TSTP Solution File: GEO255+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : GEO255+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n022.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 06:31:37 EDT 2022
% Result : Theorem 15.35s 15.57s
% Output : Proof 15.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO255+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.10/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 16:08:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 15.35/15.57 % SZS status Theorem
% 15.35/15.57 (* PROOF-FOUND *)
% 15.35/15.57 (* BEGIN-PROOF *)
% 15.35/15.57 % SZS output start Proof
% 15.35/15.57 1. (line T_0) (-. (line T_0)) ### Axiom
% 15.35/15.57 2. (-. (line (reverse_line T_0))) (line (reverse_line T_0)) ### Axiom
% 15.35/15.57 3. ((line T_0) => (line (reverse_line T_0))) (-. (line (reverse_line T_0))) (line T_0) ### Imply 1 2
% 15.35/15.57 4. (All L, ((line L) => (line (reverse_line L)))) (line T_0) (-. (line (reverse_line T_0))) ### All 3
% 15.35/15.57 5. (line T_0) (-. (line T_0)) ### Axiom
% 15.35/15.57 6. (unequally_directed_lines (reverse_line T_0) T_0) (-. (unequally_directed_lines (reverse_line T_0) T_0)) ### Axiom
% 15.35/15.57 7. (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (reverse_line T_0) (reverse_line T_0)) ### Axiom
% 15.35/15.57 8. (unequally_directed_lines T_0 (reverse_line T_0)) (-. (unequally_directed_lines T_0 (reverse_line T_0))) ### Axiom
% 15.35/15.57 9. (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (unequally_directed_lines T_0 (line_connecting T_1 T_2)) ### Axiom
% 15.35/15.57 10. (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (-. (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2))) ### Axiom
% 15.35/15.57 11. (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (reverse_line T_0) (reverse_line T_0)) ### Axiom
% 15.35/15.57 12. (-. (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0))) (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0)) ### Axiom
% 15.35/15.57 13. ((unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) => ((unequally_directed_lines (reverse_line T_0) (reverse_line T_0)) \/ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0)))) (-. (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) ### DisjTree 10 11 12
% 15.35/15.57 14. (All N, ((unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines (line_connecting T_1 T_2) N)))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (-. (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0))) ### All 13
% 15.35/15.57 15. (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (-. (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) ### All 14
% 15.35/15.57 16. (unequally_directed_lines T_0 (reverse_line T_0)) (-. (unequally_directed_lines T_0 (reverse_line T_0))) ### Axiom
% 15.35/15.57 17. (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (unequally_directed_lines T_0 (line_connecting T_2 T_1)) ### Axiom
% 15.35/15.57 18. (unequally_directed_lines (reverse_line T_0) (line_connecting T_2 T_1)) (-. (unequally_directed_lines (reverse_line T_0) (line_connecting T_2 T_1))) ### Axiom
% 15.35/15.57 19. (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (reverse_line T_0) (reverse_line T_0)) ### Axiom
% 15.35/15.57 20. (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (-. (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2))) ### Axiom
% 15.35/15.57 21. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line T_0)) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line T_0))) ### Axiom
% 15.35/15.57 22. (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2))) ### Axiom
% 15.35/15.57 23. (-. (unequally_directed_lines (reverse_line T_0) (reverse_line (line_connecting T_1 T_2)))) (unequally_directed_lines (reverse_line T_0) (reverse_line (line_connecting T_1 T_2))) ### Axiom
% 15.35/15.57 24. ((unequally_directed_lines (line_connecting T_2 T_1) (reverse_line T_0)) => ((unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2))) \/ (unequally_directed_lines (reverse_line T_0) (reverse_line (line_connecting T_1 T_2))))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line T_0)) ### DisjTree 21 22 23
