TSTP Solution File: GEO212+2 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : GEO212+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 : n024.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 06:31:10 EDT 2022
% Result : Theorem 23.44s 23.67s
% Output : Proof 23.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO212+2 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.11/0.33 % Computer : n024.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sat Jun 18 01:49:02 EDT 2022
% 0.11/0.33 % CPUTime :
% 23.44/23.67 % SZS status Theorem
% 23.44/23.67 (* PROOF-FOUND *)
% 23.44/23.67 (* BEGIN-PROOF *)
% 23.44/23.67 % SZS output start Proof
% 23.44/23.67 1. (convergent_lines T_0 T_0) (-. (convergent_lines T_0 T_0)) ### Axiom
% 23.44/23.67 2. (All X, (-. (convergent_lines X X))) (convergent_lines T_0 T_0) ### All 1
% 23.44/23.67 3. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom
% 23.44/23.67 4. (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Axiom
% 23.44/23.67 5. (convergent_lines T_1 T_0) (-. (convergent_lines T_1 T_0)) ### Axiom
% 23.44/23.67 6. (convergent_lines T_1 T_2) (-. (convergent_lines T_1 T_2)) ### Axiom
% 23.44/23.67 7. (-. (convergent_lines T_1 T_1)) (convergent_lines T_1 T_1) ### Axiom
% 23.44/23.67 8. (-. (convergent_lines T_2 T_1)) (convergent_lines T_2 T_1) ### Axiom
% 23.44/23.67 9. ((convergent_lines T_1 T_2) => ((convergent_lines T_1 T_1) \/ (convergent_lines T_2 T_1))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (convergent_lines T_1 T_2) ### DisjTree 6 7 8
% 23.44/23.67 10. (All Z, ((convergent_lines T_1 T_2) => ((convergent_lines T_1 Z) \/ (convergent_lines T_2 Z)))) (convergent_lines T_1 T_2) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) ### All 9
% 23.44/23.67 11. (All Y, (All Z, ((convergent_lines T_1 Y) => ((convergent_lines T_1 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (convergent_lines T_1 T_2) ### All 10
% 23.44/23.67 12. (convergent_lines T_0 T_2) (-. (convergent_lines T_0 T_2)) ### Axiom
% 23.44/23.67 13. (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Axiom
% 23.44/23.67 14. (-. (convergent_lines T_2 T_0)) (convergent_lines T_2 T_0) ### Axiom
% 23.44/23.67 15. ((convergent_lines T_0 T_2) => ((convergent_lines T_0 T_0) \/ (convergent_lines T_2 T_0))) (-. (convergent_lines T_2 T_0)) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_2) ### DisjTree 12 13 14
% 23.44/23.67 16. (All Z, ((convergent_lines T_0 T_2) => ((convergent_lines T_0 Z) \/ (convergent_lines T_2 Z)))) (convergent_lines T_0 T_2) (-. (convergent_lines T_0 T_0)) (-. (convergent_lines T_2 T_0)) ### All 15
% 23.44/23.67 17. (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_0)) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_2) ### All 16
% 23.44/23.67 18. ((convergent_lines T_1 T_0) => ((convergent_lines T_1 T_2) \/ (convergent_lines T_0 T_2))) (-. (convergent_lines T_0 T_0)) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All Y, (All Z, ((convergent_lines T_1 Y) => ((convergent_lines T_1 Z) \/ (convergent_lines Y Z))))) (convergent_lines T_1 T_0) ### DisjTree 5 11 17
% 23.44/23.67 19. (All Z, ((convergent_lines T_1 T_0) => ((convergent_lines T_1 Z) \/ (convergent_lines T_0 Z)))) (convergent_lines T_1 T_0) (All Y, (All Z, ((convergent_lines T_1 Y) => ((convergent_lines T_1 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_0)) (-. (convergent_lines T_0 T_0)) ### All 18
% 23.44/23.67 20. (-. (convergent_lines T_0 T_0)) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All Y, (All Z, ((convergent_lines T_1 Y) => ((convergent_lines T_1 Z) \/ (convergent_lines Y Z))))) (convergent_lines T_1 T_0) ### All 19
% 23.44/23.67 21. ((convergent_lines T_0 T_1) => ((convergent_lines T_0 T_0) \/ (convergent_lines T_1 T_0))) (All Y, (All Z, ((convergent_lines T_1 Y) => ((convergent_lines T_1 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_0)) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_1) ### DisjTree 3 4 20
