   ### DisjTree 19 22 23
% 0.20/0.55  25. (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_0 T_1) (All X, (-. (distinct_lines X X))) (-. (convergent_lines T_1 T_0))   ### All 24
% 0.20/0.55  26. (apart_point_and_line (intersection_point T_1 T_0) T_0) (-. (apart_point_and_line (intersection_point T_1 T_0) T_0))   ### Axiom
% 0.20/0.55  27. (-. ((apart_point_and_line (intersection_point T_1 T_0) T_1) \/ (apart_point_and_line (intersection_point T_1 T_0) T_0))) (apart_point_and_line (intersection_point T_1 T_0) T_0)   ### NotOr 26
% 0.20/0.55  28. (distinct_points (intersection_point T_1 T_0) (intersection_point T_1 T_0))   ### Extension/test/apart1
% 0.20/0.55  29. ((convergent_lines T_1 T_0) => (((apart_point_and_line (intersection_point T_1 T_0) T_1) \/ (apart_point_and_line (intersection_point T_1 T_0) T_0)) => (distinct_points (intersection_point T_1 T_0) (intersection_point T_1 T_0)))) (apart_point_and_line (intersection_point T_1 T_0) T_0) (All X, (-. (distinct_lines X X))) (convergent_lines T_0 T_1) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z))))   ### DisjTree 25 27 28
% 0.20/0.55  30. (All Z, ((convergent_lines T_1 T_0) => (((apart_point_and_line Z T_1) \/ (apart_point_and_line Z T_0)) => (distinct_points Z (intersection_point T_1 T_0))))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_0 T_1) (All X, (-. (distinct_lines X X))) (apart_point_and_line (intersection_point T_1 T_0) T_0)   ### All 29
% 0.20/0.55  31. (apart_point_and_line (intersection_point T_1 T_0) T_1) (-. (apart_point_and_line (intersection_point T_1 T_0) T_1))   ### Axiom
% 0.20/0.55  32. (-. ((apart_point_and_line (intersection_point T_1 T_0) T_1) \/ (apart_point_and_line (intersection_point T_1 T_0) T_0))) (apart_point_and_line (intersection_point T_1 T_0) T_1)   ### NotOr 31
% 0.20/0.55  33. ((convergent_lines T_1 T_0) => (((apart_point_and_line (intersection_point T_1 T_0) T_1) \/ (apart_point_and_line (intersection_point T_1 T_0) T_0)) => (distinct_points (intersection_point T_1 T_0) (intersection_point T_1 T_0)))) (apart_point_and_line (intersection_point T_1 T_0) T_1) (All X, (-. (distinct_lines X X))) (convergent_lines T_0 T_1) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z))))   ### DisjTree 25 32 28
% 0.20/0.55  34. (All Z, ((convergent_lines T_1 T_0) => (((apart_point_and_line Z T_1) \/ (apart_point_and_line Z T_0)) => (distinct_points Z (intersection_point T_1 T_0))))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_0 T_1) (All X, (-. (distinct_lines X X))) (apart_point_and_line (intersection_point T_1 T_0) T_1)   ### All 33
% 0.20/0.55  35. (((distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) /\ (distinct_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_1) \/ ((apart_point_and_line (intersection_point T_1 T_0) T_0) \/ (apart_point_and_line (intersection_point T_1 T_0) T_1))))) (All X, (-. (distinct_lines X X))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (All Z, ((convergent_lines T_1 T_0) => (((apart_point_and_line Z T_1) \/ (apart_point_and_line Z T_0)) => (distinct_points Z (intersection_point T_1 T_0))))) (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))))))) (convergent_lines T_0 T_1) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0))   ### DisjTree 1 3 11 18 30 34
% 0.20/0.55  36. (All V, (((distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) /\ (distinct_lines T_0 V)) => ((apart_point_and_line (intersection_point T_0 T_1) T_0) \/ ((apart_point_and_line (intersection_point T_0 T_1) V) \/ ((apart_point_and_line (intersection_point T_1 T_0) T_0) \/ (apart_point_and_line (intersection_point T_1 T_0) V)))))) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) (convergent_lines T_0 T_1) (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 Z, ((convergent_lines T_1 T_0) => (((apart_point_and_line Z T_1) \/ (apart_point_and_line Z T_0)) => (distinct_points Z (intersection_point T_1 T_0))))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (All X, (-. (distinct_lines X X)))   ### All 35
