%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO262+1 : TPTP v9.2.0. Bugfixed v6.4.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n012.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 4.20s 4.36s % Output : Proof 4.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : GEO262+1 : TPTP v9.2.0. Bugfixed v6.4.0. % 0.08/0.14 % Command : duper %s % 0.13/0.35 % Computer : n012.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 12:12:53 EDT 2025 % 0.13/0.36 % CPUTime : % 4.20/4.36 SZS status Theorem for theBenchmark.p % 4.20/4.36 SZS output start Proof for theBenchmark.p % 4.20/4.36 Clause #1 (by assumption #[]): Eq % 4.20/4.36 (∀ (L M : Iota), % 4.20/4.36 Iff (convergent_lines L M) (And (unequally_directed_lines L M) (unequally_directed_lines L (reverse_line M)))) % 4.20/4.36 True % 4.20/4.36 Clause #13 (by assumption #[]): Eq % 4.20/4.36 (∀ (L M : Iota), % 4.20/4.36 And (unequally_directed_lines L M) (unequally_directed_lines L (reverse_line M)) → % 4.20/4.36 Or (left_convergent_lines L M) (left_convergent_lines L (reverse_line M))) % 4.20/4.36 True % 4.20/4.36 Clause #15 (by assumption #[]): Eq (∀ (L M : Iota), Not (Or (left_convergent_lines L M) (left_convergent_lines L (reverse_line M)))) True % 4.20/4.36 Clause #31 (by assumption #[]): Eq % 4.20/4.36 (Not % 4.20/4.36 (∀ (L M N A B C : Iota), % 4.20/4.36 And % 4.20/4.36 (And % 4.20/4.36 (And (And (And (between_on_line L A B C) (convergent_lines L M)) (Not (apart_point_and_line B M))) % 4.20/4.36 (convergent_lines L N)) % 4.20/4.36 (convergent_lines M N)) % 4.20/4.36 (Not (apart_point_and_line B N)) → % 4.20/4.36 between_on_line M (intersection_point M (parallel_through_point N A)) B % 4.20/4.36 (intersection_point M (parallel_through_point N C)))) % 4.20/4.36 True % 4.20/4.36 Clause #66 (by clausification #[1]): ∀ (a : Iota), % 4.20/4.36 Eq % 4.20/4.36 (∀ (M : Iota), % 4.20/4.36 Iff (convergent_lines a M) (And (unequally_directed_lines a M) (unequally_directed_lines a (reverse_line M)))) % 4.20/4.36 True % 4.20/4.36 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), % 4.20/4.36 Eq % 4.20/4.36 (Iff (convergent_lines a a_1) % 4.20/4.36 (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1)))) % 4.20/4.36 True % 4.20/4.36 Clause #69 (by clausification #[67]): ∀ (a a_1 : Iota), % 4.20/4.36 Or (Eq (convergent_lines a a_1) False) % 4.20/4.36 (Eq (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1))) True) % 4.20/4.36 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 % 4.20/4.36 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 % 4.20/4.36 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 % 4.20/4.36 Clause #78 (by clausification #[76]): ∀ (a a_1 : Iota), Eq (left_convergent_lines a a_1) False % 4.20/4.36 Clause #97 (by clausification #[13]): ∀ (a : Iota), % 4.20/4.36 Eq % 4.20/4.36 (∀ (M : Iota), % 4.20/4.36 And (unequally_directed_lines a M) (unequally_directed_lines a (reverse_line M)) → % 4.20/4.36 Or (left_convergent_lines a M) (left_convergent_lines a (reverse_line M))) % 4.20/4.36 True % 4.20/4.36 Clause #98 (by clausification #[97]): ∀ (a a_1 : Iota), % 4.20/4.36 Eq % 4.20/4.36 (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1)) → % 4.20/4.36 Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) % 4.20/4.36 True % 4.20/4.36 Clause #99 (by clausification #[98]): ∀ (a a_1 : Iota), % 4.20/4.36 Or (Eq (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1))) False) % 4.20/4.36 (Eq (Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) True) % 4.20/4.36 Clause #100 (by clausification #[99]): ∀ (a a_1 : Iota), % 4.20/4.36 Or (Eq (Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) True) % 4.20/4.36 (Or (Eq (unequally_directed_lines a a_1) False) (Eq (unequally_directed_lines a (reverse_line a_1)) False)) % 4.20/4.36 Clause #101 (by clausification #[100]): ∀ (a a_1 : Iota), % 4.20/4.36 Or (Eq (unequally_directed_lines a a_1) False) % 4.20/4.36 (Or (Eq (unequally_directed_lines a (reverse_line a_1)) False) % 4.20/4.36 (Or (Eq (left_convergent_lines a a_1) True) (Eq (left_convergent_lines a (reverse_line a_1)) True))) % 4.20/4.36 Clause #102 (by forward demodulation #[101, 78]): ∀ (a a_1 : Iota), % 4.20/4.36 Or (Eq (unequally_directed_lines a a_1) False) % 4.20/4.36 (Or (Eq (unequally_directed_lines a (reverse_line a_1)) False) % 4.20/4.36 (Or (Eq False True) (Eq (left_convergent_lines a (reverse_line a_1)) True))) % 4.20/4.36 Clause #103 (by clausification #[102]): ∀ (a a_1 : Iota), % 4.20/4.36 Or (Eq (unequally_directed_lines a a_1) False) % 4.20/4.36 (Or (Eq (unequally_directed_lines a (reverse_line a_1)) False) % 4.20/4.36 (Eq (left_convergent_lines a (reverse_line a_1)) True)) % 4.20/4.38 Clause #155 (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) % 4.20/4.38 Clause #156 (by clausification #[69]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines a a_1) False) (Eq (unequally_directed_lines a a_1) True) % 4.20/4.38 Clause #233 (by clausification #[31]): Eq % 4.20/4.38 (∀ (L M N A B C : Iota), % 4.20/4.38 And % 4.20/4.38 (And % 4.20/4.38 (And (And (And (between_on_line L A B C) (convergent_lines L M)) (Not (apart_point_and_line B M))) % 4.20/4.38 (convergent_lines L N)) % 4.20/4.38 (convergent_lines M N)) % 4.20/4.38 (Not (apart_point_and_line B N)) → % 4.20/4.38 between_on_line M (intersection_point M (parallel_through_point N A)) B % 4.20/4.38 (intersection_point M (parallel_through_point N C))) % 4.20/4.38 False % 4.20/4.38 Clause #234 (by clausification #[233]): ∀ (a : Iota), % 4.20/4.38 Eq % 4.20/4.38 (Not % 4.20/4.38 (∀ (M N A B C : Iota), % 4.20/4.38 And % 4.20/4.38 (And % 4.20/4.38 (And % 4.20/4.38 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) M)) % 4.20/4.38 (Not (apart_point_and_line B M))) % 4.20/4.38 (convergent_lines (skS.0 0 a) N)) % 4.20/4.38 (convergent_lines M N)) % 4.20/4.38 (Not (apart_point_and_line B N)) → % 4.20/4.38 between_on_line M (intersection_point M (parallel_through_point N A)) B % 4.20/4.38 (intersection_point M (parallel_through_point N C)))) % 4.20/4.38 True % 4.20/4.38 Clause #235 (by clausification #[234]): ∀ (a : Iota), % 4.20/4.38 Eq % 4.20/4.38 (∀ (M N A B C : Iota), % 4.20/4.38 And % 4.20/4.38 (And % 4.20/4.38 (And % 4.20/4.38 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) M)) % 4.20/4.38 (Not (apart_point_and_line B M))) % 4.20/4.38 (convergent_lines (skS.0 0 a) N)) % 4.20/4.38 (convergent_lines M N)) % 4.20/4.38 (Not (apart_point_and_line B N)) → % 4.20/4.38 between_on_line M (intersection_point M (parallel_through_point N A)) B % 4.20/4.38 (intersection_point M (parallel_through_point N C))) % 4.20/4.38 False % 4.20/4.38 Clause #236 (by clausification #[235]): ∀ (a a_1 : Iota), % 4.20/4.38 Eq % 4.20/4.38 (Not % 4.20/4.38 (∀ (N A B C : Iota), % 4.20/4.38 And % 4.20/4.38 (And % 4.20/4.38 (And % 4.20/4.38 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.20/4.38 (Not (apart_point_and_line B (skS.0 1 a a_1)))) % 4.20/4.38 (convergent_lines (skS.0 0 a) N)) % 4.20/4.38 (convergent_lines (skS.0 1 a a_1) N)) % 4.20/4.38 (Not (apart_point_and_line B N)) → % 4.20/4.38 between_on_line (skS.0 1 a a_1) (intersection_point (skS.0 1 a a_1) (parallel_through_point N A)) B % 4.20/4.38 (intersection_point (skS.0 1 a a_1) (parallel_through_point N C)))) % 4.20/4.38 True % 4.20/4.38 Clause #237 (by clausification #[236]): ∀ (a a_1 : Iota), % 4.20/4.38 Eq % 4.20/4.38 (∀ (N A B C : Iota), % 4.20/4.38 And % 4.20/4.38 (And % 4.20/4.38 (And % 4.20/4.38 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.20/4.38 (Not (apart_point_and_line B (skS.0 1 a a_1)))) % 4.20/4.38 (convergent_lines (skS.0 0 a) N)) % 4.20/4.38 (convergent_lines (skS.0 1 a a_1) N)) % 4.20/4.38 (Not (apart_point_and_line B N)) → % 4.20/4.38 between_on_line (skS.0 1 a a_1) (intersection_point (skS.0 1 a a_1) (parallel_through_point N A)) B % 4.20/4.38 (intersection_point (skS.0 1 a a_1) (parallel_through_point N C))) % 4.20/4.38 False % 4.20/4.38 Clause #238 (by clausification #[237]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Eq % 4.20/4.38 (Not % 4.20/4.38 (∀ (A B C : Iota), % 4.20/4.38 And % 4.20/4.38 (And % 4.20/4.38 (And % 4.20/4.38 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.20/4.38 (Not (apart_point_and_line B (skS.0 1 a a_1)))) % 4.20/4.38 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.20/4.38 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.20/4.38 (Not (apart_point_and_line B (skS.0 2 a a_1 a_2))) → % 4.20/4.38 between_on_line (skS.0 1 a a_1) % 4.20/4.38 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) A)) B % 4.20/4.38 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C)))) % 4.20/4.38 True % 4.20/4.38 Clause #239 (by clausification #[238]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Eq % 4.20/4.38 (∀ (A B C : Iota), % 4.24/4.40 And % 4.24/4.40 (And % 4.24/4.40 (And % 4.24/4.40 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.24/4.40 (Not (apart_point_and_line B (skS.0 1 a a_1)))) % 4.24/4.40 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.24/4.40 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.24/4.40 (Not (apart_point_and_line B (skS.0 2 a a_1 a_2))) → % 4.24/4.40 between_on_line (skS.0 1 a a_1) % 4.24/4.40 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) A)) B % 4.24/4.40 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C))) % 4.24/4.40 False % 4.24/4.40 Clause #240 (by clausification #[239]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.40 Eq % 4.24/4.40 (Not % 4.24/4.40 (∀ (B C : Iota), % 4.24/4.40 And % 4.24/4.40 (And % 4.24/4.40 (And % 4.24/4.40 (And % 4.24/4.40 (And (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) B C) % 4.24/4.40 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.24/4.40 (Not (apart_point_and_line B (skS.0 1 a a_1)))) % 4.24/4.40 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.24/4.40 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.24/4.40 (Not (apart_point_and_line B (skS.0 2 a a_1 a_2))) → % 4.24/4.40 between_on_line (skS.0 1 a a_1) % 4.24/4.40 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) B % 4.24/4.40 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C)))) % 4.24/4.40 True % 4.24/4.40 Clause #241 (by clausification #[240]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.40 Eq % 4.24/4.40 (∀ (B C : Iota), % 4.24/4.40 And % 4.24/4.40 (And % 4.24/4.40 (And % 4.24/4.40 (And % 4.24/4.40 (And (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) B C) % 4.24/4.40 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.24/4.40 (Not (apart_point_and_line B (skS.0 1 a a_1)))) % 4.24/4.40 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.24/4.40 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.24/4.40 (Not (apart_point_and_line B (skS.0 2 a a_1 a_2))) → % 4.24/4.40 between_on_line (skS.0 1 a a_1) % 4.24/4.40 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) B % 4.24/4.40 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C))) % 4.24/4.40 False % 4.24/4.40 Clause #242 (by clausification #[241]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.24/4.40 Eq % 4.24/4.40 (Not % 4.24/4.40 (∀ (C : Iota), % 4.24/4.40 And % 4.24/4.40 (And % 4.24/4.40 (And % 4.24/4.40 (And % 4.24/4.40 (And (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4) C) % 4.24/4.40 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.24/4.40 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1)))) % 4.24/4.40 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.24/4.40 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.24/4.40 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2))) → % 4.24/4.40 between_on_line (skS.0 1 a a_1) % 4.24/4.40 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 4.24/4.40 (skS.0 4 a a_1 a_2 a_3 a_4) % 4.24/4.40 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C)))) % 4.24/4.40 True % 4.24/4.40 Clause #243 (by clausification #[242]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.24/4.40 Eq % 4.24/4.40 (∀ (C : Iota), % 4.24/4.40 And % 4.24/4.40 (And % 4.24/4.40 (And % 4.24/4.40 (And % 4.24/4.40 (And (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4) C) % 4.24/4.40 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.24/4.40 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1)))) % 4.24/4.40 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.24/4.40 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.24/4.40 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2))) → % 4.24/4.40 between_on_line (skS.0 1 a a_1) % 4.24/4.40 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 4.24/4.42 (skS.0 4 a a_1 a_2 a_3 a_4) % 4.24/4.42 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C))) % 4.24/4.42 False % 4.24/4.42 Clause #244 (by clausification #[243]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.24/4.42 Eq % 4.24/4.42 (Not % 4.24/4.42 (And % 4.24/4.42 (And % 4.24/4.42 (And % 4.24/4.42 (And % 4.24/4.42 (And % 4.24/4.42 (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4) % 4.24/4.42 (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) % 4.24/4.42 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.24/4.42 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1)))) % 4.24/4.42 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.24/4.42 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.24/4.42 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2))) → % 