%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO261+1 : TPTP v9.2.0. Bugfixed v6.4.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 07:48:24 PM UTC 2025 % Result : Theorem 4.10s 4.32s % Output : Proof 4.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.11 % Problem : GEO261+1 : TPTP v9.2.0. Bugfixed v6.4.0. % 0.02/0.12 % Command : duper %s % 0.12/0.31 % Computer : n009.cluster.edu % 0.12/0.31 % Model : x86_64 x86_64 % 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.31 % Memory : 8042.1875MB % 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.31 % CPULimit : 300 % 0.12/0.31 % WCLimit : 300 % 0.12/0.31 % DateTime : Fri Oct 3 12:49:53 EDT 2025 % 0.12/0.32 % CPUTime : % 4.10/4.32 SZS status Theorem for theBenchmark.p % 4.10/4.32 SZS output start Proof for theBenchmark.p % 4.10/4.32 Clause #1 (by assumption #[]): Eq % 4.10/4.32 (∀ (L M : Iota), % 4.10/4.32 Iff (convergent_lines L M) (And (unequally_directed_lines L M) (unequally_directed_lines L (reverse_line M)))) % 4.10/4.32 True % 4.10/4.32 Clause #13 (by assumption #[]): Eq % 4.10/4.32 (∀ (L M : Iota), % 4.10/4.32 And (unequally_directed_lines L M) (unequally_directed_lines L (reverse_line M)) → % 4.10/4.32 Or (left_convergent_lines L M) (left_convergent_lines L (reverse_line M))) % 4.10/4.32 True % 4.10/4.32 Clause #15 (by assumption #[]): Eq (∀ (L M : Iota), Not (Or (left_convergent_lines L M) (left_convergent_lines L (reverse_line M)))) True % 4.10/4.32 Clause #31 (by assumption #[]): Eq % 4.10/4.32 (Not % 4.10/4.32 (∀ (L M A B C : Iota), % 4.10/4.32 And (And (between_on_line L A B C) (convergent_lines L M)) (Not (apart_point_and_line B M)) → % 4.10/4.32 divides_points M A C)) % 4.10/4.32 True % 4.10/4.32 Clause #66 (by clausification #[1]): ∀ (a : Iota), % 4.10/4.32 Eq % 4.10/4.32 (∀ (M : Iota), % 4.10/4.32 Iff (convergent_lines a M) (And (unequally_directed_lines a M) (unequally_directed_lines a (reverse_line M)))) % 4.10/4.32 True % 4.10/4.32 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), % 4.10/4.32 Eq % 4.10/4.32 (Iff (convergent_lines a a_1) % 4.10/4.32 (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1)))) % 4.10/4.32 True % 4.10/4.32 Clause #69 (by clausification #[67]): ∀ (a a_1 : Iota), % 4.10/4.32 Or (Eq (convergent_lines a a_1) False) % 4.10/4.32 (Eq (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1))) True) % 4.10/4.32 Clause #74 (by clausification #[15]): ∀ (a : Iota), Eq (∀ (M : Iota), Not (Or (left_convergent_lines a M) (left_convergent_lines a (reverse_line M)))) True % 4.10/4.32 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), Eq (Not (Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1)))) True % 4.10/4.32 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) False % 4.10/4.32 Clause #78 (by clausification #[76]): ∀ (a a_1 : Iota), Eq (left_convergent_lines a a_1) False % 4.10/4.32 Clause #97 (by clausification #[13]): ∀ (a : Iota), % 4.10/4.32 Eq % 4.10/4.32 (∀ (M : Iota), % 4.10/4.32 And (unequally_directed_lines a M) (unequally_directed_lines a (reverse_line M)) → % 4.10/4.32 Or (left_convergent_lines a M) (left_convergent_lines a (reverse_line M))) % 4.10/4.32 True % 4.10/4.32 Clause #98 (by clausification #[97]): ∀ (a a_1 : Iota), % 4.10/4.32 Eq % 4.10/4.32 (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1)) → % 4.10/4.32 Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) % 4.10/4.32 True % 4.10/4.32 Clause #99 (by clausification #[98]): ∀ (a a_1 : Iota), % 4.10/4.32 Or (Eq (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1))) False) % 4.10/4.32 (Eq (Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) True) % 4.10/4.32 Clause #100 (by clausification #[99]): ∀ (a a_1 : Iota), % 4.10/4.32 Or (Eq (Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) True) % 4.10/4.32 (Or (Eq (unequally_directed_lines a a_1) False) (Eq (unequally_directed_lines a (reverse_line a_1)) False)) % 4.10/4.32 Clause #101 (by clausification #[100]): ∀ (a a_1 : Iota), % 4.10/4.32 