%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO263+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 4.40s 4.60s % Output : Proof 4.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : GEO263+1 : TPTP v9.2.0. Bugfixed v6.4.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n009.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 11:31:53 EDT 2025 % 0.13/0.34 % CPUTime : % 4.40/4.60 SZS status Theorem for theBenchmark.p % 4.40/4.60 SZS output start Proof for theBenchmark.p % 4.40/4.60 Clause #1 (by assumption #[]): Eq % 4.40/4.60 (∀ (L M : Iota), % 4.40/4.60 Iff (convergent_lines L M) (And (unequally_directed_lines L M) (unequally_directed_lines L (reverse_line M)))) % 4.40/4.60 True % 4.40/4.60 Clause #13 (by assumption #[]): Eq % 4.40/4.60 (∀ (L M : Iota), % 4.40/4.60 And (unequally_directed_lines L M) (unequally_directed_lines L (reverse_line M)) → % 4.40/4.60 Or (left_convergent_lines L M) (left_convergent_lines L (reverse_line M))) % 4.40/4.60 True % 4.40/4.60 Clause #15 (by assumption #[]): Eq (∀ (L M : Iota), Not (Or (left_convergent_lines L M) (left_convergent_lines L (reverse_line M)))) True % 4.40/4.60 Clause #31 (by assumption #[]): Eq % 4.40/4.60 (Not % 4.40/4.60 (∀ (L M N A B C : Iota), % 4.40/4.60 And (And (And (between_on_line L A B C) (convergent_lines L M)) (convergent_lines L N)) (convergent_lines M N) → % 4.40/4.60 between_on_line M (intersection_point M (parallel_through_point N A)) % 4.40/4.60 (intersection_point M (parallel_through_point N B)) (intersection_point M (parallel_through_point N C)))) % 4.40/4.60 True % 4.40/4.60 Clause #66 (by clausification #[1]): ∀ (a : Iota), % 4.40/4.60 Eq % 4.40/4.60 (∀ (M : Iota), % 4.40/4.60 Iff (convergent_lines a M) (And (unequally_directed_lines a M) (unequally_directed_lines a (reverse_line M)))) % 4.40/4.60 True % 4.40/4.60 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), % 4.40/4.60 Eq % 4.40/4.60 (Iff (convergent_lines a a_1) % 4.40/4.60 (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1)))) % 4.40/4.60 True % 4.40/4.60 Clause #69 (by clausification #[67]): ∀ (a a_1 : Iota), % 4.40/4.60 Or (Eq (convergent_lines a a_1) False) % 4.40/4.60 (Eq (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1))) True) % 4.40/4.60 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 % 4.40/4.60 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 % 4.40/4.60 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 % 4.40/4.60 Clause #78 (by clausification #[76]): ∀ (a a_1 : Iota), Eq (left_convergent_lines a a_1) False % 4.40/4.60 Clause #97 (by clausification #[13]): ∀ (a : Iota), % 4.40/4.60 Eq % 4.40/4.60 (∀ (M : Iota), % 4.40/4.60 And (unequally_directed_lines a M) (unequally_directed_lines a (reverse_line M)) → % 4.40/4.60 Or (left_convergent_lines a M) (left_convergent_lines a (reverse_line M))) % 4.40/4.60 True % 4.40/4.60 Clause #98 (by clausification #[97]): ∀ (a a_1 : Iota), % 4.40/4.60 Eq % 4.40/4.60 (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1)) → % 4.40/4.60 Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) % 4.40/4.60 True % 4.40/4.60 Clause #99 (by clausification #[98]): ∀ (a a_1 : Iota), % 4.40/4.60 Or (Eq (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1))) False) % 4.40/4.60 (Eq (Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) True) % 4.40/4.60 Clause #100 (by clausification #[99]): ∀ (a a_1 : Iota), % 4.40/4.60 Or (Eq (Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) True) % 4.40/4.60 (Or (Eq (unequally_directed_lines a a_1) False) (Eq (unequally_directed_lines a (reverse_line a_1)) False)) % 4.40/4.60 Clause #101 (by clausification #[100]): ∀ (a a_1 : Iota), % 4.40/4.60 Or (Eq (unequally_directed_lines a a_1) False) % 4.40/4.60 (Or (Eq (unequally_directed_lines a (reverse_line a_1)) False) % 4.40/4.60 (Or (Eq (left_convergent_lines a a_1) True) (Eq (left_convergent_lines a (reverse_line a_1)) True))) % 4.40/4.60 Clause #102 (by forward demodulation #[101, 78]): ∀ (a a_1 : Iota), % 4.40/4.60 Or (Eq (unequally_directed_lines a a_1) False) % 4.40/4.60 (Or (Eq (unequally_directed_lines a (reverse_line a_1)) False) % 4.40/4.60 (Or (Eq False True) (Eq (left_convergent_lines a (reverse_line a_1)) True))) % 4.40/4.60 Clause #103 (by clausification #[102]): ∀ (a a_1 : Iota), % 4.40/4.60 Or (Eq (unequally_directed_lines a a_1) False) % 4.40/4.60 (Or (Eq (unequally_directed_lines a (reverse_line a_1)) False) % 4.40/4.60 (Eq (left_convergent_lines a (reverse_line a_1)) True)) % 4.40/4.60 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) % 4.40/4.62 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) % 4.40/4.62 Clause #244 (by clausification #[31]): Eq % 4.40/4.62 (∀ (L M N A B C : Iota), % 4.40/4.62 And (And (And (between_on_line L A B C) (convergent_lines L M)) (convergent_lines L N)) (convergent_lines M N) → % 4.40/4.62 between_on_line M (intersection_point M (parallel_through_point N A)) % 4.40/4.62 (intersection_point M (parallel_through_point N B)) (intersection_point M (parallel_through_point N