%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO206+2 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 : 300s % DateTime : Fri Oct 3 07:48:13 PM UTC 2025 % Result : Theorem 272.96s 273.29s % Output : Proof 273.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : GEO206+2 : TPTP v9.2.0. Released v3.3.0. % 0.12/0.13 % Command : duper %s % 0.13/0.35 % Computer : n017.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 12:01:23 EDT 2025 % 0.13/0.35 % CPUTime : % 272.96/273.29 SZS status Theorem for theBenchmark.p % 272.96/273.29 SZS output start Proof for theBenchmark.p % 272.96/273.29 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), Not (distinct_lines X X)) True % 272.96/273.29 Clause #4 (by assumption #[]): Eq (∀ (X Y Z : Iota), distinct_lines X Y → Or (distinct_lines X Z) (distinct_lines Y Z)) True % 272.96/273.29 Clause #5 (by assumption #[]): Eq (∀ (X Y Z : Iota), convergent_lines X Y → Or (convergent_lines X Z) (convergent_lines Y Z)) True % 272.96/273.29 Clause #12 (by assumption #[]): Eq (∀ (X Y : Iota), Not (convergent_lines (parallel_through_point Y X) Y)) True % 272.96/273.29 Clause #13 (by assumption #[]): Eq (∀ (X Y : Iota), Not (apart_point_and_line X (parallel_through_point Y X))) True % 272.96/273.29 Clause #14 (by assumption #[]): Eq % 272.96/273.29 (∀ (X Y Z : Iota), % 272.96/273.29 distinct_lines Y Z → Or (Or (apart_point_and_line X Y) (apart_point_and_line X Z)) (convergent_lines Y Z)) % 272.96/273.29 True % 272.96/273.29 Clause #15 (by assumption #[]): Eq % 272.96/273.29 (Not % 272.96/273.29 (∀ (X Y Z : Iota), % 272.96/273.29 And (Not (apart_point_and_line X Y)) (Not (convergent_lines Y Z)) → % 272.96/273.29 Not (distinct_lines Y (parallel_through_point Z X)))) % 272.96/273.29 True % 272.96/273.29 Clause #18 (by clausification #[1]): ∀ (a : Iota), Eq (Not (distinct_lines a a)) True % 272.96/273.29 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (distinct_lines a a) False % 272.96/273.29 Clause #25 (by clausification #[13]): ∀ (a : Iota), Eq (∀ (Y : Iota), Not (apart_point_and_line a (parallel_through_point Y a))) True % 272.96/273.29 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (Not (apart_point_and_line a (parallel_through_point a_1 a))) True % 272.96/273.29 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (apart_point_and_line a (parallel_through_point a_1 a)) False % 272.96/273.29 Clause #33 (by clausification #[12]): ∀ (a : Iota), Eq (∀ (Y : Iota), Not (convergent_lines (parallel_through_point Y a) Y)) True % 272.96/273.29 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (Not (convergent_lines (parallel_through_point a a_1) a)) True % 272.96/273.29 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (convergent_lines (parallel_through_point a a_1) a) False % 272.96/273.29 Clause #48 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), convergent_lines a Y → Or (convergent_lines a Z) (convergent_lines Y Z)) True % 272.96/273.29 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), convergent_lines a a_1 → Or (convergent_lines a Z) (convergent_lines a_1 Z)) True % 272.96/273.29 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines a a_1 → Or (convergent_lines a a_2) (convergent_lines a_1 a_2)) True % 272.96/273.29 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 272.96/273.29 Or (Eq (convergent_lines a a_1) False) (Eq (Or (convergent_lines a a_2) (convergent_lines a_1 a_2)) True) % 272.96/273.29 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 272.96/273.29 Or (Eq (convergent_lines a a_1) False) (Or (Eq (convergent_lines a a_2) True) (Eq (convergent_lines a_1 a_2) True)) % 272.96/273.29 Clause #58 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), distinct_lines a Y → Or (distinct_lines a Z) (distinct_lines Y Z)) True % 272.96/273.29 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), distinct_lines a a_1 → Or (distinct_lines a Z) (distinct_lines a_1 Z)) True % 272.96/273.29 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines a a_1 → Or (distinct_lines a a_2) (distinct_lines a_1 a_2)) True % 272.96/273.29 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), % 272.96/273.29 Or (Eq (distinct_lines a a_1) False) (Eq (Or (distinct_lines a a_2) (distinct_lines a_1 a_2)) True) % 272.96/273.29 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), % 272.96/273.29 Or (Eq (distinct_lines a a_1) False) (Or (Eq (distinct_lines a a_2) True) (Eq (distinct_lines a_1 a_2) True)) % 272.96/273.29 Clause #63 (by clausification #[15]): Eq % 272.96/273.29 (∀ (X Y Z : Iota), % 272.96/273.29 And (Not (apart_point_and_line X Y)) (Not (convergent_lines Y Z)) → % 272.96/273.29 Not (distinct_lines Y (parallel_through_point Z X))) % 272.96/273.29 False % 272.96/273.29 Clause #64 (by clausification #[63]): ∀ (a : Iota), % 272.96/273.29 Eq % 272.96/273.29 (Not % 272.96/273.29 (∀ (Y Z : Iota), % 272.96/273.29 And (Not (apart_point_and_line (skS.0 0 a) Y)) (Not (convergent_lines Y Z)) → % 272.96/273.29 Not (distinct_lines Y (parallel_through_point Z (skS.0 0 a))))) % 272.96/273.29 True % 272.96/273.29 Clause #65 (by clausification #[64]): ∀ (a : Iota), % 272.96/273.31 Eq % 272.96/273.31 (∀ (Y Z : Iota), % 272.96/273.31 And (Not (apart_point_and_line (skS.0 0 a) Y)) (Not (convergent_lines Y Z)) → % 272.96/273.31 Not (distinct_lines Y (parallel_through_point Z (skS.0 0 a)))) % 272.96/273.31 False % 272.96/273.31 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), % 272.96/273.31 Eq % 272.96/273.31 (Not % 272.96/273.31 (∀ (Z : Iota), % 272.96/273.31 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) (Not (convergent_lines (skS.0 1 a a_1) Z)) → % 272.96/273.31 Not (distinct_lines (skS.0 1 a a_1) (parallel_through_point Z (skS.0 0 a))))) % 272.96/273.31 True % 272.96/273.31 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), % 272.96/273.31 Eq % 272.96/273.31 (∀ (Z : Iota), % 272.96/273.31 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) (Not (convergent_lines (skS.0 1 a a_1) Z)) → % 272.96/273.31 Not (distinct_lines (skS.0 1 a a_1) (parallel_through_point Z (skS.0 0 a)))) % 272.96/273.31 False % 272.96/273.31 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), % 272.96/273.31 Eq % 272.96/273.31 (Not % 272.96/273.31 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) % 272.96/273.31 (Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) → % 272.96/273.31 Not (distinct_lines (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a))))) % 272.96/273.31 True % 272.96/273.31 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), % 272.96/273.31 Eq % 272.96/273.31 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) % 272.96/273.31 (Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) → % 272.96/273.31 Not (distinct_lines (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a)))) % 272.96/273.31 False % 272.96/273.31 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), % 272.96/273.31 Eq % 272.96/273.31 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) % 272.96/273.31 (Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 272.96/273.31 True % 272.96/273.31 Clause #71 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), % 272.96/273.31 Eq (Not (distinct_lines (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a)))) False % 272.96/273.31 Clause #72 (by clausification #[70]): ∀ (a a_1 a_2 : Iota), Eq (Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) True % 272.96/273.31 Clause #73 (by clausification #[70]): ∀ (a a_1 : Iota), Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) True % 272.96/273.31 Clause #74 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False % 272.96/273.31 Clause #82 (by clausification #[14]): ∀ (a : Iota), % 272.96/273.31 Eq % 272.96/273.31 (∀ (Y Z : Iota), % 272.96/273.31 distinct_lines Y Z → Or (Or (apart_point_and_line a Y) (apart_point_and_line a Z)) (convergent_lines Y Z)) % 272.96/273.31 True % 272.96/273.31 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota), % 272.96/273.31 Eq % 272.96/273.31 (∀ (Z : Iota), % 272.96/273.31 distinct_lines a Z → Or (Or (apart_point_and_line a_1 a) (apart_point_and_line a_1 Z)) (convergent_lines a Z)) % 272.96/273.31 True % 272.96/273.31 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 : Iota), % 272.96/273.31 Eq % 272.96/273.31 (distinct_lines a a_1 → % 272.96/273.31 Or (Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1)) (convergent_lines a a_1)) % 272.96/273.31 True % 272.96/273.31 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 : Iota), % 272.96/273.31 Or (Eq (distinct_lines a a_1) False) % 272.96/273.31 (Eq (Or (Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1)) (convergent_lines a a_1)) True) % 272.96/273.31 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota), % 272.96/273.31 Or (Eq (distinct_lines a a_1) False) % 272.96/273.31 (Or (Eq (Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1)) True) (Eq (convergent_lines a a_1) True)) % 272.96/273.31 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota), % 272.96/273.31 Or (Eq (distinct_lines a a_1) False) % 272.96/273.31 (Or (Eq (convergent_lines a a_1) True) % 272.96/273.31 (Or (Eq (apart_point_and_line a_2 a) True) (Eq (apart_point_and_line a_2 a_1) True))) % 272.96/273.31 Clause #97 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1)) False % 272.96/273.31 Clause #98 