TSTP Solution File: GEO213+2 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : GEO213+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 : n004.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 06:31:11 EDT 2022
% Result : Theorem 21.90s 22.14s
% Output : Proof 22.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO213+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.14/0.33 % Computer : n004.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Sat Jun 18 13:49:08 EDT 2022
% 0.14/0.33 % CPUTime :
% 21.90/22.14 % SZS status Theorem
% 21.90/22.14 (* PROOF-FOUND *)
% 21.90/22.14 (* BEGIN-PROOF *)
% 21.90/22.14 % SZS output start Proof
% 21.90/22.14 1. (convergent_lines T_0 T_0) (-. (convergent_lines T_0 T_0)) ### Axiom
% 21.90/22.14 2. (All X, (-. (convergent_lines X X))) (convergent_lines T_0 T_0) ### All 1
% 21.90/22.14 3. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom
% 21.90/22.14 4. (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Axiom
% 21.90/22.14 5. (convergent_lines T_0 T_2) (-. (convergent_lines T_0 T_2)) ### Axiom
% 21.90/22.14 6. (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Axiom
% 21.90/22.14 7. (-. (convergent_lines T_2 T_0)) (convergent_lines T_2 T_0) ### Axiom
% 21.90/22.14 8. ((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 5 6 7
% 21.90/22.14 9. (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 8
% 21.90/22.14 10. (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 9
% 21.90/22.14 11. (convergent_lines T_1 T_0) (-. (convergent_lines T_1 T_0)) ### Axiom
% 21.90/22.14 12. (-. (convergent_lines T_1 T_2)) (convergent_lines T_1 T_2) ### Axiom
% 21.90/22.14 13. (-. (convergent_lines T_0 T_2)) (convergent_lines T_0 T_2) ### Axiom
% 21.90/22.14 14. ((convergent_lines T_1 T_0) => ((convergent_lines T_1 T_2) \/ (convergent_lines T_0 T_2))) (-. (convergent_lines T_0 T_2)) (-. (convergent_lines T_1 T_2)) (convergent_lines T_1 T_0) ### DisjTree 11 12 13
% 21.90/22.14 15. (All Z, ((convergent_lines T_1 T_0) => ((convergent_lines T_1 Z) \/ (convergent_lines T_0 Z)))) (convergent_lines T_1 T_0) (-. (convergent_lines T_1 T_2)) (-. (convergent_lines T_0 T_2)) ### All 14
% 21.90/22.14 16. (distinct_lines T_1 T_2) (-. (distinct_lines T_1 T_2)) ### Axiom
% 21.90/22.14 17. (-. (distinct_lines T_1 T_1)) (distinct_lines T_1 T_1) ### Axiom
% 21.90/22.14 18. (-. (distinct_lines T_2 T_1)) (distinct_lines T_2 T_1) ### Axiom
% 21.90/22.14 19. ((distinct_lines T_1 T_2) => ((distinct_lines T_1 T_1) \/ (distinct_lines T_2 T_1))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (distinct_lines T_1 T_2) ### DisjTree 16 17 18
% 21.90/22.14 20. (All Z, ((distinct_lines T_1 T_2) => ((distinct_lines T_1 Z) \/ (distinct_lines T_2 Z)))) (distinct_lines T_1 T_2) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) ### All 19
% 21.90/22.14 21. (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (distinct_lines T_1 T_2) ### All 20
% 21.90/22.14 22. ((convergent_lines T_1 T_2) => (distinct_lines T_1 T_2)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (-. (convergent_lines T_0 T_2)) (convergent_lines T_1 T_0) (All Z, ((convergent_lines T_1 T_0) => ((convergent_lines T_1 Z) \/ (convergent_lines T_0 Z)))) ### Imply 15 21
% 21.90/22.14 23. (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) (All Z, ((convergent_lines T_1 T_0) => ((convergent_lines T_1 Z) \/ (convergent_lines T_0 Z)))) (convergent_lines T_1 T_0) (-. (convergent_lines T_0 T_2)) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) ### All 22
% 21.90/22.14 24. (unorthogonal_lines T_0 T_2) (-. (unorthogonal_lines T_0 T_2)) ### Axiom
% 21.90/22.14 25. (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_1) ### Axiom
% 21.90/22.14 26. ((convergent_lines T_0 T_1) /\ (unorthogonal_lines T_0 T_1)) (-. (unorthogonal_lines T_0 T_1)) ### And 25
% 21.90/22.14 27. (-. (convergent_lines T_2 T_1)) (convergent_lines T_2 T_1) ### Axiom
% 21.90/22.14 28. ((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) (-. (convergent_lines T_2 T_1)) ### And 27
% 21.90/22.14 29. (((convergent_lines T_0 T_2) /\ (unorthogonal_lines T_0 T_2)) => (((convergent_lines T_0 T_1) /\ (unorthogonal_lines T_0 T_1)) \/ ((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_2) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (convergent_lines T_1 T_0) (All Z, ((convergent_lines T_1 T_0) => ((convergent_lines T_1 Z) \/ (convergent_lines T_0 Z)))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) ### DisjTree 23 24 26 28
% 21.90/22.14 30. (All N, (((convergent_lines T_0 T_2) /\ (unorthogonal_lines T_0 T_2)) => (((convergent_lines T_0 N) /\ (unorthogonal_lines T_0 N)) \/ ((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N))))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) (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, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (unorthogonal_lines T_0 T_2) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_1)) ### All 29