% 23.44/23.67 22. (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_0)) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All Y, (All Z, ((convergent_lines T_1 Y) => ((convergent_lines T_1 Z) \/ (convergent_lines Y Z))))) ### All 21
% 23.44/23.67 23. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_0)) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_1) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) ### All 22
% 23.44/23.67 24. (unorthogonal_lines T_0 T_0) (-. (unorthogonal_lines T_0 T_0)) ### Axiom
% 23.44/23.67 25. (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_1) ### Axiom
% 23.44/23.67 26. ((convergent_lines T_0 T_1) /\ (unorthogonal_lines T_0 T_1)) (-. (unorthogonal_lines T_0 T_1)) ### And 25
% 23.44/23.68 27. (((convergent_lines T_0 T_0) /\ (unorthogonal_lines T_0 T_0)) => (((convergent_lines T_0 T_1) /\ (unorthogonal_lines T_0 T_1)) \/ ((convergent_lines T_0 T_1) /\ (unorthogonal_lines T_0 T_1)))) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 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) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### DisjTree 23 24 26 26
% 23.44/23.68 28. (All N, (((convergent_lines T_0 T_0) /\ (unorthogonal_lines T_0 T_0)) => (((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N)) \/ ((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_0)) (convergent_lines T_0 T_1) (All Z, ((convergent_lines T_0 T_1) => ((convergent_lines T_0 Z) \/ (convergent_lines T_1 Z)))) (unorthogonal_lines T_0 T_0) (-. (unorthogonal_lines T_0 T_1)) ### All 27
% 23.44/23.68 29. (All M, (All N, (((convergent_lines T_0 M) /\ (unorthogonal_lines T_0 M)) => (((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N)))))) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 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) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### All 28
% 23.44/23.68 30. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_0)) (convergent_lines T_0 T_1) (unorthogonal_lines T_0 T_0) (-. (unorthogonal_lines T_0 T_1)) (All M, (All N, (((convergent_lines T_0 M) /\ (unorthogonal_lines T_0 M)) => (((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N)))))) ### All 29
% 23.44/23.68 31. (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_0) (convergent_lines T_0 T_1) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### All 30
% 23.55/23.73 32. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_0)) (convergent_lines T_0 T_1) (unorthogonal_lines T_0 T_0) (-. (unorthogonal_lines T_0 T_1)) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) ### All 31
% 23.55/23.73 33. ((convergent_lines T_0 T_0) \/ (unorthogonal_lines T_0 T_0)) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (-. (unorthogonal_lines T_0 T_1)) (convergent_lines T_0 T_1) (-. (convergent_lines T_2 T_0)) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (-. (convergent_lines X X))) ### Or 2 32
% 23.55/23.73 34. (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_0)) (convergent_lines T_0 T_1) (-. (unorthogonal_lines T_0 T_1)) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) ### All 33
% 23.55/23.73 35. (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_1) ### Axiom
% 23.55/23.73 36. ((convergent_lines T_0 T_1) \/ (unorthogonal_lines T_0 T_1)) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_0)) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (-. (convergent_lines X X))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) ### Or 34 35
% 23.55/23.73 37. (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_0)) (-. (unorthogonal_lines T_0 T_1)) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) ### All 36
% 23.55/23.73 38. (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_0)) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (-. (convergent_lines X X))) ### All 37
% 23.55/23.73 39. (unorthogonal_lines T_2 T_0) (-. (unorthogonal_lines T_2 T_0)) ### Axiom
% 23.55/23.73 40. (convergent_lines T_2 T_0) (-. (convergent_lines T_2 T_0)) ### Axiom
% 23.55/23.73 41. (unorthogonal_lines T_2 T_0) (-. (unorthogonal_lines T_2 T_0)) ### Axiom
% 23.55/23.73 42. (-. (convergent_lines T_2 T_1)) (convergent_lines T_2 T_1) ### Axiom
