%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO206+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %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 : 300s % DateTime : Fri Oct 3 07:48:13 PM UTC 2025 % Result : Theorem 251.46s 251.64s % Output : Proof 251.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.10 % Problem : GEO206+1 : TPTP v9.2.0. Released v3.3.0. % 0.02/0.11 % Command : duper %s % 0.11/0.31 % Computer : n008.cluster.edu % 0.11/0.31 % Model : x86_64 x86_64 % 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.31 % Memory : 8042.1875MB % 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 300 % 0.11/0.31 % DateTime : Fri Oct 3 12:26:53 EDT 2025 % 0.11/0.31 % CPUTime : % 251.46/251.64 SZS status Theorem for theBenchmark.p % 251.46/251.64 SZS output start Proof for theBenchmark.p % 251.46/251.64 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), Not (distinct_lines X X)) True % 251.46/251.64 Clause #4 (by assumption #[]): Eq (∀ (X Y Z : Iota), distinct_lines X Y → Or (distinct_lines X Z) (distinct_lines Y Z)) True % 251.46/251.64 Clause #5 (by assumption #[]): Eq (∀ (X Y Z : Iota), convergent_lines X Y → Or (convergent_lines X Z) (convergent_lines Y Z)) True % 251.46/251.64 Clause #14 (by assumption #[]): Eq (∀ (X Y : Iota), Not (convergent_lines (parallel_through_point Y X) Y)) True % 251.46/251.64 Clause #15 (by assumption #[]): Eq (∀ (X Y : Iota), Not (apart_point_and_line X (parallel_through_point Y X))) True % 251.46/251.64 Clause #16 (by assumption #[]): Eq % 251.46/251.64 (∀ (X Y Z : Iota), % 251.46/251.64 distinct_lines Y Z → Or (Or (apart_point_and_line X Y) (apart_point_and_line X Z)) (convergent_lines Y Z)) % 251.46/251.64 True % 251.46/251.64 Clause #17 (by assumption #[]): Eq % 251.46/251.64 (Not % 251.46/251.64 (∀ (X Y Z : Iota), % 251.46/251.64 And (Not (apart_point_and_line X Y)) (Not (convergent_lines Y Z)) → % 251.46/251.64 Not (distinct_lines Y (parallel_through_point Z X)))) % 251.46/251.64 True % 251.46/251.64 Clause #20 (by clausification #[1]): ∀ (a : Iota), Eq (Not (distinct_lines a a)) True % 251.46/251.64 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (distinct_lines a a) False % 251.46/251.64 Clause #24 (by clausification #[15]): ∀ (a : Iota), Eq (∀ (Y : Iota), Not (apart_point_and_line a (parallel_through_point Y a))) True % 251.46/251.64 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (Not (apart_point_and_line a (parallel_through_point a_1 a))) True % 251.46/251.64 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (apart_point_and_line a (parallel_through_point a_1 a)) False % 251.46/251.64 Clause #27 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (Y : Iota), Not (convergent_lines (parallel_through_point Y a) Y)) True % 251.46/251.64 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (Not (convergent_lines (parallel_through_point a a_1) a)) True % 251.46/251.64 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (convergent_lines (parallel_through_point a a_1) a) False % 251.46/251.64 Clause #56 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), distinct_lines a Y → Or (distinct_lines a Z) (distinct_lines Y Z)) True % 251.46/251.64 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), distinct_lines a a_1 → Or (distinct_lines a Z) (distinct_lines a_1 Z)) True % 251.46/251.64 Clause #58 (by clausification #[57]): ∀ (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 % 251.46/251.64 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), % 251.46/251.64 Or (Eq (distinct_lines a a_1) False) (Eq (Or (distinct_lines a a_2) (distinct_lines a_1 a_2)) True) % 251.46/251.64 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), % 251.46/251.64 Or (Eq (distinct_lines a a_1) False) (Or (Eq (distinct_lines a a_2) True) (Eq (distinct_lines a_1 a_2) True)) % 251.46/251.64 Clause #66 (by clausification #[17]): Eq % 251.46/251.64 (∀ (X Y Z : Iota), % 251.46/251.64 And (Not (apart_point_and_line X Y)) (Not (convergent_lines Y Z)) → % 251.46/251.64 Not (distinct_lines Y (parallel_through_point Z X))) % 251.46/251.64 False % 251.46/251.64 Clause #67 (by clausification #[66]): ∀ (a : Iota), % 251.46/251.64 Eq % 251.46/251.64 (Not % 251.46/251.64 (∀ (Y Z : Iota), % 251.46/251.64 And (Not (apart_point_and_line (skS.0 0 a) Y)) (Not (convergent_lines Y Z)) → % 251.46/251.64 Not (distinct_lines Y (parallel_through_point Z (skS.0 0 a))))) % 251.46/251.64 True % 251.46/251.64 Clause #68 (by clausification #[67]): ∀ (a : Iota), % 251.46/251.64 Eq % 251.46/251.64 (∀ (Y Z : Iota), % 251.46/251.64 And (Not (apart_point_and_line (skS.0 0 a) Y)) (Not (convergent_lines Y Z)) → % 251.46/251.64 Not (distinct_lines Y (parallel_through_point Z (skS.0 0 a)))) % 251.46/251.64 False % 251.46/251.64 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota), % 251.46/251.64 Eq % 251.46/251.64 (Not % 251.46/251.64 (∀ (Z : Iota), % 251.46/251.64 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)) → % 251.46/251.64 Not (distinct_lines (skS.0 1 a a_1) (parallel_through_point Z (skS.0 0 a))))) % 251.46/251.64 True % 