% 15.35/15.57 25. (All N, ((unequally_directed_lines (line_connecting T_2 T_1) (reverse_line T_0)) => ((unequally_directed_lines (line_connecting T_2 T_1) N) \/ (unequally_directed_lines (reverse_line T_0) N)))) (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line T_0)) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line (line_connecting T_1 T_2)))) ### All 24
% 15.35/15.57 26. (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (reverse_line T_0) (reverse_line T_0)) ### Axiom
% 15.35/15.57 27. ((unequally_directed_lines (reverse_line T_0) T_0) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) ### And 26
% 15.35/15.57 28. (-. (unequally_directed_lines (line_connecting T_1 T_2) T_0)) (unequally_directed_lines (line_connecting T_1 T_2) T_0) ### Axiom
% 15.35/15.57 29. ((unequally_directed_lines (line_connecting T_1 T_2) T_0) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0))) (-. (unequally_directed_lines (line_connecting T_1 T_2) T_0)) ### And 28
% 15.35/15.57 30. (((unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line (line_connecting T_1 T_2)))) => (((unequally_directed_lines (reverse_line T_0) T_0) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) \/ ((unequally_directed_lines (line_connecting T_1 T_2) T_0) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0))))) (-. (unequally_directed_lines (line_connecting T_1 T_2) T_0)) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line T_0)) (All N, ((unequally_directed_lines (line_connecting T_2 T_1) (reverse_line T_0)) => ((unequally_directed_lines (line_connecting T_2 T_1) N) \/ (unequally_directed_lines (reverse_line T_0) N)))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) ### DisjTree 20 25 27 29
% 15.35/15.57 31. (All N, (((unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line (line_connecting T_1 T_2)))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines (line_connecting T_1 T_2) N) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line N)))))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (All N, ((unequally_directed_lines (line_connecting T_2 T_1) (reverse_line T_0)) => ((unequally_directed_lines (line_connecting T_2 T_1) N) \/ (unequally_directed_lines (reverse_line T_0) N)))) (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line T_0)) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (-. (unequally_directed_lines (line_connecting T_1 T_2) T_0)) ### All 30
% 15.35/15.57 32. (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (-. (unequally_directed_lines (line_connecting T_1 T_2) T_0)) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line T_0)) (All N, ((unequally_directed_lines (line_connecting T_2 T_1) (reverse_line T_0)) => ((unequally_directed_lines (line_connecting T_2 T_1) N) \/ (unequally_directed_lines (reverse_line T_0) N)))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) ### All 31
% 15.44/15.62 33. (All M, (All N, ((unequally_directed_lines (line_connecting T_2 T_1) M) => ((unequally_directed_lines (line_connecting T_2 T_1) N) \/ (unequally_directed_lines M N))))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line T_0)) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (-. (unequally_directed_lines (line_connecting T_1 T_2) T_0)) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) ### All 32
% 15.44/15.62 34. (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (-. (unequally_directed_lines (line_connecting T_1 T_2) T_0)) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line T_0)) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) ### All 33
% 15.44/15.62 35. ((unequally_directed_lines (reverse_line T_0) (line_connecting T_2 T_1)) => ((unequally_directed_lines (reverse_line T_0) (reverse_line T_0)) \/ (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line T_0)))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines (line_connecting T_1 T_2) T_0)) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_2 T_1)) ### DisjTree 18 19 34
% 15.44/15.62 36. (All N, ((unequally_directed_lines (reverse_line T_0) (line_connecting T_2 T_1)) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines (line_connecting T_2 T_1) N)))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_2 T_1)) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (-. (unequally_directed_lines (line_connecting T_1 T_2) T_0)) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) ### All 35