% 21.90/22.14 31. (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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_2) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (convergent_lines T_1 T_0) (All Z, ((convergent_lines T_1 T_0) => ((convergent_lines T_1 Z) \/ (convergent_lines T_0 Z)))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) ### All 30
% 21.90/22.14 32. ((convergent_lines T_0 T_2) \/ (unorthogonal_lines T_0 T_2)) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) (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, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 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)))))) (-. (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))))) ### Or 10 31
% 21.90/22.14 33. (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (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 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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (convergent_lines T_1 T_0) (All Z, ((convergent_lines T_1 T_0) => ((convergent_lines T_1 Z) \/ (convergent_lines T_0 Z)))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) ### All 32
% 21.90/22.14 34. (All Y, (All Z, ((convergent_lines T_1 Y) => ((convergent_lines T_1 Z) \/ (convergent_lines Y Z))))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) (convergent_lines T_1 T_0) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 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)))))) (-. (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))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) ### All 33
% 22.03/22.21 35. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (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 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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (convergent_lines T_1 T_0) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) ### All 34
% 22.03/22.21 36. ((convergent_lines T_0 T_1) => ((convergent_lines T_0 T_0) \/ (convergent_lines T_1 T_0))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 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)))))) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_1) ### DisjTree 3 4 35
% 22.03/22.21 37. (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)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_0)) (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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All Y, (All Z, ((distinct_lines T_1 Y) => ((distinct_lines T_1 Z) \/ (distinct_lines Y Z))))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) ### All 36
% 22.03/22.21 38. (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 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)))))) (-. (convergent_lines T_2 T_0)) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (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 37
% 22.03/22.21 39. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_0)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_0)) (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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) ### All 38
% 22.03/22.21 40. (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All Y, ((convergent_lines T_1 Y) => (distinct_lines T_1 Y))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 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)))))) (-. (convergent_lines T_2 T_0)) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_1) ### All 39
% 22.03/22.21 41. (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_0)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (-. (convergent_lines T_2 T_0)) (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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) ### All 40
% 22.03/22.21 42. (unorthogonal_lines T_2 T_0) (-. (unorthogonal_lines T_2 T_0)) ### Axiom
% 22.03/22.21 43. (convergent_lines T_2 T_0) (-. (convergent_lines T_2 T_0)) ### Axiom
% 22.03/22.21 44. (unorthogonal_lines T_2 T_0) (-. (unorthogonal_lines T_2 T_0)) ### Axiom
% 22.03/22.21 45. (((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 43 44 28 26
% 22.03/22.21 46. (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 45
% 22.03/22.21 47. ((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 46
% 22.03/22.21 48. (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Axiom
% 22.03/22.21 49. ((convergent_lines T_0 T_0) /\ (unorthogonal_lines T_0 T_0)) (-. (convergent_lines T_0 T_0)) ### And 48
% 22.03/22.21 50. (((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, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 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 M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) ### DisjTree 41 42 47 49
% 22.27/22.46 51. (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_0)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (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 50