% 0.20/0.55  37. (All U, (All V, (((distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) /\ (distinct_lines U V)) => ((apart_point_and_line (intersection_point T_0 T_1) U) \/ ((apart_point_and_line (intersection_point T_0 T_1) V) \/ ((apart_point_and_line (intersection_point T_1 T_0) U) \/ (apart_point_and_line (intersection_point T_1 T_0) V))))))) (All X, (-. (distinct_lines X X))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (All Z, ((convergent_lines T_1 T_0) => (((apart_point_and_line Z T_1) \/ (apart_point_and_line Z T_0)) => (distinct_points Z (intersection_point T_1 T_0))))) (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))))))) (convergent_lines T_0 T_1) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0))   ### All 36
% 0.20/0.55  38. (All Y, (All U, (All V, (((distinct_points (intersection_point T_0 T_1) Y) /\ (distinct_lines U V)) => ((apart_point_and_line (intersection_point T_0 T_1) U) \/ ((apart_point_and_line (intersection_point T_0 T_1) V) \/ ((apart_point_and_line Y U) \/ (apart_point_and_line Y V)))))))) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) (convergent_lines T_0 T_1) (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 Z, ((convergent_lines T_1 T_0) => (((apart_point_and_line Z T_1) \/ (apart_point_and_line Z T_0)) => (distinct_points Z (intersection_point T_1 T_0))))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (All X, (-. (distinct_lines X X)))   ### All 37
% 0.20/0.55  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 X, (-. (distinct_lines X X))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (All Z, ((convergent_lines T_1 T_0) => (((apart_point_and_line Z T_1) \/ (apart_point_and_line Z T_0)) => (distinct_points Z (intersection_point T_1 T_0))))) (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))))))) (convergent_lines T_0 T_1) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0))   ### All 38
% 0.20/0.55  40. (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)))))) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) (convergent_lines T_0 T_1) (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 Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (All X, (-. (distinct_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 39
% 0.20/0.55  41. (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_lines X X))) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (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))))))) (convergent_lines T_0 T_1) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0))   ### All 40
% 0.20/0.55  42. (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)) (convergent_lines T_0 T_1) (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, (-. (distinct_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 41
% 0.20/0.55  43. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines 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 X, (-. (distinct_lines X X))) (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))))))) (convergent_lines T_0 T_1) (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0))   ### All 42
% 0.20/0.55  44. (-. (-. (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0)))) (convergent_lines T_0 T_1) (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, (-. (distinct_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, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z))))))   ### NotNot 43
% 0.20/0.55  45. (-. ((convergent_lines T_0 T_1) => (-. (distinct_points (intersection_point T_0 T_1) (intersection_point T_1 T_0))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines 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 X, (-. (distinct_lines X X))) (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)))))))   ### NotImply 44
% 0.20/0.55  46. (-. (All Y, ((convergent_lines T_0 Y) => (-. (distinct_points (intersection_point T_0 Y) (intersection_point Y T_0)))))) (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, (-. (distinct_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, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z))))))   ### NotAllEx 45
% 0.20/0.55  47. (-. (All X, (All Y, ((convergent_lines X Y) => (-. (distinct_points (intersection_point X Y) (intersection_point Y X))))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines 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 X, (-. (distinct_lines X X))) (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)))))))   ### NotAllEx 46
% 0.20/0.55  % SZS output end Proof
% 0.20/0.55  (* END-PROOF *)
%------------------------------------------------------------------------------