% 15.44/15.62 37. (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines (line_connecting T_1 T_2) T_0)) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_2 T_1)) ### All 36
% 15.44/15.62 38. ((unequally_directed_lines T_0 (reverse_line T_0)) => ((unequally_directed_lines T_0 (line_connecting T_2 T_1)) \/ (unequally_directed_lines (reverse_line T_0) (line_connecting T_2 T_1)))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (-. (unequally_directed_lines (line_connecting T_1 T_2) T_0)) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (unequally_directed_lines T_0 (reverse_line T_0)) ### DisjTree 16 17 37
% 15.44/15.62 39. (All N, ((unequally_directed_lines T_0 (reverse_line T_0)) => ((unequally_directed_lines T_0 N) \/ (unequally_directed_lines (reverse_line T_0) N)))) (unequally_directed_lines T_0 (reverse_line T_0)) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines (line_connecting T_1 T_2) T_0)) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) ### All 38
% 15.44/15.62 40. (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0)) (-. (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0))) ### Axiom
% 15.44/15.62 41. (unequally_directed_lines (line_connecting T_1 T_2) T_0) (-. (unequally_directed_lines (line_connecting T_1 T_2) T_0)) ### Axiom
% 15.74/15.96 42. (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0)) (-. (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0))) ### Axiom
% 15.74/15.96 43. (unequally_directed_lines (line_connecting T_1 T_2) (line_connecting T_1 T_2)) (-. (unequally_directed_lines (line_connecting T_1 T_2) (line_connecting T_1 T_2))) ### Axiom
% 15.74/15.96 44. (All L, (-. (unequally_directed_lines L L))) (unequally_directed_lines (line_connecting T_1 T_2) (line_connecting T_1 T_2)) ### All 43
% 15.74/15.96 45. ((unequally_directed_lines (line_connecting T_1 T_2) (line_connecting T_1 T_2)) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line (line_connecting T_1 T_2)))) (All L, (-. (unequally_directed_lines L L))) ### And 44
% 15.74/15.96 46. (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (unequally_directed_lines T_0 (line_connecting T_1 T_2)) ### Axiom
% 15.74/15.96 47. ((unequally_directed_lines T_0 (line_connecting T_1 T_2)) /\ (unequally_directed_lines T_0 (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) ### And 46
% 15.74/15.96 48. (((unequally_directed_lines (line_connecting T_1 T_2) T_0) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0))) => (((unequally_directed_lines (line_connecting T_1 T_2) (line_connecting T_1 T_2)) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line (line_connecting T_1 T_2)))) \/ ((unequally_directed_lines T_0 (line_connecting T_1 T_2)) /\ (unequally_directed_lines T_0 (reverse_line (line_connecting T_1 T_2)))))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All L, (-. (unequally_directed_lines L L))) (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0)) (unequally_directed_lines (line_connecting T_1 T_2) T_0) ### DisjTree 41 42 45 47
% 15.74/15.96 49. (All N, (((unequally_directed_lines (line_connecting T_1 T_2) T_0) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0))) => (((unequally_directed_lines (line_connecting T_1 T_2) N) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line N))) \/ ((unequally_directed_lines T_0 N) /\ (unequally_directed_lines T_0 (reverse_line N)))))) (unequally_directed_lines (line_connecting T_1 T_2) T_0) (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0)) (All L, (-. (unequally_directed_lines L L))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) ### All 48
% 15.74/15.96 50. ((unequally_directed_lines (line_connecting T_1 T_2) T_0) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All L, (-. (unequally_directed_lines L L))) (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0)) (All N, (((unequally_directed_lines (line_connecting T_1 T_2) T_0) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0))) => (((unequally_directed_lines (line_connecting T_1 T_2) N) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line N))) \/ ((unequally_directed_lines T_0 N) /\ (unequally_directed_lines T_0 (reverse_line N)))))) ### And 49
% 15.74/15.96 51. (-. (unequally_directed_lines T_0 T_0)) (unequally_directed_lines T_0 T_0) ### Axiom