251.46/251.64 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota), % 251.46/251.64 Eq % 251.46/251.64 (∀ (Z : Iota), % 251.46/251.64 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)) → % 251.46/251.64 Not (distinct_lines (skS.0 1 a a_1) (parallel_through_point Z (skS.0 0 a)))) % 251.46/251.64 False % 251.46/251.66 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 : Iota), % 251.46/251.66 Eq % 251.46/251.66 (Not % 251.46/251.66 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) % 251.46/251.66 (Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) → % 251.46/251.66 Not (distinct_lines (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a))))) % 251.46/251.66 True % 251.46/251.66 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), % 251.46/251.66 Eq % 251.46/251.66 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) % 251.46/251.66 (Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) → % 251.46/251.66 Not (distinct_lines (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a)))) % 251.46/251.66 False % 251.46/251.66 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), % 251.46/251.66 Eq % 251.46/251.66 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) % 251.46/251.66 (Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 251.46/251.66 True % 251.46/251.66 Clause #74 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), % 251.46/251.66 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 % 251.46/251.66 Clause #75 (by clausification #[73]): ∀ (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 % 251.46/251.66 Clause #76 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) True % 251.46/251.66 Clause #77 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False % 251.46/251.66 Clause #78 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), convergent_lines a Y → Or (convergent_lines a Z) (convergent_lines Y Z)) True % 251.46/251.66 Clause #79 (by clausification #[78]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), convergent_lines a a_1 → Or (convergent_lines a Z) (convergent_lines a_1 Z)) True % 251.46/251.66 Clause #80 (by clausification #[79]): ∀ (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 % 251.46/251.66 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 : Iota), % 251.46/251.66 Or (Eq (convergent_lines a a_1) False) (Eq (Or (convergent_lines a a_2) (convergent_lines a_1 a_2)) True) % 251.46/251.66 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 : Iota), % 251.46/251.66 Or (Eq (convergent_lines a a_1) False) (Or (Eq (convergent_lines a a_2) True) (Eq (convergent_lines a_1 a_2) True)) % 251.46/251.66 Clause #88 (by clausification #[16]): ∀ (a : Iota), % 251.46/251.66 Eq % 251.46/251.66 (∀ (Y Z : Iota), % 251.46/251.66 distinct_lines Y Z → Or (Or (apart_point_and_line a Y) (apart_point_and_line a Z)) (convergent_lines Y Z)) % 251.46/251.66 True % 251.46/251.66 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), % 251.46/251.66 Eq % 251.46/251.66 (∀ (Z : Iota), % 251.46/251.66 distinct_lines a Z → Or (Or (apart_point_and_line a_1 a) (apart_point_and_line a_1 Z)) (convergent_lines a Z)) % 251.46/251.66 True % 251.46/251.66 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 : Iota), % 251.46/251.66 Eq % 251.46/251.66 (distinct_lines a a_1 → % 251.46/251.66 Or (Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1)) (convergent_lines a a_1)) % 251.46/251.66 True % 251.46/251.66 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 : Iota), % 251.46/251.66 Or (Eq (distinct_lines a a_1) False) % 251.46/251.66 (Eq (Or (Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1)) (convergent_lines a a_1)) True) % 251.46/251.66 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 : Iota), % 251.46/251.66 Or (Eq (distinct_lines a a_1) False) % 251.46/251.66 (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)) % 251.46/251.66 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 : Iota), % 251.46/251.66 Or (Eq (distinct_lines a a_1) False) % 251.46/251.66 (Or (Eq (convergent_lines a a_1) True) % 251.46/251.66 (Or (Eq (apart_point_and_line a_2 a) True) (Eq (apart_point_and_line a_2 a_1) True))) % 251.46/251.66 Clause #103 (by clausification #[76]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1)) False % 251.46/251.66 Clause #104 (by clausification #[74]): ∀ (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 % 251.46/251.66 Clause #105 (by superposition #[104, 60]): ∀ (a a_1 a_2 a_3 : Iota), % 251.46/251.66 Or (Eq True False) % 251.46/251.66 (Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 251.46/251.66 (Eq (distinct_lines (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a)) a_2) True)) % 251.46/251.66 Clause #107 (by clausification #[105]): ∀ (a a_1 a_2 a_3 : Iota), % 251.49/251.68 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 251.49/251.68 (Eq (distinct_lines (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a)) a_2) True) % 251.49/251.68 Clause #109 (by superposition #[107, 60]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 251.49/251.68 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 