TSTP Solution File: GEO218+3 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : GEO218+3 : TPTP v8.1.0. Released v4.0.0.
% 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 06:31:15 EDT 2022
% Result : Theorem 68.10s 68.30s
% Output : Proof 68.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO218+3 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.35 % Computer : n004.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 : Sat Jun 18 04:20:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 68.10/68.30 % SZS status Theorem
% 68.10/68.30 (* PROOF-FOUND *)
% 68.10/68.30 (* BEGIN-PROOF *)
% 68.10/68.30 % SZS output start Proof
% 68.10/68.30 1. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_1)) ### Axiom
% 68.10/68.30 2. (-. (convergent_lines T_0 T_2)) (convergent_lines T_0 T_2) ### Axiom
% 68.10/68.30 3. (convergent_lines T_1 T_2) (-. (convergent_lines T_1 T_2)) ### Axiom
% 68.10/68.30 4. (-. (convergent_lines T_1 T_1)) (convergent_lines T_1 T_1) ### Axiom
% 68.10/68.30 5. (-. (convergent_lines T_2 T_1)) (convergent_lines T_2 T_1) ### Axiom
% 68.10/68.30 6. ((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 3 4 5
% 68.10/68.30 7. (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 6
% 68.10/68.30 8. (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 7
% 68.10/68.30 9. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines T_1 T_2) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) ### All 8
% 68.10/68.30 10. ((convergent_lines T_0 T_1) => ((convergent_lines T_0 T_2) \/ (convergent_lines T_1 T_2))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_2)) (convergent_lines T_0 T_1) ### DisjTree 1 2 9
% 68.10/68.30 11. (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_2)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) ### All 10
% 68.10/68.30 12. (All Y, (All Z, ((convergent_lines T_0 Y) => ((convergent_lines T_0 Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_2 T_1)) (-. (convergent_lines T_1 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_2)) (convergent_lines T_0 T_1) ### All 11
% 68.10/68.30 13. (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_2)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_1 T_1)) (-. (convergent_lines T_2 T_1)) ### All 12
% 68.10/68.30 14. (All X, (-. (convergent_lines X X))) (-. (convergent_lines T_2 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_2)) (convergent_lines T_0 T_1) ### All 13
% 68.10/68.30 15. (unorthogonal_lines T_2 T_1) (-. (unorthogonal_lines T_2 T_1)) ### Axiom
% 68.10/68.30 16. (-. (convergent_lines T_2 T_2)) (convergent_lines T_2 T_2) ### Axiom
% 68.10/68.30 17. ((convergent_lines T_2 T_2) /\ (unorthogonal_lines T_2 T_2)) (-. (convergent_lines T_2 T_2)) ### And 16
% 68.10/68.30 18. (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_1) ### Axiom
% 68.10/68.30 19. (-. (-. (unorthogonal_lines T_0 T_1))) (-. (unorthogonal_lines T_0 T_1)) ### NotNot 18
% 68.10/68.30 20. (-. ((-. (convergent_lines T_0 T_1)) \/ (-. (unorthogonal_lines T_0 T_1)))) (-. (unorthogonal_lines T_0 T_1)) ### NotOr 19
% 68.10/68.30 21. (-. (convergent_lines T_0 T_2)) (convergent_lines T_0 T_2) ### Axiom
% 68.10/68.30 22. (-. (-. (convergent_lines T_0 T_2))) (-. (convergent_lines T_0 T_2)) ### NotNot 21
% 68.10/68.30 23. (-. ((-. (convergent_lines T_0 T_2)) \/ (-. (unorthogonal_lines T_0 T_2)))) (-. (convergent_lines T_0 T_2)) ### NotOr 22
% 68.10/68.30 24. (convergent_lines T_1 T_2) (-. (convergent_lines T_1 T_2)) ### Axiom
% 68.10/68.30 25. (unorthogonal_lines T_1 T_2) (-. (unorthogonal_lines T_1 T_2)) ### Axiom
% 68.10/68.30 26. ((((-. (convergent_lines T_0 T_1)) \/ (-. (unorthogonal_lines T_0 T_1))) /\ ((-. (convergent_lines T_0 T_2)) \/ (-. (unorthogonal_lines T_0 T_2)))) => ((-. (convergent_lines T_1 T_2)) \/ (-. (unorthogonal_lines T_1 T_2)))) (unorthogonal_lines T_1 T_2) (convergent_lines T_1 T_2) (-. (convergent_lines T_0 T_2)) (-. (unorthogonal_lines T_0 T_1)) ### DisjTree 20 23 24 25
% 68.10/68.31 27. (All N, ((((-. (convergent_lines T_0 T_1)) \/ (-. (unorthogonal_lines T_0 T_1))) /\ ((-. (convergent_lines T_0 N)) \/ (-. (unorthogonal_lines T_0 N)))) => ((-. (convergent_lines T_1 N)) \/ (-. (unorthogonal_lines T_1 N))))) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_0 T_2)) (convergent_lines T_1 T_2) (unorthogonal_lines T_1 T_2) ### All 26
% 68.10/68.31 28. (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_1 T_2) (convergent_lines T_1 T_2) (-. (convergent_lines T_0 T_2)) (-. (unorthogonal_lines T_0 T_1)) ### All 27
% 68.10/68.31 29. ((convergent_lines T_1 T_2) /\ (unorthogonal_lines T_1 T_2)) (-. (unorthogonal_lines T_0 T_1)) (-. (convergent_lines T_0 T_2)) (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)))))) ### And 28
% 68.10/68.31 30. (((convergent_lines T_2 T_1) /\ (unorthogonal_lines T_2 T_1)) => (((convergent_lines T_2 T_2) /\ (unorthogonal_lines T_2 T_2)) \/ ((convergent_lines T_1 T_2) /\ (unorthogonal_lines T_1 T_2)))) (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)) (-. (convergent_lines T_2 T_2)) (unorthogonal_lines T_2 T_1) (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_2)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (-. (convergent_lines X X))) ### DisjTree 14 15 17 29
