TSTP Solution File: GEO179+2 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : GEO179+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 06:30:42 EDT 2022
% Result : Theorem 2.34s 2.51s
% Output : Proof 2.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO179+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 18 01:02:37 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.34/2.51 % SZS status Theorem
% 2.34/2.51 (* PROOF-FOUND *)
% 2.34/2.51 (* BEGIN-PROOF *)
% 2.34/2.51 % SZS output start Proof
% 2.34/2.51 1. (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (apart_point_and_line T_0 (line_connecting T_1 T_2))) ### Axiom
% 2.34/2.51 2. (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1)) ### Axiom
% 2.34/2.51 3. (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (apart_point_and_line T_0 (line_connecting T_1 T_2))) ### Axiom
% 2.34/2.51 4. (distinct_points T_0 T_1) (-. (distinct_points T_0 T_1)) ### Axiom
% 2.34/2.51 5. (apart_point_and_line T_0 (line_connecting T_0 T_1)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_1))) ### Axiom
% 2.34/2.51 6. (distinct_points T_0 T_0) ### Extension/test/apart1
% 2.34/2.51 7. ((distinct_points T_0 T_0) /\ (distinct_points T_0 T_1)) ### And 6
% 2.34/2.51 8. ((distinct_points T_0 T_1) => ((apart_point_and_line T_0 (line_connecting T_0 T_1)) => ((distinct_points T_0 T_0) /\ (distinct_points T_0 T_1)))) (apart_point_and_line T_0 (line_connecting T_0 T_1)) (distinct_points T_0 T_1) ### DisjTree 4 5 7
% 2.34/2.52 9. (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (distinct_points T_0 T_1) (apart_point_and_line T_0 (line_connecting T_0 T_1)) ### All 8
% 2.34/2.52 10. (distinct_points T_1 T_2) (-. (distinct_points T_1 T_2)) ### Axiom
% 2.34/2.52 11. (apart_point_and_line T_1 (line_connecting T_1 T_2)) (-. (apart_point_and_line T_1 (line_connecting T_1 T_2))) ### Axiom
% 2.34/2.52 12. (distinct_points T_1 T_1) ### Extension/test/apart1
% 2.34/2.52 13. ((distinct_points T_1 T_1) /\ (distinct_points T_1 T_2)) ### And 12
% 2.34/2.52 14. ((distinct_points T_1 T_2) => ((apart_point_and_line T_1 (line_connecting T_1 T_2)) => ((distinct_points T_1 T_1) /\ (distinct_points T_1 T_2)))) (apart_point_and_line T_1 (line_connecting T_1 T_2)) (distinct_points T_1 T_2) ### DisjTree 10 11 13
% 2.34/2.52 15. (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) (apart_point_and_line T_1 (line_connecting T_1 T_2)) ### All 14
% 2.34/2.52 16. ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 T_1) \/ (apart_point_and_line T_1 (line_connecting T_1 T_2)))) (distinct_points T_1 T_2) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (apart_point_and_line T_0 (line_connecting T_0 T_1)) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) ### DisjTree 3 9 15
% 2.34/2.52 17. (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z (line_connecting T_1 T_2))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (apart_point_and_line T_0 (line_connecting T_0 T_1)) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) ### All 16
% 2.34/2.52 18. ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1)) \/ (apart_point_and_line T_0 (line_connecting T_0 T_1)))) (distinct_points T_1 T_2) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z (line_connecting T_1 T_2))))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) ### DisjTree 1 2 17
% 2.34/2.52 19. (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z (line_connecting T_1 T_2))))) (All Z, ((distinct_points T_0 T_1) => ((apart_point_and_line Z (line_connecting T_0 T_1)) => ((distinct_points Z T_0) /\ (distinct_points Z T_1))))) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) ### All 18
% 2.34/2.52 20. (All Y, (All Z, ((distinct_points T_0 Y) => ((apart_point_and_line Z (line_connecting T_0 Y)) => ((distinct_points Z T_0) /\ (distinct_points Z Y)))))) (distinct_points T_1 T_2) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z (line_connecting T_1 T_2))))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) ### All 19
% 2.34/2.52 21. (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z (line_connecting T_1 T_2))))) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) ### All 20