% 15.74/15.96 52. ((unequally_directed_lines T_0 T_0) /\ (unequally_directed_lines T_0 (reverse_line T_0))) (-. (unequally_directed_lines T_0 T_0)) ### And 51
% 15.74/15.96 53. (((unequally_directed_lines (line_connecting T_1 T_2) T_0) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0))) => (((unequally_directed_lines (line_connecting T_1 T_2) T_0) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0))) \/ ((unequally_directed_lines T_0 T_0) /\ (unequally_directed_lines T_0 (reverse_line T_0))))) (-. (unequally_directed_lines T_0 T_0)) (All N, (((unequally_directed_lines (line_connecting T_1 T_2) T_0) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0))) => (((unequally_directed_lines (line_connecting T_1 T_2) N) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line N))) \/ ((unequally_directed_lines T_0 N) /\ (unequally_directed_lines T_0 (reverse_line N)))))) (All L, (-. (unequally_directed_lines L L))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0)) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (unequally_directed_lines T_0 (reverse_line T_0)) (All N, ((unequally_directed_lines T_0 (reverse_line T_0)) => ((unequally_directed_lines T_0 N) \/ (unequally_directed_lines (reverse_line T_0) N)))) ### DisjTree 39 40 50 52
% 15.74/15.96 54. (All N, ((unequally_directed_lines T_0 (reverse_line T_0)) => ((unequally_directed_lines T_0 N) \/ (unequally_directed_lines (reverse_line T_0) N)))) (unequally_directed_lines T_0 (reverse_line T_0)) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0)) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All L, (-. (unequally_directed_lines L L))) (All N, (((unequally_directed_lines (line_connecting T_1 T_2) T_0) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0))) => (((unequally_directed_lines (line_connecting T_1 T_2) N) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line N))) \/ ((unequally_directed_lines T_0 N) /\ (unequally_directed_lines T_0 (reverse_line N)))))) (-. (unequally_directed_lines T_0 T_0)) ### All 53
% 15.74/15.96 55. (All M, (All N, (((unequally_directed_lines (line_connecting T_1 T_2) M) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line M))) => (((unequally_directed_lines (line_connecting T_1 T_2) N) /\ (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (-. (unequally_directed_lines T_0 T_0)) (All L, (-. (unequally_directed_lines L L))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0)) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (unequally_directed_lines T_0 (reverse_line T_0)) (All N, ((unequally_directed_lines T_0 (reverse_line T_0)) => ((unequally_directed_lines T_0 N) \/ (unequally_directed_lines (reverse_line T_0) N)))) ### All 54
% 15.74/15.97 56. (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (All N, ((unequally_directed_lines T_0 (reverse_line T_0)) => ((unequally_directed_lines T_0 N) \/ (unequally_directed_lines (reverse_line T_0) N)))) (unequally_directed_lines T_0 (reverse_line T_0)) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0)) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All L, (-. (unequally_directed_lines L L))) (-. (unequally_directed_lines T_0 T_0)) ### All 55
% 15.74/15.97 57. (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (reverse_line T_0) (reverse_line T_0)) ### Axiom
% 15.74/15.97 58. ((unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0)) => ((unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0)) \/ (unequally_directed_lines (reverse_line T_0) (reverse_line T_0)))) (-. (unequally_directed_lines T_0 T_0)) (All L, (-. (unequally_directed_lines L L))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (unequally_directed_lines T_0 (reverse_line T_0)) (All N, ((unequally_directed_lines T_0 (reverse_line T_0)) => ((unequally_directed_lines T_0 N) \/ (unequally_directed_lines (reverse_line T_0) N)))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) ### DisjTree 15 56 57
% 15.74/15.97 59. (All N, ((unequally_directed_lines (line_connecting T_1 T_2) (reverse_line T_0)) => ((unequally_directed_lines (line_connecting T_1 T_2) N) \/ (unequally_directed_lines (reverse_line T_0) N)))) (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (All N, ((unequally_directed_lines T_0 (reverse_line T_0)) => ((unequally_directed_lines T_0 N) \/ (unequally_directed_lines (reverse_line T_0) N)))) (unequally_directed_lines T_0 (reverse_line T_0)) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All L, (-. (unequally_directed_lines L L))) (-. (unequally_directed_lines T_0 T_0)) ### All 58