Or (Eq (unequally_directed_lines a a_1) False) % 4.10/4.32 (Or (Eq (unequally_directed_lines a (reverse_line a_1)) False) % 4.10/4.32 (Or (Eq (left_convergent_lines a a_1) True) (Eq (left_convergent_lines a (reverse_line a_1)) True))) % 4.10/4.32 Clause #102 (by forward demodulation #[101, 78]): ∀ (a a_1 : Iota), % 4.10/4.32 Or (Eq (unequally_directed_lines a a_1) False) % 4.10/4.32 (Or (Eq (unequally_directed_lines a (reverse_line a_1)) False) % 4.10/4.32 (Or (Eq False True) (Eq (left_convergent_lines a (reverse_line a_1)) True))) % 4.10/4.32 Clause #103 (by clausification #[102]): ∀ (a a_1 : Iota), % 4.10/4.32 Or (Eq (unequally_directed_lines a a_1) False) % 4.10/4.32 (Or (Eq (unequally_directed_lines a (reverse_line a_1)) False) % 4.10/4.32 (Eq (left_convergent_lines a (reverse_line a_1)) True)) % 4.10/4.32 Clause #140 (by clausification #[31]): Eq % 4.10/4.32 (∀ (L M A B C : Iota), % 4.10/4.32 And (And (between_on_line L A B C) (convergent_lines L M)) (Not (apart_point_and_line B M)) → divides_points M A C) % 4.10/4.32 False % 4.10/4.32 Clause #141 (by clausification #[140]): ∀ (a : Iota), % 4.10/4.32 Eq % 4.10/4.32 (Not % 4.10/4.34 (∀ (M A B C : Iota), % 4.10/4.34 And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) M)) % 4.10/4.34 (Not (apart_point_and_line B M)) → % 4.10/4.34 divides_points M A C)) % 4.10/4.34 True % 4.10/4.34 Clause #142 (by clausification #[141]): ∀ (a : Iota), % 4.10/4.34 Eq % 4.10/4.34 (∀ (M A B C : Iota), % 4.10/4.34 And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) M)) (Not (apart_point_and_line B M)) → % 4.10/4.34 divides_points M A C) % 4.10/4.34 False % 4.10/4.34 Clause #143 (by clausification #[142]): ∀ (a a_1 : Iota), % 4.10/4.34 Eq % 4.10/4.34 (Not % 4.10/4.34 (∀ (A B C : Iota), % 4.10/4.34 And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.10/4.34 (Not (apart_point_and_line B (skS.0 1 a a_1))) → % 4.10/4.34 divides_points (skS.0 1 a a_1) A C)) % 4.10/4.34 True % 4.10/4.34 Clause #144 (by clausification #[143]): ∀ (a a_1 : Iota), % 4.10/4.34 Eq % 4.10/4.34 (∀ (A B C : Iota), % 4.10/4.34 And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.10/4.34 (Not (apart_point_and_line B (skS.0 1 a a_1))) → % 4.10/4.34 divides_points (skS.0 1 a a_1) A C) % 4.10/4.34 False % 4.10/4.34 Clause #145 (by clausification #[144]): ∀ (a a_1 a_2 : Iota), % 4.10/4.34 Eq % 4.10/4.34 (Not % 4.10/4.34 (∀ (B C : Iota), % 4.10/4.34 And (And (between_on_line (skS.0 0 a) (skS.0 2 a a_1 a_2) B C) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.10/4.34 (Not (apart_point_and_line B (skS.0 1 a a_1))) → % 4.10/4.34 divides_points (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) C)) % 4.10/4.34 True % 4.10/4.34 Clause #146 (by clausification #[145]): ∀ (a a_1 a_2 : Iota), % 4.10/4.34 Eq % 4.10/4.34 (∀ (B C : Iota), % 4.10/4.34 And (And (between_on_line (skS.0 0 a) (skS.0 2 a a_1 a_2) B C) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.10/4.34 (Not (apart_point_and_line B (skS.0 1 a a_1))) → % 4.10/4.34 divides_points (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) C) % 4.10/4.34 False % 4.10/4.34 Clause #147 (by clausification #[146]): ∀ (a a_1 a_2 a_3 : Iota), % 4.10/4.34 Eq % 4.10/4.34 (Not % 4.10/4.34 (∀ (C : Iota), % 4.10/4.34 And % 4.10/4.34 (And (between_on_line (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) C) % 4.10/4.34 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.10/4.34 (Not (apart_point_and_line (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1))) → % 4.10/4.34 divides_points (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) C)) % 4.10/4.34 True % 4.10/4.34 Clause #148 (by clausification #[147]): ∀ (a a_1 a_2 a_3 : Iota), % 4.10/4.34 Eq % 4.10/4.34 (∀ (C : Iota), % 4.10/4.34 And % 4.10/4.34 (And (between_on_line (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) C) % 4.10/4.34 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.10/4.34 (Not (apart_point_and_line (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1))) → % 