% 2.34/2.52 22. (All Y, (All Z, ((apart_point_and_line T_0 Y) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z Y))))) (distinct_points T_1 T_2) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) ### All 21
% 2.34/2.52 23. (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) ### All 22
% 2.34/2.52 24. (All Y, (All Z, ((distinct_points T_1 Y) => ((apart_point_and_line Z (line_connecting T_1 Y)) => ((distinct_points Z T_1) /\ (distinct_points Z Y)))))) (distinct_points T_1 T_2) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) ### All 23
% 2.34/2.54 25. (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (distinct_points T_1 T_2) ### All 24
% 2.34/2.54 26. (All Y, (All Z, ((apart_point_and_line T_0 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_0 Z))))) (distinct_points T_1 T_2) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) ### All 25
% 2.34/2.54 27. (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1))) (distinct_points T_1 T_2) ### All 26
% 2.34/2.54 28. (distinct_points T_1 T_2) (-. (distinct_points T_1 T_2)) ### Axiom
% 2.34/2.54 29. (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (apart_point_and_line T_0 (line_connecting T_1 T_2))) ### Axiom
% 2.34/2.54 30. (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (apart_point_and_line T_0 (line_connecting T_1 T_2))) ### Axiom
% 2.34/2.54 31. (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2)) ### Axiom
% 2.34/2.54 32. (distinct_points T_0 T_2) (-. (distinct_points T_0 T_2)) ### Axiom
% 2.34/2.54 33. (apart_point_and_line T_0 (line_connecting T_0 T_2)) (-. (apart_point_and_line T_0 (line_connecting T_0 T_2))) ### Axiom
% 2.34/2.54 34. ((distinct_points T_0 T_0) /\ (distinct_points T_0 T_2)) ### And 6
% 2.34/2.54 35. ((distinct_points T_0 T_2) => ((apart_point_and_line T_0 (line_connecting T_0 T_2)) => ((distinct_points T_0 T_0) /\ (distinct_points T_0 T_2)))) (apart_point_and_line T_0 (line_connecting T_0 T_2)) (distinct_points T_0 T_2) ### DisjTree 32 33 34
% 2.34/2.54 36. (All Z, ((distinct_points T_0 T_2) => ((apart_point_and_line Z (line_connecting T_0 T_2)) => ((distinct_points Z T_0) /\ (distinct_points Z T_2))))) (distinct_points T_0 T_2) (apart_point_and_line T_0 (line_connecting T_0 T_2)) ### All 35
% 2.34/2.54 37. ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2)) \/ (apart_point_and_line T_0 (line_connecting T_0 T_2)))) (distinct_points T_0 T_2) (All Z, ((distinct_points T_0 T_2) => ((apart_point_and_line Z (line_connecting T_0 T_2)) => ((distinct_points Z T_0) /\ (distinct_points Z T_2))))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) ### DisjTree 30 31 36
% 2.34/2.54 38. (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (All Z, ((distinct_points T_0 T_2) => ((apart_point_and_line Z (line_connecting T_0 T_2)) => ((distinct_points Z T_0) /\ (distinct_points Z T_2))))) (distinct_points T_0 T_2) ### All 37
% 2.34/2.54 39. (All Y, (All Z, ((distinct_points T_0 Y) => ((apart_point_and_line Z (line_connecting T_0 Y)) => ((distinct_points Z T_0) /\ (distinct_points Z Y)))))) (distinct_points T_0 T_2) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) ### All 38
% 2.34/2.54 40. (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (distinct_points T_0 T_2) ### All 39
% 2.34/2.54 41. (-. (apart_point_and_line T_2 (line_connecting T_1 T_2))) (apart_point_and_line T_2 (line_connecting T_1 T_2)) ### Axiom
% 2.34/2.54 42. ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 T_2) \/ (apart_point_and_line T_2 (line_connecting T_1 T_2)))) (-. (apart_point_and_line T_2 (line_connecting T_1 T_2))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) ### DisjTree 29 40 41
% 2.34/2.54 43. (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z (line_connecting T_1 T_2))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (-. (apart_point_and_line T_2 (line_connecting T_1 T_2))) ### All 42
% 2.34/2.54 44. (distinct_points T_2 T_2) ### Extension/test/apart1
% 2.34/2.54 45. ((distinct_points T_2 T_1) /\ (distinct_points T_2 T_2)) ### And 44
