TSTP Solution File: GEO206+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : GEO206+1 : 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 : n027.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 06:31:05 EDT 2022
% Result : Theorem 43.95s 44.17s
% Output : Proof 43.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO206+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n027.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 02:22:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 43.95/44.17 % SZS status Theorem
% 43.95/44.17 (* PROOF-FOUND *)
% 43.95/44.17 (* BEGIN-PROOF *)
% 43.95/44.17 % SZS output start Proof
% 43.95/44.17 1. (distinct_lines T_0 (parallel_through_point T_1 T_2)) (-. (distinct_lines T_0 (parallel_through_point T_1 T_2))) ### Axiom
% 43.95/44.17 2. (-. (apart_point_and_line T_2 T_0)) (apart_point_and_line T_2 T_0) ### Axiom
% 43.95/44.17 3. (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (apart_point_and_line T_2 (parallel_through_point T_1 T_2)) ### Axiom
% 43.95/44.17 4. (-. (convergent_lines T_0 (parallel_through_point T_1 T_2))) (convergent_lines T_0 (parallel_through_point T_1 T_2)) ### Axiom
% 43.95/44.17 5. ((distinct_lines T_0 (parallel_through_point T_1 T_2)) => ((apart_point_and_line T_2 T_0) \/ ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ (convergent_lines T_0 (parallel_through_point T_1 T_2))))) (-. (convergent_lines T_0 (parallel_through_point T_1 T_2))) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (-. (apart_point_and_line T_2 T_0)) (distinct_lines T_0 (parallel_through_point T_1 T_2)) ### DisjTree 1 2 3 4
% 43.95/44.17 6. (All Z, ((distinct_lines T_0 Z) => ((apart_point_and_line T_2 T_0) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines T_0 Z))))) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (-. (convergent_lines T_0 (parallel_through_point T_1 T_2))) ### All 5
% 43.95/44.17 7. (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 (parallel_through_point T_1 T_2))) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (-. (apart_point_and_line T_2 T_0)) (distinct_lines T_0 (parallel_through_point T_1 T_2)) ### All 6
% 43.95/44.17 8. (distinct_lines (parallel_through_point T_1 T_2) T_0) (-. (distinct_lines (parallel_through_point T_1 T_2) T_0)) ### Axiom
% 43.95/44.17 9. (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (apart_point_and_line T_2 (parallel_through_point T_1 T_2)) ### Axiom
% 43.95/44.17 10. (-. (apart_point_and_line T_2 T_0)) (apart_point_and_line T_2 T_0) ### Axiom
% 43.95/44.17 11. (convergent_lines (parallel_through_point T_1 T_2) T_0) (-. (convergent_lines (parallel_through_point T_1 T_2) T_0)) ### Axiom
% 43.95/44.17 12. (-. (convergent_lines (parallel_through_point T_1 T_2) T_1)) (convergent_lines (parallel_through_point T_1 T_2) T_1) ### Axiom
% 43.95/44.17 13. (-. (convergent_lines T_0 T_1)) (convergent_lines T_0 T_1) ### Axiom
% 43.95/44.17 14. ((convergent_lines (parallel_through_point T_1 T_2) T_0) => ((convergent_lines (parallel_through_point T_1 T_2) T_1) \/ (convergent_lines T_0 T_1))) (-. (convergent_lines T_0 T_1)) (-. (convergent_lines (parallel_through_point T_1 T_2) T_1)) (convergent_lines (parallel_through_point T_1 T_2) T_0) ### DisjTree 11 12 13
% 43.95/44.17 15. (All Z, ((convergent_lines (parallel_through_point T_1 T_2) T_0) => ((convergent_lines (parallel_through_point T_1 T_2) Z) \/ (convergent_lines T_0 Z)))) (convergent_lines (parallel_through_point T_1 T_2) T_0) (-. (convergent_lines (parallel_through_point T_1 T_2) T_1)) (-. (convergent_lines T_0 T_1)) ### All 14
% 43.95/44.17 16. (All Y, (All Z, ((convergent_lines (parallel_through_point T_1 T_2) Y) => ((convergent_lines (parallel_through_point T_1 T_2) Z) \/ (convergent_lines Y Z))))) (-. (convergent_lines T_0 T_1)) (-. (convergent_lines (parallel_through_point T_1 T_2) T_1)) (convergent_lines (parallel_through_point T_1 T_2) T_0) ### All 15
% 43.95/44.17 17. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines (parallel_through_point T_1 T_2) T_0) (-. (convergent_lines (parallel_through_point T_1 T_2) T_1)) (-. (convergent_lines T_0 T_1)) ### All 16