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a))) True % 272.96/273.31 Clause #99 (by superposition #[98, 62]): ∀ (a a_1 a_2 a_3 : Iota), % 272.96/273.31 Or (Eq True False) % 272.96/273.31 (Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 272.96/273.31 (Eq (distinct_lines (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a)) a_2) True)) % 272.96/273.31 Clause #101 (by clausification #[99]): ∀ (a a_1 a_2 a_3 : Iota), % 273.22/273.51 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 273.22/273.51 (Eq (distinct_lines (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a)) a_2) True) % 273.22/273.51 Clause #104 (by superposition #[101, 87]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 273.22/273.51 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 273.22/273.51 (Or (Eq True False) % 273.22/273.51 (Or (Eq (convergent_lines (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a)) a_2) True) % 273.22/273.51 (Or (Eq (apart_point_and_line a_4 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True) % 273.22/273.51 (Eq (apart_point_and_line a_4 a_2) True)))) % 273.22/273.51 Clause #146 (by clausification #[104]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 273.22/273.51 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 273.22/273.51 (Or (Eq (convergent_lines (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a)) a_2) True) % 273.22/273.51 (Or (Eq (apart_point_and_line a_4 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True) % 273.22/273.51 (Eq (apart_point_and_line a_4 a_2) True))) % 273.22/273.51 Clause #153 (by superposition #[146, 27]): ∀ (a a_1 a_2 a_3 : Iota), % 273.22/273.51 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 273.22/273.51 (Or (Eq (convergent_lines (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a)) a_2) True) % 273.22/273.51 (Or (Eq (apart_point_and_line (skS.0 0 a) a_2) True) (Eq True False))) % 273.22/273.51 Clause #939 (by clausification #[153]): ∀ (a a_1 a_2 a_3 : Iota), % 273.22/273.51 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 273.22/273.51 (Or (Eq (convergent_lines (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a)) a_2) True) % 273.22/273.51 (Eq (apart_point_and_line (skS.0 0 a) a_2) True)) % 273.22/273.51 Clause #943 (by superposition #[939, 52]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 273.22/273.51 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 273.22/273.51 (Or (Eq (apart_point_and_line (skS.0 0 a) a_2) True) % 273.22/273.51 (Or (Eq True False) % 273.22/273.51 (Or (Eq (convergent_lines (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a)) a_4) True) % 273.22/273.51 (Eq (convergent_lines a_2 a_4) True)))) % 273.22/273.51 Clause #4722 (by clausification #[943]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 273.22/273.51 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 273.22/273.51 (Or (Eq (apart_point_and_line (skS.0 0 a) a_2) True) % 273.22/273.51 (Or (Eq (convergent_lines (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a)) a_4) True) % 273.22/273.51 (Eq (convergent_lines a_2 a_4) True))) % 273.22/273.51 Clause #4726 (by superposition #[4722, 35]): ∀ (a a_1 a_2 a_3 : Iota), % 273.22/273.51 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 273.22/273.51 (Or (Eq (apart_point_and_line (skS.0 0 a) a_2) True) % 273.22/273.51 (Or (Eq (convergent_lines a_2 (skS.0 2 a a_1 a_3)) True) (Eq True False))) % 273.22/273.51 Clause #4740 (by clausification #[4726]): ∀ (a a_1 a_2 a_3 : Iota), % 273.22/273.51 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 273.22/273.51 (Or (Eq (apart_point_and_line (skS.0 0 a) a_2) True) (Eq (convergent_lines a_2 (skS.0 2 a a_1 a_3)) True)) % 273.22/273.51 Clause #4741 (by superposition #[4740, 74]): ∀ (a a_1 : Iota), % 273.22/273.51 Or (Eq (distinct_lines (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 273.22/273.51 (Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False)) % 273.22/273.51 Clause #4751 (by clausification #[4741]): ∀ (a a_1 : Iota), % 273.22/273.51 Or (Eq (distinct_lines (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 273.22/273.51 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1)) True) % 273.22/273.51 Clause #4752 (by forward demodulation #[4751, 97]): ∀ (a a_1 : Iota), Or (Eq (distinct_lines (skS.0 1 a a_1) (skS.0 1 a a_1)) True) (Eq False True) % 273.22/273.51 Clause #4753 (by clausification #[4752]): ∀ (a a_1 : Iota), Eq (distinct_lines (skS.0 1 a a_1) (skS.0 1 a a_1)) True % 273.22/273.51 Clause #4754 (by superposition #[4753, 19]): Eq True False % 273.22/273.51 Clause #4757 (by clausification #[4754]): False % 273.22/273.51 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------