% 22.27/22.46 52. (unorthogonal_lines T_0 T_0) (-. (unorthogonal_lines T_0 T_0)) ### Axiom
% 22.27/22.46 53. (((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_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, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 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 M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) ### DisjTree 51 52 26 26
% 22.27/22.46 54. (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, ((convergent_lines X Y) => (distinct_lines X Y)))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (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))))) (unorthogonal_lines T_0 T_0) ### All 53
% 22.27/22.46 55. (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, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 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 M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) ### All 54
% 22.27/22.46 56. (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 X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (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)))))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (unorthogonal_lines T_2 T_0) (unorthogonal_lines T_0 T_0) ### All 55
% 22.27/22.46 57. (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_0) (unorthogonal_lines T_2 T_0) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_2 T_1)) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (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 56
% 22.27/22.46 58. (-. (convergent_lines T_2 T_1)) (convergent_lines T_2 T_1) ### Axiom
% 22.27/22.46 59. (-. (unorthogonal_lines T_2 T_1)) (unorthogonal_lines T_2 T_1) ### Axiom
% 22.27/22.46 60. ((convergent_lines T_2 T_1) \/ (unorthogonal_lines T_2 T_1)) (-. (unorthogonal_lines T_2 T_1)) (-. (convergent_lines T_2 T_1)) ### Or 58 59
% 22.27/22.46 61. (All M, ((convergent_lines T_2 M) \/ (unorthogonal_lines T_2 M))) (-. (convergent_lines T_2 T_1)) (-. (unorthogonal_lines T_2 T_1)) ### All 60
% 22.27/22.46 62. (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (-. (unorthogonal_lines T_2 T_1)) (-. (convergent_lines T_2 T_1)) ### All 61
% 22.27/22.46 63. (-. (distinct_lines T_2 T_1)) (distinct_lines T_2 T_1) ### Axiom
% 22.27/22.46 64. ((convergent_lines T_2 T_1) => (distinct_lines T_2 T_1)) (-. (distinct_lines T_2 T_1)) (-. (unorthogonal_lines T_2 T_1)) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### Imply 62 63
% 22.27/22.46 65. (All Y, ((convergent_lines T_2 Y) => (distinct_lines T_2 Y))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (-. (unorthogonal_lines T_2 T_1)) (-. (distinct_lines T_2 T_1)) ### All 64
% 22.27/22.46 66. (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (-. (distinct_lines T_2 T_1)) (-. (unorthogonal_lines T_2 T_1)) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### All 65
% 22.27/22.47 67. (convergent_lines T_2 T_1) (-. (convergent_lines T_2 T_1)) ### Axiom
% 22.27/22.47 68. (-. (distinct_lines T_2 T_1)) (distinct_lines T_2 T_1) ### Axiom
% 22.27/22.47 69. ((convergent_lines T_2 T_1) => (distinct_lines T_2 T_1)) (-. (distinct_lines T_2 T_1)) (convergent_lines T_2 T_1) ### Imply 67 68
% 22.27/22.47 70. (All Y, ((convergent_lines T_2 Y) => (distinct_lines T_2 Y))) (convergent_lines T_2 T_1) (-. (distinct_lines T_2 T_1)) ### All 69
% 22.27/22.47 71. (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (-. (distinct_lines T_2 T_1)) (convergent_lines T_2 T_1) ### All 70
% 22.27/22.47 72. ((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) ### And 71
% 22.27/22.47 73. (-. (convergent_lines T_1 T_1)) (convergent_lines T_1 T_1) ### Axiom
% 22.27/22.47 74. ((convergent_lines T_1 T_1) /\ (unorthogonal_lines T_1 T_1)) (-. (convergent_lines T_1 T_1)) ### And 73
% 22.27/22.47 75. (((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) => (((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) \/ ((convergent_lines T_1 T_1) /\ (unorthogonal_lines T_1 T_1)))) (-. (convergent_lines T_1 T_1)) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (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 X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (unorthogonal_lines T_2 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))))))) ### DisjTree 57 66 72 74
% 22.27/22.47 76. (All N, (((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) => (((convergent_lines T_2 N) /\ (unorthogonal_lines T_2 N)) \/ ((convergent_lines T_1 N) /\ (unorthogonal_lines T_1 N))))) (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_0) (unorthogonal_lines T_2 T_0) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (distinct_lines T_1 T_1)) (-. (unorthogonal_lines T_0 T_1)) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (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 L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (-. (convergent_lines T_1 T_1)) ### All 75