% 23.55/23.73 43. ((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) (-. (convergent_lines T_2 T_1)) ### And 42
% 23.55/23.73 44. (((convergent_lines T_2 T_0) /\ (unorthogonal_lines T_2 T_0)) => (((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) \/ ((convergent_lines T_0 T_1) /\ (unorthogonal_lines T_0 T_1)))) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_1)) (unorthogonal_lines T_2 T_0) (convergent_lines T_2 T_0) ### DisjTree 40 41 43 26
% 23.55/23.73 45. (All N, (((convergent_lines T_2 T_0) /\ (unorthogonal_lines T_2 T_0)) => (((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N)) \/ ((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N))))) (convergent_lines T_2 T_0) (unorthogonal_lines T_2 T_0) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) ### All 44
% 23.55/23.73 46. ((convergent_lines T_2 T_0) /\ (unorthogonal_lines T_2 T_0)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_1)) (unorthogonal_lines T_2 T_0) (All N, (((convergent_lines T_2 T_0) /\ (unorthogonal_lines T_2 T_0)) => (((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N)) \/ ((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N))))) ### And 45
% 23.55/23.73 47. ((convergent_lines T_0 T_0) /\ (unorthogonal_lines T_0 T_0)) (All X, (-. (convergent_lines X X))) ### And 2
% 23.55/23.73 48. (((convergent_lines T_2 T_0) /\ (unorthogonal_lines T_2 T_0)) => (((convergent_lines T_2 T_0) /\ (unorthogonal_lines T_2 T_0)) \/ ((convergent_lines T_0 T_0) /\ (unorthogonal_lines T_0 T_0)))) (All N, (((convergent_lines T_2 T_0) /\ (unorthogonal_lines T_2 T_0)) => (((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N)) \/ ((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N))))) (unorthogonal_lines T_2 T_0) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### DisjTree 38 39 46 47
% 23.55/23.73 49. (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (-. (convergent_lines X X))) (unorthogonal_lines T_2 T_0) (All N, (((convergent_lines T_2 T_0) /\ (unorthogonal_lines T_2 T_0)) => (((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N)) \/ ((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N))))) ### All 48
% 23.55/23.73 50. (All M, (All N, (((convergent_lines T_2 M) /\ (unorthogonal_lines T_2 M)) => (((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N)))))) (unorthogonal_lines T_2 T_0) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### All 49
% 23.55/23.73 51. (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (-. (convergent_lines X X))) (unorthogonal_lines T_2 T_0) (All M, (All N, (((convergent_lines T_2 M) /\ (unorthogonal_lines T_2 M)) => (((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N)))))) ### All 50
% 23.74/23.92 52. (unorthogonal_lines T_2 T_0) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### All 51
% 23.74/23.92 53. (-. ((unorthogonal_lines T_2 T_0) => ((convergent_lines T_2 T_1) \/ (unorthogonal_lines T_0 T_1)))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (-. (convergent_lines X X))) ### ConjTree 52
% 23.74/23.92 54. (-. (All N, ((unorthogonal_lines T_2 T_0) => ((convergent_lines T_2 N) \/ (unorthogonal_lines T_0 N))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### NotAllEx 53
% 23.74/23.92 55. (-. (All M, (All N, ((unorthogonal_lines T_2 M) => ((convergent_lines T_2 N) \/ (unorthogonal_lines M N)))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (-. (convergent_lines X X))) ### NotAllEx 54
% 23.74/23.92 56. (-. (All L, (All M, (All N, ((unorthogonal_lines L M) => ((convergent_lines L N) \/ (unorthogonal_lines M N))))))) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All L, (All M, (All N, (((convergent_lines L M) /\ (unorthogonal_lines L M)) => (((convergent_lines L N) /\ (unorthogonal_lines L N)) \/ ((convergent_lines M N) /\ (unorthogonal_lines M N))))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### NotAllEx 55
% 23.74/23.92 % SZS output end Proof
% 23.74/23.92 (* END-PROOF *)
%------------------------------------------------------------------------------