% 15.74/15.97 60. (All M, (All N, ((unequally_directed_lines (line_connecting T_1 T_2) M) => ((unequally_directed_lines (line_connecting T_1 T_2) N) \/ (unequally_directed_lines M N))))) (-. (unequally_directed_lines T_0 T_0)) (All L, (-. (unequally_directed_lines L L))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (unequally_directed_lines T_0 (reverse_line T_0)) (All N, ((unequally_directed_lines T_0 (reverse_line T_0)) => ((unequally_directed_lines T_0 N) \/ (unequally_directed_lines (reverse_line T_0) N)))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) ### All 59
% 15.74/15.97 61. (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (All N, ((unequally_directed_lines T_0 (reverse_line T_0)) => ((unequally_directed_lines T_0 N) \/ (unequally_directed_lines (reverse_line T_0) N)))) (unequally_directed_lines T_0 (reverse_line T_0)) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All L, (-. (unequally_directed_lines L L))) (-. (unequally_directed_lines T_0 T_0)) ### All 60
% 15.74/15.97 62. ((unequally_directed_lines T_0 (reverse_line T_0)) => ((unequally_directed_lines T_0 (line_connecting T_1 T_2)) \/ (unequally_directed_lines (reverse_line T_0) (line_connecting T_1 T_2)))) (-. (unequally_directed_lines T_0 T_0)) (All L, (-. (unequally_directed_lines L L))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (All N, ((unequally_directed_lines T_0 (reverse_line T_0)) => ((unequally_directed_lines T_0 N) \/ (unequally_directed_lines (reverse_line T_0) N)))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (unequally_directed_lines T_0 (reverse_line T_0)) ### DisjTree 8 9 61
% 15.74/15.97 63. (unequally_directed_lines T_0 (reverse_line T_0)) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (All N, ((unequally_directed_lines T_0 (reverse_line T_0)) => ((unequally_directed_lines T_0 N) \/ (unequally_directed_lines (reverse_line T_0) N)))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All L, (-. (unequally_directed_lines L L))) (-. (unequally_directed_lines T_0 T_0)) ### All 62
% 15.74/15.97 64. (All M, (All N, ((unequally_directed_lines T_0 M) => ((unequally_directed_lines T_0 N) \/ (unequally_directed_lines M N))))) (-. (unequally_directed_lines T_0 T_0)) (All L, (-. (unequally_directed_lines L L))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (unequally_directed_lines T_0 (reverse_line T_0)) ### All 63
% 15.74/15.97 65. (unequally_directed_lines T_0 (reverse_line T_0)) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All L, (-. (unequally_directed_lines L L))) (-. (unequally_directed_lines T_0 T_0)) ### All 64
% 15.74/15.97 66. ((unequally_directed_lines (reverse_line T_0) T_0) => ((unequally_directed_lines (reverse_line T_0) (reverse_line T_0)) \/ (unequally_directed_lines T_0 (reverse_line T_0)))) (-. (unequally_directed_lines T_0 T_0)) (All L, (-. (unequally_directed_lines L L))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (reverse_line T_0) T_0) ### DisjTree 6 7 65
% 15.81/16.01 67. (All N, ((unequally_directed_lines (reverse_line T_0) T_0) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines T_0 N)))) (unequally_directed_lines (reverse_line T_0) T_0) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All L, (-. (unequally_directed_lines L L))) (-. (unequally_directed_lines T_0 T_0)) ### All 66
% 15.81/16.01 68. (-. (unequally_directed_lines T_0 T_0)) (All L, (-. (unequally_directed_lines L L))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (All M, (All N, ((unequally_directed_lines (reverse_line T_0) M) => ((unequally_directed_lines (reverse_line T_0) N) \/ (unequally_directed_lines M N))))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (reverse_line T_0) T_0) ### All 67