% 2.34/2.54 46. ((distinct_points T_1 T_2) => ((apart_point_and_line T_2 (line_connecting T_1 T_2)) => ((distinct_points T_2 T_1) /\ (distinct_points T_2 T_2)))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z (line_connecting T_1 T_2))))) (distinct_points T_1 T_2) ### DisjTree 28 43 45
% 2.34/2.54 47. (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z (line_connecting T_1 T_2))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) ### All 46
% 2.44/2.63 48. (All Y, (All Z, ((apart_point_and_line T_0 Y) => ((distinct_points T_0 Z) \/ (apart_point_and_line Z Y))))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (distinct_points T_1 T_2) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) ### All 47
% 2.44/2.63 49. (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All Z, ((distinct_points T_1 T_2) => ((apart_point_and_line Z (line_connecting T_1 T_2)) => ((distinct_points Z T_1) /\ (distinct_points Z T_2))))) (distinct_points T_1 T_2) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) ### All 48
% 2.44/2.63 50. (All Y, (All Z, ((distinct_points T_1 Y) => ((apart_point_and_line Z (line_connecting T_1 Y)) => ((distinct_points Z T_1) /\ (distinct_points Z Y)))))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (distinct_points T_1 T_2) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) ### All 49
% 2.44/2.63 51. (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (distinct_points T_1 T_2) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All Z, ((apart_point_and_line T_0 (line_connecting T_1 T_2)) => ((distinct_lines (line_connecting T_1 T_2) Z) \/ (apart_point_and_line T_0 Z)))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) ### All 50
% 2.44/2.63 52. (All Y, (All Z, ((apart_point_and_line T_0 Y) => ((distinct_lines Y Z) \/ (apart_point_and_line T_0 Z))))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (distinct_points T_1 T_2) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) ### All 51
% 2.44/2.63 53. (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (distinct_points T_1 T_2) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (-. (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))) ### All 52
% 2.44/2.63 54. (-. ((distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1)) /\ (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2)))) (distinct_points T_1 T_2) (apart_point_and_line T_0 (line_connecting T_1 T_2)) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) ### NotAnd 27 53
% 2.44/2.63 55. (-. (((distinct_points T_1 T_2) /\ (apart_point_and_line T_0 (line_connecting T_1 T_2))) => ((distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_1)) /\ (distinct_lines (line_connecting T_1 T_2) (line_connecting T_0 T_2))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) ### ConjTree 54
% 2.44/2.63 56. (-. (All Z, (((distinct_points T_1 T_2) /\ (apart_point_and_line Z (line_connecting T_1 T_2))) => ((distinct_lines (line_connecting T_1 T_2) (line_connecting Z T_1)) /\ (distinct_lines (line_connecting T_1 T_2) (line_connecting Z T_2)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) ### NotAllEx 55
% 2.44/2.63 57. (-. (All Y, (All Z, (((distinct_points T_1 Y) /\ (apart_point_and_line Z (line_connecting T_1 Y))) => ((distinct_lines (line_connecting T_1 Y) (line_connecting Z T_1)) /\ (distinct_lines (line_connecting T_1 Y) (line_connecting Z Y))))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) ### NotAllEx 56
% 2.44/2.63 58. (-. (All X, (All Y, (All Z, (((distinct_points X Y) /\ (apart_point_and_line Z (line_connecting X Y))) => ((distinct_lines (line_connecting X Y) (line_connecting Z X)) /\ (distinct_lines (line_connecting X Y) (line_connecting Z Y)))))))) (All X, (All Y, (All Z, ((distinct_points X Y) => ((apart_point_and_line Z (line_connecting X Y)) => ((distinct_points Z X) /\ (distinct_points Z Y))))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_points X Z) \/ (apart_point_and_line Z Y)))))) (All X, (All Y, (All Z, ((apart_point_and_line X Y) => ((distinct_lines Y Z) \/ (apart_point_and_line X Z)))))) ### NotAllEx 57
% 2.44/2.63 % SZS output end Proof
% 2.44/2.63 (* END-PROOF *)
%------------------------------------------------------------------------------