4.10/4.34 divides_points (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) C) % 4.10/4.34 False % 4.10/4.34 Clause #149 (by clausification #[148]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.10/4.34 Eq % 4.10/4.34 (Not % 4.10/4.34 (And % 4.10/4.34 (And (between_on_line (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) % 4.10/4.34 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.10/4.34 (Not (apart_point_and_line (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1))) → % 4.10/4.34 divides_points (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4))) % 4.10/4.34 True % 4.10/4.34 Clause #150 (by clausification #[149]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.10/4.34 Eq % 4.10/4.34 (And % 4.10/4.34 (And (between_on_line (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) % 4.10/4.34 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.10/4.34 (Not (apart_point_and_line (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1))) → % 4.10/4.34 divides_points (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4)) % 4.10/4.34 False % 4.10/4.34 Clause #151 (by clausification #[150]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.10/4.34 Eq % 4.10/4.34 (And % 4.10/4.34 (And (between_on_line (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) % 4.10/4.34 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.10/4.34 (Not (apart_point_and_line (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1)))) % 4.10/4.34 True % 4.10/4.34 Clause #154 (by clausification #[151]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.10/4.34 Eq % 4.10/4.34 (And (between_on_line (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)) % 4.10/4.34 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.18/4.35 True % 4.18/4.35 Clause #180 (by clausification #[69]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines a a_1) False) (Eq (unequally_directed_lines a (reverse_line a_1)) True) % 4.18/4.35 Clause #181 (by clausification #[69]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines a a_1) False) (Eq (unequally_directed_lines a a_1) True) % 4.18/4.35 Clause #283 (by clausification #[154]): ∀ (a a_1 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) True % 4.18/4.35 Clause #285 (by superposition #[283, 180]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (unequally_directed_lines (skS.0 0 a) (reverse_line (skS.0 1 a a_1))) True) % 4.18/4.35 Clause #286 (by superposition #[283, 181]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (unequally_directed_lines (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.18/4.35 Clause #287 (by clausification #[286]): ∀ (a a_1 : Iota), Eq (unequally_directed_lines (skS.0 0 a) (skS.0 1 a a_1)) True % 4.18/4.35 Clause #289 (by superposition #[287, 103]): ∀ (a a_1 : Iota), % 4.18/4.35 Or (Eq True False) % 4.18/4.35 (Or (Eq (unequally_directed_lines (skS.0 0 a) (reverse_line (skS.0 1 a a_1))) False) % 4.18/4.35 (Eq (left_convergent_lines (skS.0 0 a) (reverse_line (skS.0 1 a a_1))) True)) % 4.18/4.35 Clause #295 (by clausification #[285]): ∀ (a a_1 : Iota), Eq (unequally_directed_lines (skS.0 0 a) (reverse_line (skS.0 1 a a_1))) True % 4.18/4.35 Clause #404 (by clausification #[289]): ∀ (a a_1 : Iota), % 4.18/4.35 Or (Eq (unequally_directed_lines (skS.0 0 a) (reverse_line (skS.0 1 a a_1))) False) % 4.18/4.35 (Eq (left_convergent_lines (skS.0 0 a) (reverse_line (skS.0 1 a a_1))) True) % 4.18/4.35 Clause #405 (by forward demodulation #[404, 295]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (left_convergent_lines (skS.0 0 a) (reverse_line (skS.0 1 a a_1))) True) % 4.18/4.35 Clause #406 (by clausification #[405]): ∀ (a a_1 : Iota), Eq (left_convergent_lines (skS.0 0 a) (reverse_line (skS.0 1 a a_1))) True % 4.18/4.35 Clause #407 (by superposition #[406, 78]): Eq True False % 4.18/4.35 Clause #408 (by clausification #[407]): False % 4.18/4.35 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------