% 15.81/16.01 69. (unequally_directed_lines (reverse_line T_0) T_0) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (All M, (All N, (((unequally_directed_lines (reverse_line T_0) M) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line M))) => (((unequally_directed_lines (reverse_line T_0) N) /\ (unequally_directed_lines (reverse_line T_0) (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N))))))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All L, (-. (unequally_directed_lines L L))) (-. (unequally_directed_lines T_0 T_0)) ### All 68
% 15.81/16.01 70. (-. (unequally_directed_lines T_0 T_0)) (All L, (-. (unequally_directed_lines L L))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (reverse_line T_0) T_0) ### All 69
% 15.81/16.01 71. (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (unequally_directed_lines (reverse_line T_0) (reverse_line T_0)) ### Axiom
% 15.81/16.01 72. (((line (reverse_line T_0)) /\ (line T_0)) => ((unequally_directed_lines (reverse_line T_0) T_0) \/ (unequally_directed_lines (reverse_line T_0) (reverse_line T_0)))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All L, (-. (unequally_directed_lines L L))) (-. (unequally_directed_lines T_0 T_0)) (line T_0) (All L, ((line L) => (line (reverse_line L)))) ### DisjTree 4 5 70 71
% 15.81/16.01 73. (All M, (((line (reverse_line T_0)) /\ (line M)) => ((unequally_directed_lines (reverse_line T_0) M) \/ (unequally_directed_lines (reverse_line T_0) (reverse_line M))))) (All L, ((line L) => (line (reverse_line L)))) (line T_0) (-. (unequally_directed_lines T_0 T_0)) (All L, (-. (unequally_directed_lines L L))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) ### All 72
% 15.81/16.01 74. (All L, (All M, (((line L) /\ (line M)) => ((unequally_directed_lines L M) \/ (unequally_directed_lines L (reverse_line M)))))) (-. (unequally_directed_lines (reverse_line T_0) (reverse_line T_0))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All L, (-. (unequally_directed_lines L L))) (-. (unequally_directed_lines T_0 T_0)) (line T_0) (All L, ((line L) => (line (reverse_line L)))) ### All 73
% 15.81/16.02 75. (All L, ((line L) => (line (reverse_line L)))) (line T_0) (-. (unequally_directed_lines T_0 T_0)) (All L, (-. (unequally_directed_lines L L))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All L, (All M, (((line L) /\ (line M)) => ((unequally_directed_lines L M) \/ (unequally_directed_lines L (reverse_line M)))))) ### All 74
% 15.81/16.02 76. (All L, (All M, (((line L) /\ (line M)) => ((unequally_directed_lines L M) \/ (unequally_directed_lines L (reverse_line M)))))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (-. (unequally_directed_lines (line_connecting T_2 T_1) (reverse_line (line_connecting T_1 T_2)))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All L, (-. (unequally_directed_lines L L))) (line T_0) (All L, ((line L) => (line (reverse_line L)))) ### All 75
% 15.81/16.02 77. (All B, (-. (unequally_directed_lines (line_connecting T_2 B) (reverse_line (line_connecting B T_2))))) (All L, ((line L) => (line (reverse_line L)))) (line T_0) (All L, (-. (unequally_directed_lines L L))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All L, (All M, (((line L) /\ (line M)) => ((unequally_directed_lines L M) \/ (unequally_directed_lines L (reverse_line M)))))) ### All 76
% 15.81/16.02 78. (All A, (All B, (-. (unequally_directed_lines (line_connecting A B) (reverse_line (line_connecting B A)))))) (All L, (All M, (((line L) /\ (line M)) => ((unequally_directed_lines L M) \/ (unequally_directed_lines L (reverse_line M)))))) (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All L, (-. (unequally_directed_lines L L))) (line T_0) (All L, ((line L) => (line (reverse_line L)))) ### All 77
% 15.81/16.02 79. ((distinct_points T_1 T_2) /\ ((-. ((left_apart_point T_1 T_0) \/ (left_apart_point T_1 (reverse_line T_0)))) /\ ((-. ((left_apart_point T_2 T_0) \/ (left_apart_point T_2 (reverse_line T_0)))) /\ (-. (unequally_directed_lines T_0 (line_connecting T_1 T_2)))))) (All L, ((line L) => (line (reverse_line L)))) (line T_0) (All L, (-. (unequally_directed_lines L L))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (All L, (All M, (((line L) /\ (line M)) => ((unequally_directed_lines L M) \/ (unequally_directed_lines L (reverse_line M)))))) (All A, (All B, (-. (unequally_directed_lines (line_connecting A B) (reverse_line (line_connecting B A)))))) ### ConjTree 78
