%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO249+3 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 07:48:22 PM UTC 2025 % Result : Theorem 4.20s 4.38s % Output : Proof 4.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO249+3 : TPTP v9.2.0. Released v4.0.0. % 0.13/0.14 % Command : duper %s % 0.13/0.35 % Computer : n024.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 11:55:53 EDT 2025 % 0.13/0.35 % CPUTime : % 4.20/4.38 SZS status Theorem for theBenchmark.p % 4.20/4.38 SZS output start Proof for theBenchmark.p % 4.20/4.38 Clause #1 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (right_apart_point X Y) (left_apart_point X (reverse_line Y))) True % 4.20/4.38 Clause #19 (by assumption #[]): Eq (∀ (A L : Iota), Not (Or (left_apart_point A L) (left_apart_point A (reverse_line L)))) True % 4.20/4.38 Clause #36 (by assumption #[]): Eq % 4.20/4.38 (Not % 4.20/4.38 (∀ (A B L : Iota), % 4.20/4.38 And (right_apart_point A L) (right_apart_point B (parallel_through_point L A)) → right_apart_point B L)) % 4.20/4.38 True % 4.20/4.38 Clause #67 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (right_apart_point a Y) (left_apart_point a (reverse_line Y))) True % 4.20/4.38 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (Iff (right_apart_point a a_1) (left_apart_point a (reverse_line a_1))) True % 4.20/4.38 Clause #70 (by clausification #[68]): ∀ (a a_1 : Iota), Or (Eq (right_apart_point a a_1) False) (Eq (left_apart_point a (reverse_line a_1)) True) % 4.20/4.38 Clause #74 (by clausification #[36]): Eq % 4.20/4.38 (∀ (A B L : Iota), % 4.20/4.38 And (right_apart_point A L) (right_apart_point B (parallel_through_point L A)) → right_apart_point B L) % 4.20/4.38 False % 4.20/4.38 Clause #75 (by clausification #[74]): ∀ (a : Iota), % 4.20/4.38 Eq % 4.20/4.38 (Not % 4.20/4.38 (∀ (B L : Iota), % 4.20/4.38 And (right_apart_point (skS.0 0 a) L) (right_apart_point B (parallel_through_point L (skS.0 0 a))) → % 4.20/4.38 right_apart_point B L)) % 4.20/4.38 True % 4.20/4.38 Clause #76 (by clausification #[75]): ∀ (a : Iota), % 4.20/4.38 Eq % 4.20/4.38 (∀ (B L : Iota), % 4.20/4.38 And (right_apart_point (skS.0 0 a) L) (right_apart_point B (parallel_through_point L (skS.0 0 a))) → % 4.20/4.38 right_apart_point B L) % 4.20/4.38 False % 4.20/4.38 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota), % 4.20/4.38 Eq % 4.20/4.38 (Not % 4.20/4.38 (∀ (L : Iota), % 4.20/4.38 And (right_apart_point (skS.0 0 a) L) % 4.20/4.38 (right_apart_point (skS.0 1 a a_1) (parallel_through_point L (skS.0 0 a))) → % 4.20/4.38 right_apart_point (skS.0 1 a a_1) L)) % 4.20/4.38 True % 4.20/4.38 Clause #78 (by clausification #[77]): ∀ (a a_1 : Iota), % 4.20/4.38 Eq % 4.20/4.38 (∀ (L : Iota), % 4.20/4.38 And (right_apart_point (skS.0 0 a) L) (right_apart_point (skS.0 1 a a_1) (parallel_through_point L (skS.0 0 a))) → % 4.20/4.38 right_apart_point (skS.0 1 a a_1) L) % 4.20/4.38 False % 4.20/4.38 Clause #79 (by clausification #[78]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Eq % 4.20/4.38 (Not % 4.20/4.38 (And (right_apart_point (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 4.20/4.38 (right_apart_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a))) → % 4.20/4.38 right_apart_point (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.20/4.38 True % 4.20/4.38 Clause #80 (by clausification #[79]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Eq % 4.20/4.38 (And (right_apart_point (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 4.20/4.38 (right_apart_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a))) → % 4.20/4.38 right_apart_point (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) % 4.20/4.38 False % 4.20/4.38 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Eq % 4.20/4.38 (And (right_apart_point (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 4.20/4.38 (right_apart_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a)))) % 4.20/4.38 True % 4.20/4.38 Clause #83 (by clausification #[81]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Eq (right_apart_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a))) True % 4.20/4.38 Clause #85 (by superposition #[83, 70]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Or (Eq True False) % 4.20/4.38 (Eq (left_apart_point (skS.0 1 a a_1) (reverse_line (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a)))) True) % 4.20/4.38 Clause #184 (by clausification #[19]): ∀ (a : Iota), Eq (∀ (L : Iota), Not (Or (left_apart_point a L) (left_apart_point a (reverse_line L)))) True % 4.20/4.38 Clause #185 (by clausification #[184]): ∀ (a a_1 : Iota), Eq (Not (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1)))) True % 4.20/4.38 Clause #186 (by clausification #[185]): ∀ (a a_1 : Iota), Eq (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1))) False % 4.20/4.38 Clause #188 (by clausification #[186]): ∀ (a a_1 : Iota), Eq (left_apart_point a a_1) False % 4.20/4.38 Clause #403 (by clausification #[85]): ∀ (a a_1 a_2 : Iota), % 4.20/4.38 Eq (left_apart_point (skS.0 1 a a_1) (reverse_line (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a)))) True % 4.20/4.38 Clause #404 (by superposition #[403, 188]): Eq True False % 4.20/4.38 Clause #405 (by clausification #[404]): False % 4.20/4.38 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------