C))) % 4.40/4.62 False % 4.40/4.62 Clause #245 (by clausification #[244]): ∀ (a : Iota), % 4.40/4.62 Eq % 4.40/4.62 (Not % 4.40/4.62 (∀ (M N A B C : Iota), % 4.40/4.62 And % 4.40/4.62 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) M)) % 4.40/4.62 (convergent_lines (skS.0 0 a) N)) % 4.40/4.62 (convergent_lines M N) → % 4.40/4.62 between_on_line M (intersection_point M (parallel_through_point N A)) % 4.40/4.62 (intersection_point M (parallel_through_point N B)) (intersection_point M (parallel_through_point N C)))) % 4.40/4.62 True % 4.40/4.62 Clause #246 (by clausification #[245]): ∀ (a : Iota), % 4.40/4.62 Eq % 4.40/4.62 (∀ (M N A B C : Iota), % 4.40/4.62 And % 4.40/4.62 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) M)) % 4.40/4.62 (convergent_lines (skS.0 0 a) N)) % 4.40/4.62 (convergent_lines M N) → % 4.40/4.62 between_on_line M (intersection_point M (parallel_through_point N A)) % 4.40/4.62 (intersection_point M (parallel_through_point N B)) (intersection_point M (parallel_through_point N C))) % 4.40/4.62 False % 4.40/4.62 Clause #247 (by clausification #[246]): ∀ (a a_1 : Iota), % 4.40/4.62 Eq % 4.40/4.62 (Not % 4.40/4.62 (∀ (N A B C : Iota), % 4.40/4.62 And % 4.40/4.62 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.40/4.62 (convergent_lines (skS.0 0 a) N)) % 4.40/4.62 (convergent_lines (skS.0 1 a a_1) N) → % 4.40/4.62 between_on_line (skS.0 1 a a_1) (intersection_point (skS.0 1 a a_1) (parallel_through_point N A)) % 4.40/4.62 (intersection_point (skS.0 1 a a_1) (parallel_through_point N B)) % 4.40/4.62 (intersection_point (skS.0 1 a a_1) (parallel_through_point N C)))) % 4.40/4.62 True % 4.40/4.62 Clause #248 (by clausification #[247]): ∀ (a a_1 : Iota), % 4.40/4.62 Eq % 4.40/4.62 (∀ (N A B C : Iota), % 4.40/4.62 And % 4.40/4.62 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.40/4.62 (convergent_lines (skS.0 0 a) N)) % 4.40/4.62 (convergent_lines (skS.0 1 a a_1) N) → % 4.40/4.62 between_on_line (skS.0 1 a a_1) (intersection_point (skS.0 1 a a_1) (parallel_through_point N A)) % 4.40/4.62 (intersection_point (skS.0 1 a a_1) (parallel_through_point N B)) % 4.40/4.62 (intersection_point (skS.0 1 a a_1) (parallel_through_point N C))) % 4.40/4.62 False % 4.40/4.62 Clause #249 (by clausification #[248]): ∀ (a a_1 a_2 : Iota), % 4.40/4.62 Eq % 4.40/4.62 (Not % 4.40/4.62 (∀ (A B C : Iota), % 4.40/4.62 And % 4.40/4.62 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.40/4.62 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.40/4.62 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 4.40/4.62 between_on_line (skS.0 1 a a_1) % 4.40/4.62 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) A)) % 4.40/4.62 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) B)) % 4.40/4.62 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C)))) % 4.40/4.62 True % 4.40/4.62 Clause #250 (by clausification #[249]): ∀ (a a_1 a_2 : Iota), % 4.40/4.62 Eq % 4.40/4.62 (∀ (A B C : Iota), % 4.40/4.62 And % 4.40/4.62 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.40/4.62 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.40/4.62 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 4.40/4.62 between_on_line (skS.0 1 a a_1) % 4.40/4.62 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) A)) % 4.40/4.62 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) B)) % 4.40/4.62 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C))) % 4.46/4.64 False % 4.46/4.64 Clause #251 (by clausification #[250]): ∀ (a a_1 a_2 a_3 : Iota), % 4.46/4.64 Eq % 4.46/4.64 (Not % 4.46/4.64 (∀ (B C : Iota), % 4.46/4.64 And % 4.46/4.64 (And % 4.46/4.64 (And (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) B C) % 4.46/4.64 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.46/4.64 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.46/4.64 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 4.46/4.64 between_on_line (skS.0 1 a a_1) % 4.46/4.64 (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))) % 4.46/4.64 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) B)) % 4.46/4.64 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C)))) % 4.46/4.64 True % 4.46/4.64 Clause #252 (by clausification #[251]): ∀ (a a_1 a_2 a_3 : Iota), % 4.46/4.64 Eq % 4.46/4.64 (∀ (B C : Iota), % 4.46/4.64 And % 4.46/4.64 (And % 4.46/4.64 (And (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) B C) % 4.46/4.64 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.46/4.64 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.46/4.64 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 4.46/4.64 between_on_line (skS.0 1 a a_1) % 4.46/4.64 (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))) % 4.46/4.64 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) B)) % 4.46/4.64 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C))) % 4.46/4.64 False % 4.46/4.64 Clause #253 (by clausification #[252]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.46/4.64 Eq % 4.46/4.64 (Not % 4.46/4.64 (∀ (C : Iota), % 4.46/4.64 And % 4.46/4.64 (And % 