%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO253+1 : TPTP v9.2.0. Bugfixed v6.4.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 07:48:23 PM UTC 2025 % Result : Theorem 3.82s 3.98s % Output : Proof 3.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO253+1 : TPTP v9.2.0. Bugfixed v6.4.0. % 0.03/0.13 % Command : duper %s % 0.15/0.35 % Computer : n002.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Oct 3 12:36:08 EDT 2025 % 0.15/0.35 % CPUTime : % 3.82/3.98 SZS status Theorem for theBenchmark.p % 3.82/3.98 SZS output start Proof for theBenchmark.p % 3.82/3.98 Clause #0 (by assumption #[]): Eq (∀ (A L : Iota), Iff (apart_point_and_line A L) (Or (left_apart_point A L) (left_apart_point A (reverse_line L)))) % 3.82/3.98 True % 3.82/3.98 Clause #14 (by assumption #[]): Eq (∀ (A L : Iota), Not (Or (left_apart_point A L) (left_apart_point A (reverse_line L)))) True % 3.82/3.98 Clause #31 (by assumption #[]): Eq % 3.82/3.98 (Not % 3.82/3.98 (∀ (A B L : Iota), % 3.82/3.98 And (apart_point_and_line A L) (Not (apart_point_and_line B (parallel_through_point L A))) → % 3.82/3.98 apart_point_and_line B L)) % 3.82/3.98 True % 3.82/3.98 Clause #42 (by clausification #[0]): ∀ (a : Iota), % 3.82/3.98 Eq (∀ (L : Iota), Iff (apart_point_and_line a L) (Or (left_apart_point a L) (left_apart_point a (reverse_line L)))) % 3.82/3.98 True % 3.82/3.98 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), % 3.82/3.98 Eq (Iff (apart_point_and_line a a_1) (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1)))) True % 3.82/3.98 Clause #45 (by clausification #[43]): ∀ (a a_1 : Iota), % 3.82/3.98 Or (Eq (apart_point_and_line a a_1) False) % 3.82/3.98 (Eq (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1))) True) % 3.82/3.98 Clause #63 (by clausification #[31]): Eq % 3.82/3.98 (∀ (A B L : Iota), % 3.82/3.98 And (apart_point_and_line A L) (Not (apart_point_and_line B (parallel_through_point L A))) → % 3.82/3.98 apart_point_and_line B L) % 3.82/3.98 False % 3.82/3.98 Clause #64 (by clausification #[63]): ∀ (a : Iota), % 3.82/3.98 Eq % 3.82/3.98 (Not % 3.82/3.98 (∀ (B L : Iota), % 3.82/3.98 And (apart_point_and_line (skS.0 0 a) L) (Not (apart_point_and_line B (parallel_through_point L (skS.0 0 a)))) → % 3.82/3.98 apart_point_and_line B L)) % 3.82/3.98 True % 3.82/3.98 Clause #65 (by clausification #[64]): ∀ (a : Iota), % 3.82/3.98 Eq % 3.82/3.98 (∀ (B L : Iota), % 3.82/3.98 And (apart_point_and_line (skS.0 0 a) L) (Not (apart_point_and_line B (parallel_through_point L (skS.0 0 a)))) → % 3.82/3.98 apart_point_and_line B L) % 3.82/3.98 False % 3.82/3.98 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), % 3.82/3.98 Eq % 3.82/3.98 (Not % 3.82/3.98 (∀ (L : Iota), % 3.82/3.98 And (apart_point_and_line (skS.0 0 a) L) % 3.82/3.98 (Not (apart_point_and_line (skS.0 1 a a_1) (parallel_through_point L (skS.0 0 a)))) → % 3.82/3.98 apart_point_and_line (skS.0 1 a a_1) L)) % 3.82/3.98 True % 3.82/3.98 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), % 3.82/3.98 Eq % 3.82/3.98 (∀ (L : Iota), % 3.82/3.98 And (apart_point_and_line (skS.0 0 a) L) % 3.82/3.98 (Not (apart_point_and_line (skS.0 1 a a_1) (parallel_through_point L (skS.0 0 a)))) → % 3.82/3.98 apart_point_and_line (skS.0 1 a a_1) L) % 3.82/3.98 False % 3.82/3.98 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), % 3.82/3.98 Eq % 3.82/3.98 (Not % 3.82/3.98 (And (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 3.82/3.98 (Not (apart_point_and_line (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a)))) → % 3.82/3.98 apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 3.82/3.98 True % 3.82/3.98 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), % 3.82/3.98 Eq % 3.82/3.98 (And (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 3.82/3.98 (Not (apart_point_and_line (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a)))) → % 3.82/3.98 apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) % 3.82/3.98 False % 3.82/3.98 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), % 3.82/3.98 Eq % 3.82/3.98 (And (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 3.82/3.98 (Not (apart_point_and_line (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a))))) % 3.82/3.98 True % 3.82/3.98 Clause #73 (by clausification #[70]): ∀ (a a_1 a_2 : Iota), Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True % 3.82/3.98 Clause #119 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (L : Iota), Not (Or (left_apart_point a L) (left_apart_point a (reverse_line L)))) True % 3.82/3.98 Clause #120 (by clausification #[119]): ∀ (a a_1 : Iota), Eq (Not (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1)))) True % 3.82/3.98 Clause #121 (by clausification #[120]): ∀ (a a_1 : Iota), Eq (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1))) False % 3.82/3.98 Clause #123 (by clausification #[121]): ∀ (a a_1 : Iota), Eq (left_apart_point a a_1) False % 3.82/3.98 Clause #182 (by clausification #[45]): ∀ (a a_1 : Iota), % 3.82/3.98 Or (Eq (apart_point_and_line a a_1) False) % 3.82/3.98 (Or (Eq (left_apart_point a a_1) True) (Eq (left_apart_point a (reverse_line a_1)) True)) % 3.82/3.98 Clause #183 (by forward demodulation #[182, 123]): ∀ (a a_1 : Iota), % 3.82/3.98 Or (Eq (apart_point_and_line a a_1) False) (Or (Eq False True) (Eq (left_apart_point a (reverse_line a_1)) True)) % 3.82/3.98 Clause #184 (by clausification #[183]): ∀ (a a_1 : Iota), Or (Eq (apart_point_and_line a a_1) False) (Eq (left_apart_point a (reverse_line a_1)) True) % 3.82/3.98 Clause #222 (by superposition #[73, 184]): ∀ (a a_1 a_2 : Iota), Or (Eq (left_apart_point (skS.0 0 a) (reverse_line (skS.0 2 a a_1 a_2))) True) (Eq False True) % 3.82/3.98 Clause #223 (by clausification #[222]): ∀ (a a_1 a_2 : Iota), Eq (left_apart_point (skS.0 0 a) (reverse_line (skS.0 2 a a_1 a_2))) True % 3.82/3.98 Clause #224 (by superposition #[223, 123]): Eq True False % 3.82/3.98 Clause #246 (by clausification #[224]): False % 3.82/3.98 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------