% 68.10/68.31 31. (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 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_0 T_2)) (convergent_lines T_0 T_1) (unorthogonal_lines T_2 T_1) (-. (convergent_lines T_2 T_2)) (-. (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 30
% 68.10/68.31 32. (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_2)) (unorthogonal_lines T_2 T_1) (convergent_lines T_0 T_1) (-. (convergent_lines T_0 T_2)) (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 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 31
% 68.10/68.31 33. (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, (-. (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_0 T_2)) (convergent_lines T_0 T_1) (unorthogonal_lines T_2 T_1) (-. (convergent_lines T_2 T_2)) (-. (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 32
% 68.10/68.32 34. (-. (unorthogonal_lines T_0 T_1)) (unorthogonal_lines T_0 T_1) ### Axiom
% 68.10/68.32 35. ((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_2)) (unorthogonal_lines T_2 T_1) (-. (convergent_lines T_0 T_2)) (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, (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)))))) ### Or 33 34
% 68.10/68.32 36. (All M, ((convergent_lines T_0 M) \/ (unorthogonal_lines T_0 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, (-. (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_0 T_2)) (unorthogonal_lines T_2 T_1) (-. (convergent_lines T_2 T_2)) (-. (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 35
% 68.10/68.32 37. (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, (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_2)) (unorthogonal_lines T_2 T_1) (-. (convergent_lines T_0 T_2)) (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))) ### All 36
% 68.10/68.32 38. (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L 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_0 T_2)) (unorthogonal_lines T_2 T_1) (-. (convergent_lines T_2 T_2)) (-. (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, (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 37
% 68.10/68.32 39. (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, (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_2 T_1) (-. (convergent_lines T_0 T_2)) (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 L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### All 38
% 68.10/68.32 40. (-. (-. (unorthogonal_lines T_2 T_1))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L 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_0 T_2)) (-. (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, (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))))))) ### NotNot 39
% 68.10/68.32 41. (-. (orthogonal_lines T_2 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, (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_2)) (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 L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### Definition-Pseudo(orthogonal_lines) 40
% 68.10/68.32 42. (orthogonal_lines T_0 T_1) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L 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_0 T_2)) (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, (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))))))) (-. (orthogonal_lines T_2 T_1)) ### Definition-Pseudo(orthogonal_lines) 41
% 68.10/68.32 43. (parallel_lines T_0 T_2) (-. (orthogonal_lines T_2 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, (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))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) (orthogonal_lines T_0 T_1) ### Definition-Pseudo(parallel_lines) 42
% 68.10/68.32 44. (-. (((parallel_lines T_0 T_2) /\ (orthogonal_lines T_0 T_1)) => (orthogonal_lines T_2 T_1))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L 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)))))) (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, (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))))))) ### ConjTree 43
% 68.10/68.32 45. (-. (All N, (((parallel_lines T_0 T_2) /\ (orthogonal_lines T_0 N)) => (orthogonal_lines T_2 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))))))) (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))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### NotAllEx 44
% 68.10/68.33 46. (-. (All M, (All N, (((parallel_lines T_0 M) /\ (orthogonal_lines T_0 N)) => (orthogonal_lines M N))))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L 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)))))) (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, (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))))))) ### NotAllEx 45
% 68.10/68.33 47. (-. (All L, (All M, (All N, (((parallel_lines L M) /\ (orthogonal_lines L N)) => (orthogonal_lines M 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))))))) (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))) (All L, (All M, ((convergent_lines L M) \/ (unorthogonal_lines L M)))) ### NotAllEx 46
% 68.10/68.33 % SZS output end Proof
% 68.10/68.33 (* END-PROOF *)
%------------------------------------------------------------------------------