% 43.95/44.17 18. (All Y, (-. (convergent_lines (parallel_through_point Y T_2) Y))) (-. (convergent_lines T_0 T_1)) (convergent_lines (parallel_through_point T_1 T_2) T_0) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) ### All 17
% 43.95/44.17 19. (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (convergent_lines (parallel_through_point T_1 T_2) T_0) (-. (convergent_lines T_0 T_1)) ### All 18
% 43.95/44.17 20. ((distinct_lines (parallel_through_point T_1 T_2) T_0) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 T_0) \/ (convergent_lines (parallel_through_point T_1 T_2) T_0)))) (-. (convergent_lines T_0 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (distinct_lines (parallel_through_point T_1 T_2) T_0) ### DisjTree 8 9 10 19
% 43.95/44.17 21. (All Z, ((distinct_lines (parallel_through_point T_1 T_2) Z) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines (parallel_through_point T_1 T_2) Z))))) (distinct_lines (parallel_through_point T_1 T_2) T_0) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (-. (apart_point_and_line T_2 T_0)) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_1)) ### All 20
% 43.95/44.17 22. (-. (convergent_lines T_0 T_0)) (convergent_lines T_0 T_0) ### Axiom
% 43.95/44.17 23. ((convergent_lines T_0 (parallel_through_point T_1 T_2)) => ((distinct_lines (parallel_through_point T_1 T_2) T_0) \/ (convergent_lines T_0 T_0))) (-. (convergent_lines T_0 T_0)) (-. (convergent_lines T_0 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All Z, ((distinct_lines (parallel_through_point T_1 T_2) Z) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines (parallel_through_point T_1 T_2) Z))))) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) ### DisjTree 7 21 22
% 43.95/44.17 24. (All Z, ((convergent_lines T_0 (parallel_through_point T_1 T_2)) => ((distinct_lines (parallel_through_point T_1 T_2) Z) \/ (convergent_lines T_0 Z)))) (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (-. (apart_point_and_line T_2 T_0)) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (All Z, ((distinct_lines (parallel_through_point T_1 T_2) Z) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines (parallel_through_point T_1 T_2) Z))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_1)) (-. (convergent_lines T_0 T_0)) ### All 23
% 43.95/44.17 25. (All X, (-. (convergent_lines X X))) (-. (convergent_lines T_0 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All Z, ((distinct_lines (parallel_through_point T_1 T_2) Z) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines (parallel_through_point T_1 T_2) Z))))) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) (All Z, ((convergent_lines T_0 (parallel_through_point T_1 T_2)) => ((distinct_lines (parallel_through_point T_1 T_2) Z) \/ (convergent_lines T_0 Z)))) ### All 24
% 43.95/44.19 26. (All Y, (All Z, ((convergent_lines T_0 Y) => ((distinct_lines Y Z) \/ (convergent_lines T_0 Z))))) (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (-. (apart_point_and_line T_2 T_0)) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (All Z, ((distinct_lines (parallel_through_point T_1 T_2) Z) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines (parallel_through_point T_1 T_2) Z))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_1)) (All X, (-. (convergent_lines X X))) ### All 25
% 43.95/44.19 27. (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (-. (convergent_lines T_0 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All Z, ((distinct_lines (parallel_through_point T_1 T_2) Z) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines (parallel_through_point T_1 T_2) Z))))) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (-. (apart_point_and_line T_2 T_0)) (-. (apart_point_and_line T_2 (parallel_through_point T_1 T_2))) (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) ### All 26
% 43.95/44.19 28. (All Y, (-. (apart_point_and_line T_2 (parallel_through_point Y T_2)))) (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) (-. (apart_point_and_line T_2 T_0)) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (All Z, ((distinct_lines (parallel_through_point T_1 T_2) Z) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines (parallel_through_point T_1 T_2) Z))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_1)) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) ### All 27