4.46/4.64 (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) % 4.46/4.64 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.46/4.64 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.46/4.64 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 4.46/4.64 between_on_line (skS.0 1 a a_1) % 4.46/4.64 (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))) % 4.46/4.64 (intersection_point (skS.0 1 a a_1) % 4.46/4.64 (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4))) % 4.46/4.64 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C)))) % 4.46/4.64 True % 4.46/4.64 Clause #254 (by clausification #[253]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.46/4.64 Eq % 4.46/4.64 (∀ (C : Iota), % 4.46/4.64 And % 4.46/4.64 (And % 4.46/4.64 (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) % 4.46/4.64 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.46/4.64 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.46/4.64 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 4.46/4.64 between_on_line (skS.0 1 a a_1) % 4.46/4.64 (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))) % 4.46/4.64 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4))) % 4.46/4.64 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C))) % 4.46/4.64 False % 4.46/4.64 Clause #255 (by clausification #[254]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.46/4.64 Eq % 4.46/4.64 (Not % 4.46/4.64 (And % 4.46/4.64 (And % 4.46/4.64 (And % 4.46/4.64 (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) % 4.46/4.64 (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) % 4.46/4.64 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.46/4.64 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.46/4.64 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 4.46/4.64 between_on_line (skS.0 1 a a_1) % 4.46/4.64 (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))) % 4.46/4.64 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4))) % 4.46/4.64 (intersection_point (skS.0 1 a a_1) % 4.46/4.64 (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))))) % 4.46/4.64 True % 4.46/4.64 Clause #256 (by clausification #[255]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.49/4.66 Eq % 4.49/4.66 (And % 4.49/4.66 (And % 4.49/4.66 (And % 4.49/4.66 (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) % 4.49/4.66 (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) % 4.49/4.66 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.49/4.66 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.49/4.66 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 4.49/4.66 between_on_line (skS.0 1 a a_1) % 4.49/4.66 (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))) % 4.49/4.66 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4))) % 4.49/4.66 (intersection_point (skS.0 1 a a_1) % 4.49/4.66 (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)))) % 4.49/4.66 False % 4.49/4.66 Clause #257 (by clausification #[256]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.49/4.66 Eq % 4.49/4.66 (And % 4.49/4.66 (And % 4.49/4.66 (And % 4.49/4.66 (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) % 4.49/4.66 (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) % 4.49/4.66 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.49/4.66 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.49/4.66 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.49/4.66 True % 4.49/4.66 Clause #259 (by clausification #[257]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True % 4.49/4.66 Clause #261 (by superposition #[259, 155]): ∀ (a a_1 a_2 : Iota), % 4.49/4.66 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) % 4.49/4.66 Clause #262 (by superposition #[259, 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) % 4.49/4.66 Clause #265 (by clausification #[262]): ∀ (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 % 4.49/4.66 Clause #267 (by superposition #[265, 103]): ∀ (a a_1 a_2 : Iota), % 4.49/4.66 Or (Eq True False) % 4.49/4.66 (Or (Eq (unequally_directed_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) False) % 4.49/4.66 (Eq (left_convergent_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) True)) % 4.49/4.66 Clause #273 (by clausification #[261]): ∀ (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 % 4.49/4.66 Clause #397 (by clausification #[267]): ∀ (a a_1 a_2 : Iota), % 4.49/4.66 Or (Eq (unequally_directed_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) False) % 4.49/4.66 (Eq (left_convergent_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) True) % 4.49/4.66 Clause #398 (by forward demodulation #[397, 273]): ∀ (a a_1 a_2 : Iota), % 4.49/4.66 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) % 4.49/4.66 Clause #399 (by clausification #[398]): ∀ (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 % 4.49/4.66 Clause #400 (by superposition #[399, 78]): Eq True False % 4.49/4.66 Clause #401 (by clausification #[400]): False % 4.49/4.66 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------