% 15.81/16.02 80. (before_on_line T_0 T_1 T_2) (All A, (All B, (-. (unequally_directed_lines (line_connecting A B) (reverse_line (line_connecting B A)))))) (All L, (All M, (((line L) /\ (line M)) => ((unequally_directed_lines L M) \/ (unequally_directed_lines L (reverse_line M)))))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All L, (-. (unequally_directed_lines L L))) (line T_0) (All L, ((line L) => (line (reverse_line L)))) ### Definition-Pseudo(before_on_line) 79
% 15.81/16.02 81. ((distinct_points T_2 T_1) /\ ((-. ((left_apart_point T_2 T_0) \/ (left_apart_point T_2 (reverse_line T_0)))) /\ ((-. ((left_apart_point T_1 T_0) \/ (left_apart_point T_1 (reverse_line T_0)))) /\ (-. (unequally_directed_lines T_0 (line_connecting T_2 T_1)))))) (All L, ((line L) => (line (reverse_line L)))) (line T_0) (All L, (-. (unequally_directed_lines L L))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (All L, (All M, (((line L) /\ (line M)) => ((unequally_directed_lines L M) \/ (unequally_directed_lines L (reverse_line M)))))) (All A, (All B, (-. (unequally_directed_lines (line_connecting A B) (reverse_line (line_connecting B A)))))) (before_on_line T_0 T_1 T_2) ### ConjTree 80
% 15.81/16.02 82. (before_on_line T_0 T_2 T_1) (before_on_line T_0 T_1 T_2) (All A, (All B, (-. (unequally_directed_lines (line_connecting A B) (reverse_line (line_connecting B A)))))) (All L, (All M, (((line L) /\ (line M)) => ((unequally_directed_lines L M) \/ (unequally_directed_lines L (reverse_line M)))))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All L, (-. (unequally_directed_lines L L))) (line T_0) (All L, ((line L) => (line (reverse_line L)))) ### Definition-Pseudo(before_on_line) 81
% 15.81/16.02 83. (-. (((line T_0) /\ (distinct_points T_2 T_1)) => (-. ((before_on_line T_0 T_2 T_1) /\ (before_on_line T_0 T_1 T_2))))) (All L, ((line L) => (line (reverse_line L)))) (All L, (-. (unequally_directed_lines L L))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (All L, (All M, (((line L) /\ (line M)) => ((unequally_directed_lines L M) \/ (unequally_directed_lines L (reverse_line M)))))) (All A, (All B, (-. (unequally_directed_lines (line_connecting A B) (reverse_line (line_connecting B A)))))) ### ConjTree 82
% 15.81/16.02 84. (-. (All B, (((line T_0) /\ (distinct_points T_2 B)) => (-. ((before_on_line T_0 T_2 B) /\ (before_on_line T_0 B T_2)))))) (All A, (All B, (-. (unequally_directed_lines (line_connecting A B) (reverse_line (line_connecting B A)))))) (All L, (All M, (((line L) /\ (line M)) => ((unequally_directed_lines L M) \/ (unequally_directed_lines L (reverse_line M)))))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All L, (-. (unequally_directed_lines L L))) (All L, ((line L) => (line (reverse_line L)))) ### NotAllEx 83
% 15.81/16.02 85. (-. (All A, (All B, (((line T_0) /\ (distinct_points A B)) => (-. ((before_on_line T_0 A B) /\ (before_on_line T_0 B A))))))) (All L, ((line L) => (line (reverse_line L)))) (All L, (-. (unequally_directed_lines L L))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (All L, (All M, (((line L) /\ (line M)) => ((unequally_directed_lines L M) \/ (unequally_directed_lines L (reverse_line M)))))) (All A, (All B, (-. (unequally_directed_lines (line_connecting A B) (reverse_line (line_connecting B A)))))) ### NotAllEx 84
% 15.81/16.02 86. (-. (All L, (All A, (All B, (((line L) /\ (distinct_points A B)) => (-. ((before_on_line L A B) /\ (before_on_line L B A)))))))) (All A, (All B, (-. (unequally_directed_lines (line_connecting A B) (reverse_line (line_connecting B A)))))) (All L, (All M, (((line L) /\ (line M)) => ((unequally_directed_lines L M) \/ (unequally_directed_lines L (reverse_line M)))))) (All L, (All M, (All N, (((unequally_directed_lines L M) /\ (unequally_directed_lines L (reverse_line M))) => (((unequally_directed_lines L N) /\ (unequally_directed_lines L (reverse_line N))) \/ ((unequally_directed_lines M N) /\ (unequally_directed_lines M (reverse_line N)))))))) (All L, (All M, (All N, ((unequally_directed_lines L M) => ((unequally_directed_lines L N) \/ (unequally_directed_lines M N)))))) (All L, (-. (unequally_directed_lines L L))) (All L, ((line L) => (line (reverse_line L)))) ### NotAllEx 85
% 15.81/16.02 % SZS output end Proof
% 15.81/16.02 (* END-PROOF *)
%------------------------------------------------------------------------------