% 22.27/22.47 77. (-. (convergent_lines T_1 T_1)) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (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 X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_1 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (unorthogonal_lines T_2 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))))))) ### All 76
% 22.27/22.47 78. (All X, (-. (distinct_lines X X))) (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_0) (unorthogonal_lines T_2 T_0) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (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 L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (-. (convergent_lines T_1 T_1)) ### All 77
% 22.27/22.47 79. ((convergent_lines T_0 T_0) \/ (unorthogonal_lines T_0 T_0)) (-. (convergent_lines T_1 T_1)) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (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 X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (unorthogonal_lines T_2 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))))))) (All X, (-. (distinct_lines X X))) (All X, (-. (convergent_lines X X))) ### Or 2 78
% 22.27/22.47 80. (All X, (-. (convergent_lines X X))) (All X, (-. (distinct_lines X X))) (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_2 T_0) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (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 L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (-. (convergent_lines T_1 T_1)) ### All 79
% 22.27/22.47 81. (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (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 X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (convergent_lines T_0 T_1) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (unorthogonal_lines T_2 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))))))) (All X, (-. (distinct_lines X X))) (All X, (-. (convergent_lines X X))) ### All 80
% 22.27/22.47 82. (All X, (-. (convergent_lines X X))) (All X, (-. (distinct_lines X X))) (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_2 T_0) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_0 T_1) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### All 81
% 22.27/22.47 83. (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_1) ### Axiom
% 22.27/22.47 84. ((convergent_lines T_0 T_1) \/ (unorthogonal_lines T_0 T_1)) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (unorthogonal_lines T_2 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))))))) (All X, (-. (distinct_lines X X))) (All X, (-. (convergent_lines X X))) ### Or 82 83
% 22.27/22.47 85. (All X, (-. (convergent_lines X X))) (All X, (-. (distinct_lines X X))) (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_2 T_0) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (-. (distinct_lines T_2 T_1)) (-. (unorthogonal_lines T_0 T_1)) (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 M))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### All 84
% 22.27/22.47 86. (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (unorthogonal_lines T_0 T_1)) (-. (distinct_lines T_2 T_1)) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (unorthogonal_lines T_2 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))))))) (All X, (-. (distinct_lines X X))) (All X, (-. (convergent_lines X X))) ### All 85
% 22.27/22.47 87. (-. ((unorthogonal_lines T_2 T_0) => ((distinct_lines T_2 T_1) \/ (unorthogonal_lines T_0 T_1)))) (All X, (-. (convergent_lines X X))) (All X, (-. (distinct_lines X X))) (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, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### ConjTree 86
% 22.27/22.47 88. (-. (All N, ((unorthogonal_lines T_2 T_0) => ((distinct_lines T_2 N) \/ (unorthogonal_lines T_0 N))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_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 X, (-. (distinct_lines X X))) (All X, (-. (convergent_lines X X))) ### NotAllEx 87
% 22.27/22.47 89. (-. (All M, (All N, ((unorthogonal_lines T_2 M) => ((distinct_lines T_2 N) \/ (unorthogonal_lines M N)))))) (All X, (-. (convergent_lines X X))) (All X, (-. (distinct_lines X X))) (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, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_lines Y Z)))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### NotAllEx 88
% 22.27/22.47 90. (-. (All L, (All M, (All N, ((unorthogonal_lines L M) => ((distinct_lines L N) \/ (unorthogonal_lines M N))))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (All X, (All Y, ((convergent_lines X Y) => (distinct_lines X Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (All Z, ((distinct_lines X Y) => ((distinct_lines X Z) \/ (distinct_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 X, (-. (distinct_lines X X))) (All X, (-. (convergent_lines X X))) ### NotAllEx 89
% 22.27/22.47 % SZS output end Proof
% 22.27/22.47 (* END-PROOF *)
%------------------------------------------------------------------------------