%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO208+2 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 4.01s 4.20s % Output : Proof 4.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO208+2 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.13 % Command : duper %s % 0.13/0.35 % Computer : n019.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 12:39:08 EDT 2025 % 0.13/0.35 % CPUTime : % 4.01/4.20 SZS status Theorem for theBenchmark.p % 4.01/4.20 SZS output start Proof for theBenchmark.p % 4.01/4.20 Clause #14 (by assumption #[]): Eq % 4.01/4.20 (∀ (X Y Z : Iota), % 4.01/4.20 distinct_lines Y Z → Or (Or (apart_point_and_line X Y) (apart_point_and_line X Z)) (convergent_lines Y Z)) % 4.01/4.20 True % 4.01/4.20 Clause #15 (by assumption #[]): Eq % 4.01/4.20 (Not % 4.01/4.20 (∀ (X Y Z : Iota), % 4.01/4.20 And (And (Not (apart_point_and_line X Y)) (Not (apart_point_and_line X Z))) (Not (convergent_lines Y Z)) → % 4.01/4.20 Not (distinct_lines Y Z))) % 4.01/4.20 True % 4.01/4.20 Clause #36 (by clausification #[15]): Eq % 4.01/4.20 (∀ (X Y Z : Iota), % 4.01/4.20 And (And (Not (apart_point_and_line X Y)) (Not (apart_point_and_line X Z))) (Not (convergent_lines Y Z)) → % 4.01/4.20 Not (distinct_lines Y Z)) % 4.01/4.20 False % 4.01/4.20 Clause #37 (by clausification #[36]): ∀ (a : Iota), % 4.01/4.20 Eq % 4.01/4.20 (Not % 4.01/4.20 (∀ (Y Z : Iota), % 4.01/4.20 And (And (Not (apart_point_and_line (skS.0 0 a) Y)) (Not (apart_point_and_line (skS.0 0 a) Z))) % 4.01/4.20 (Not (convergent_lines Y Z)) → % 4.01/4.20 Not (distinct_lines Y Z))) % 4.01/4.20 True % 4.01/4.20 Clause #38 (by clausification #[37]): ∀ (a : Iota), % 4.01/4.20 Eq % 4.01/4.20 (∀ (Y Z : Iota), % 4.01/4.20 And (And (Not (apart_point_and_line (skS.0 0 a) Y)) (Not (apart_point_and_line (skS.0 0 a) Z))) % 4.01/4.20 (Not (convergent_lines Y Z)) → % 4.01/4.20 Not (distinct_lines Y Z)) % 4.01/4.20 False % 4.01/4.20 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), % 4.01/4.20 Eq % 4.01/4.20 (Not % 4.01/4.20 (∀ (Z : Iota), % 4.01/4.20 And (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) (Not (apart_point_and_line (skS.0 0 a) Z))) % 4.01/4.20 (Not (convergent_lines (skS.0 1 a a_1) Z)) → % 4.01/4.20 Not (distinct_lines (skS.0 1 a a_1) Z))) % 4.01/4.20 True % 4.01/4.20 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 4.01/4.20 Eq % 4.01/4.20 (∀ (Z : Iota), % 4.01/4.20 And (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) (Not (apart_point_and_line (skS.0 0 a) Z))) % 4.01/4.20 (Not (convergent_lines (skS.0 1 a a_1) Z)) → % 4.01/4.20 Not (distinct_lines (skS.0 1 a a_1) Z)) % 4.01/4.20 False % 4.01/4.20 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 4.01/4.20 Eq % 4.01/4.20 (Not % 4.01/4.20 (And % 4.01/4.20 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) % 4.01/4.20 (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)))) % 4.01/4.20 (Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) → % 4.01/4.20 Not (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 4.01/4.20 True % 4.01/4.20 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 4.01/4.20 Eq % 4.01/4.20 (And % 4.01/4.20 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) % 4.01/4.20 (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)))) % 4.01/4.20 (Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) → % 4.01/4.20 Not (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.01/4.20 False % 4.01/4.20 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 4.01/4.20 Eq % 4.01/4.20 (And % 4.01/4.20 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) % 4.01/4.20 (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)))) % 4.01/4.20 (Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 4.01/4.20 True % 4.01/4.20 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Eq (Not (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) False % 4.01/4.20 Clause #45 (by clausification #[43]): ∀ (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 % 4.01/4.20 Clause #46 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), % 4.01/4.20 Eq % 4.01/4.20 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) % 4.01/4.20 (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)))) % 4.01/4.20 True % 4.01/4.20 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False % 4.01/4.20 Clause #82 (by clausification #[14]): ∀ (a : Iota), % 4.01/4.20 Eq % 4.01/4.20 (∀ (Y Z : Iota), % 4.01/4.20 distinct_lines Y Z → Or (Or (apart_point_and_line a Y) (apart_point_and_line a Z)) (convergent_lines Y Z)) % 4.01/4.20 True % 4.01/4.20 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota), % 4.01/4.20 Eq % 4.01/4.20 (∀ (Z : Iota), % 4.01/4.20 distinct_lines a Z → Or (Or (apart_point_and_line a_1 a) (apart_point_and_line a_1 Z)) (convergent_lines a Z)) % 4.01/4.20 True % 4.01/4.20 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 : Iota), % 4.01/4.20 Eq % 4.01/4.20 (distinct_lines a a_1 → % 4.01/4.20 Or (Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1)) (convergent_lines a a_1)) % 4.01/4.21 True % 4.01/4.21 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 : Iota), % 4.01/4.21 Or (Eq (distinct_lines a a_1) False) % 4.01/4.21 (Eq (Or (Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1)) (convergent_lines a a_1)) True) % 4.01/4.21 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota), % 4.01/4.21 Or (Eq (distinct_lines a a_1) False) % 4.01/4.21 (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)) % 4.01/4.21 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota), % 4.01/4.21 Or (Eq (distinct_lines a a_1) False) % 4.01/4.21 (Or (Eq (convergent_lines a a_1) True) % 4.01/4.21 (Or (Eq (apart_point_and_line a_2 a) True) (Eq (apart_point_and_line a_2 a_1) True))) % 4.01/4.21 Clause #97 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True % 4.01/4.21 Clause #99 (by superposition #[97, 87]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.21 Or (Eq True False) % 4.01/4.21 (Or (Eq (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True) % 4.01/4.21 (Or (Eq (apart_point_and_line a_3 (skS.0 1 a a_1)) True) % 4.01/4.21 (Eq (apart_point_and_line a_3 (skS.0 2 a a_1 a_2)) True))) % 4.01/4.21 Clause #115 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) True % 4.01/4.21 Clause #116 (by clausification #[46]): ∀ (a a_1 : Iota), Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) True % 4.01/4.21 Clause #117 (by clausification #[115]): ∀ (a a_1 a_2 : Iota), Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) False % 4.01/4.21 Clause #118 (by clausification #[116]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1)) False % 4.01/4.21 Clause #140 (by clausification #[99]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.21 Or (Eq (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True) % 4.01/4.21 (Or (Eq (apart_point_and_line a_3 (skS.0 1 a a_1)) True) (Eq (apart_point_and_line a_3 (skS.0 2 a a_1 a_2)) True)) % 4.01/4.21 Clause #141 (by superposition #[140, 47]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.21 Or (Eq (apart_point_and_line a (skS.0 1 a_1 a_2)) True) % 4.01/4.21 (Or (Eq (apart_point_and_line a (skS.0 2 a_1 a_2 a_3)) True) (Eq True False)) % 4.01/4.21 Clause #148 (by clausification #[141]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.21 Or (Eq (apart_point_and_line a (skS.0 1 a_1 a_2)) True) (Eq (apart_point_and_line a (skS.0 2 a_1 a_2 a_3)) True) % 4.01/4.21 Clause #149 (by superposition #[148, 117]): ∀ (a a_1 : Iota), Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False) % 4.01/4.21 Clause #152 (by clausification #[149]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1)) True % 4.01/4.21 Clause #153 (by superposition #[152, 118]): Eq True False % 4.01/4.21 Clause #156 (by clausification #[153]): False % 4.01/4.21 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------