4.24/4.42 between_on_line (skS.0 1 a a_1) % 4.24/4.42 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 4.24/4.42 (skS.0 4 a a_1 a_2 a_3 a_4) % 4.24/4.42 (intersection_point (skS.0 1 a a_1) % 4.24/4.42 (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))))) % 4.24/4.42 True % 4.24/4.42 Clause #245 (by clausification #[244]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.24/4.42 Eq % 4.24/4.42 (And % 4.24/4.42 (And % 4.24/4.42 (And % 4.24/4.42 (And % 4.24/4.42 (And % 4.24/4.42 (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4) % 4.24/4.42 (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) % 4.24/4.42 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.24/4.42 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1)))) % 4.24/4.42 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.24/4.42 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.24/4.42 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2))) → % 4.24/4.42 between_on_line (skS.0 1 a a_1) % 4.24/4.42 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 4.24/4.42 (skS.0 4 a a_1 a_2 a_3 a_4) % 4.24/4.42 (intersection_point (skS.0 1 a a_1) % 4.24/4.42 (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)))) % 4.24/4.42 False % 4.24/4.42 Clause #246 (by clausification #[245]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.24/4.42 Eq % 4.24/4.42 (And % 4.24/4.42 (And % 4.24/4.42 (And % 4.24/4.42 (And % 4.24/4.42 (And % 4.24/4.42 (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4) % 4.24/4.42 (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) % 4.24/4.42 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.24/4.42 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1)))) % 4.24/4.42 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.24/4.42 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.24/4.42 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2)))) % 4.24/4.42 True % 4.24/4.42 Clause #249 (by clausification #[246]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.24/4.42 Eq % 4.24/4.42 (And % 4.24/4.42 (And % 4.24/4.42 (And % 4.24/4.42 (And % 4.24/4.42 (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4) % 4.24/4.42 (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) % 4.24/4.42 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.24/4.42 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1)))) % 4.24/4.42 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.24/4.42 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.24/4.42 True % 4.24/4.42 Clause #285 (by clausification #[249]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True % 4.24/4.42 Clause #287 (by superposition #[285, 155]): ∀ (a a_1 a_2 : Iota), % 4.24/4.42 Or (Eq True False) (Eq (unequally_directed_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) True) % 4.24/4.42 Clause #288 (by superposition #[285, 156]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (unequally_directed_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True) % 4.24/4.42 Clause #289 (by clausification #[288]): ∀ (a a_1 a_2 : Iota), Eq (unequally_directed_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True % 4.24/4.42 Clause #291 (by superposition #[289, 103]): ∀ (a a_1 a_2 : Iota), % 4.24/4.42 Or (Eq True False) % 4.24/4.42 (Or (Eq (unequally_directed_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) False) % 4.24/4.42 (Eq (left_convergent_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) True)) % 4.24/4.42 Clause #297 (by clausification #[287]): ∀ (a a_1 a_2 : Iota), Eq (unequally_directed_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) True % 4.24/4.42 Clause #400 (by clausification #[291]): ∀ (a a_1 a_2 : Iota), % 4.24/4.42 Or (Eq (unequally_directed_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) False) % 4.24/4.42 (Eq (left_convergent_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) True) % 4.24/4.42 Clause #401 (by forward demodulation #[400, 297]): ∀ (a a_1 a_2 : Iota), % 4.24/4.42 Or (Eq True False) (Eq (left_convergent_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) True) % 4.24/4.42 Clause #402 (by clausification #[401]): ∀ (a a_1 a_2 : Iota), Eq (left_convergent_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) True % 4.24/4.42 Clause #403 (by superposition #[402, 78]): Eq True False % 4.24/4.42 Clause #404 (by clausification #[403]): False % 4.24/4.42 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------