251.49/251.68 (Or (Eq True False) % 251.49/251.68 (Or (Eq (distinct_lines (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a)) a_4) True) % 251.49/251.68 (Eq (distinct_lines a_2 a_4) True))) % 251.49/251.68 Clause #111 (by clausification #[109]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 251.49/251.68 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 251.49/251.68 (Or (Eq (distinct_lines (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a)) a_4) True) % 251.49/251.68 (Eq (distinct_lines a_2 a_4) True)) % 251.49/251.68 Clause #115 (by superposition #[111, 21]): ∀ (a a_1 a_2 a_3 : Iota), % 251.49/251.68 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 251.49/251.68 (Or (Eq (distinct_lines a_2 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True) (Eq True False)) % 251.49/251.68 Clause #129 (by clausification #[115]): ∀ (a a_1 a_2 a_3 : Iota), % 251.49/251.68 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 251.49/251.68 (Eq (distinct_lines a_2 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True) % 251.49/251.68 Clause #131 (by superposition #[129, 93]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 251.49/251.68 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 251.49/251.68 (Or (Eq True False) % 251.49/251.68 (Or (Eq (convergent_lines a_2 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True) % 251.49/251.68 (Or (Eq (apart_point_and_line a_4 a_2) True) % 251.49/251.68 (Eq (apart_point_and_line a_4 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True)))) % 251.49/251.68 Clause #571 (by clausification #[131]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 251.49/251.68 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 251.49/251.68 (Or (Eq (convergent_lines a_2 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True) % 251.49/251.68 (Or (Eq (apart_point_and_line a_4 a_2) True) % 251.49/251.68 (Eq (apart_point_and_line a_4 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True))) % 251.49/251.68 Clause #584 (by superposition #[571, 26]): ∀ (a a_1 a_2 a_3 : Iota), % 251.49/251.68 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 251.49/251.68 (Or (Eq (convergent_lines a_2 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True) % 251.49/251.68 (Or (Eq (apart_point_and_line (skS.0 0 a) a_2) True) (Eq True False))) % 251.49/251.68 Clause #936 (by clausification #[584]): ∀ (a a_1 a_2 a_3 : Iota), % 251.49/251.68 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 251.49/251.68 (Or (Eq (convergent_lines a_2 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True) % 251.49/251.68 (Eq (apart_point_and_line (skS.0 0 a) a_2) True)) % 251.49/251.68 Clause #941 (by superposition #[936, 82]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 251.49/251.68 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 251.49/251.68 (Or (Eq (apart_point_and_line (skS.0 0 a) a_2) True) % 251.49/251.68 (Or (Eq True False) % 251.49/251.68 (Or (Eq (convergent_lines a_2 a_3) True) % 251.49/251.68 (Eq (convergent_lines (parallel_through_point (skS.0 2 a a_1 a_4) (skS.0 0 a)) a_3) True)))) % 251.49/251.68 Clause #5354 (by clausification #[941]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 251.49/251.68 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 251.49/251.68 (Or (Eq (apart_point_and_line (skS.0 0 a) a_2) True) % 251.49/251.68 (Or (Eq (convergent_lines a_2 a_3) True) % 251.49/251.68 (Eq (convergent_lines (parallel_through_point (skS.0 2 a a_1 a_4) (skS.0 0 a)) a_3) True))) % 251.49/251.68 Clause #5364 (by superposition #[5354, 29]): ∀ (a a_1 a_2 a_3 : Iota), % 251.49/251.68 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 251.49/251.68 (Or (Eq (apart_point_and_line (skS.0 0 a) a_2) True) % 251.49/251.68 (Or (Eq (convergent_lines a_2 (skS.0 2 a a_1 a_3)) True) (Eq True False))) % 251.49/251.68 Clause #5371 (by clausification #[5364]): ∀ (a a_1 a_2 a_3 : Iota), % 251.49/251.68 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True) % 251.49/251.68 (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)) % 251.49/251.68 Clause #5372 (by superposition #[5371, 77]): ∀ (a a_1 : Iota), % 251.49/251.68 Or (Eq (distinct_lines (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 251.49/251.68 (Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False)) % 251.49/251.68 Clause #5378 (by clausification #[5372]): ∀ (a a_1 : Iota), % 251.49/251.68 Or (Eq (distinct_lines (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 251.49/251.68 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1)) True) % 251.70/251.87 Clause #5379 (by forward demodulation #[5378, 103]): ∀ (a a_1 : Iota), Or (Eq (distinct_lines (skS.0 1 a a_1) (skS.0 1 a a_1)) True) (Eq False True) % 251.70/251.87 Clause #5380 (by clausification #[5379]): ∀ (a a_1 : Iota), Eq (distinct_lines (skS.0 1 a a_1) (skS.0 1 a a_1)) True % 251.70/251.87 Clause #5381 (by superposition #[5380, 21]): Eq True False % 251.70/251.87 Clause #5428 (by clausification #[5381]): False % 251.70/251.87 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------