% 43.95/44.19 29. (All X, (All Y, (-. (apart_point_and_line X (parallel_through_point Y X))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (-. (convergent_lines T_0 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All Z, ((distinct_lines (parallel_through_point T_1 T_2) Z) => ((apart_point_and_line T_2 (parallel_through_point T_1 T_2)) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines (parallel_through_point T_1 T_2) Z))))) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (-. (apart_point_and_line T_2 T_0)) (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) ### All 28
% 43.95/44.19 30. (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line T_2 Y) \/ ((apart_point_and_line T_2 Z) \/ (convergent_lines Y Z)))))) (-. (apart_point_and_line T_2 T_0)) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (-. (convergent_lines T_0 T_1)) (All X, (-. (convergent_lines X X))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (All Y, (-. (apart_point_and_line X (parallel_through_point Y X))))) ### All 29
% 43.95/44.19 31. (All X, (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line X Y) \/ ((apart_point_and_line X Z) \/ (convergent_lines Y Z))))))) (All X, (All Y, (-. (apart_point_and_line X (parallel_through_point Y X))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (-. (convergent_lines X X))) (-. (convergent_lines T_0 T_1)) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((convergent_lines X Z) \/ (convergent_lines Y Z)))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (distinct_lines T_0 (parallel_through_point T_1 T_2)) (-. (apart_point_and_line T_2 T_0)) ### All 30
% 43.95/44.19 32. (-. (((-. (apart_point_and_line T_2 T_0)) /\ (-. (convergent_lines T_0 T_1))) => (-. (distinct_lines T_0 (parallel_through_point T_1 T_2))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (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 X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (All Y, (-. (apart_point_and_line X (parallel_through_point Y X))))) (All X, (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line X Y) \/ ((apart_point_and_line X Z) \/ (convergent_lines Y Z))))))) ### ConjTree 31
% 43.95/44.19 33. (-. (All Z, (((-. (apart_point_and_line T_2 T_0)) /\ (-. (convergent_lines T_0 Z))) => (-. (distinct_lines T_0 (parallel_through_point Z T_2)))))) (All X, (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line X Y) \/ ((apart_point_and_line X Z) \/ (convergent_lines Y Z))))))) (All X, (All Y, (-. (apart_point_and_line X (parallel_through_point Y X))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (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 X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) ### NotAllEx 32
% 43.95/44.19 34. (-. (All Y, (All Z, (((-. (apart_point_and_line T_2 Y)) /\ (-. (convergent_lines Y Z))) => (-. (distinct_lines Y (parallel_through_point Z T_2))))))) (All X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) (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 X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (All X, (All Y, (-. (apart_point_and_line X (parallel_through_point Y X))))) (All X, (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line X Y) \/ ((apart_point_and_line X Z) \/ (convergent_lines Y Z))))))) ### NotAllEx 33
% 43.95/44.19 35. (-. (All X, (All Y, (All Z, (((-. (apart_point_and_line X Y)) /\ (-. (convergent_lines Y Z))) => (-. (distinct_lines Y (parallel_through_point Z X)))))))) (All X, (All Y, (All Z, ((distinct_lines Y Z) => ((apart_point_and_line X Y) \/ ((apart_point_and_line X Z) \/ (convergent_lines Y Z))))))) (All X, (All Y, (-. (apart_point_and_line X (parallel_through_point Y X))))) (All X, (All Y, (All Z, ((convergent_lines X Y) => ((distinct_lines Y Z) \/ (convergent_lines X Z)))))) (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 X, (All Y, (-. (convergent_lines (parallel_through_point Y X) Y)))) ### NotAllEx 34
% 43.95/44.19 % SZS output end Proof
% 43.95/44.19 (* END-PROOF *)
%------------------------------------------------------------------------------