%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO251+3 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 4.06s 4.31s % Output : Proof 4.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : GEO251+3 : TPTP v9.2.0. Released v4.0.0. % 0.10/0.13 % Command : duper %s % 0.13/0.34 % Computer : n025.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 11:26:23 EDT 2025 % 0.13/0.34 % CPUTime : % 4.06/4.31 SZS status Theorem for theBenchmark.p % 4.06/4.31 SZS output start Proof for theBenchmark.p % 4.06/4.31 Clause #1 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (right_apart_point X Y) (left_apart_point X (reverse_line Y))) True % 4.06/4.31 Clause #19 (by assumption #[]): Eq (∀ (A L : Iota), Not (Or (left_apart_point A L) (left_apart_point A (reverse_line L)))) True % 4.06/4.31 Clause #36 (by assumption #[]): Eq % 4.06/4.31 (Not % 4.06/4.31 (∀ (A B L : Iota), % 4.06/4.31 right_apart_point B (parallel_through_point L A) → left_apart_point A (parallel_through_point L B))) % 4.06/4.31 True % 4.06/4.31 Clause #67 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (right_apart_point a Y) (left_apart_point a (reverse_line Y))) True % 4.06/4.31 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 % 4.06/4.31 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) % 4.06/4.31 Clause #74 (by clausification #[36]): Eq % 4.06/4.31 (∀ (A B L : Iota), right_apart_point B (parallel_through_point L A) → left_apart_point A (parallel_through_point L B)) % 4.06/4.31 False % 4.06/4.31 Clause #75 (by clausification #[74]): ∀ (a : Iota), % 4.06/4.31 Eq % 4.06/4.31 (Not % 4.06/4.31 (∀ (B L : Iota), % 4.06/4.31 right_apart_point B (parallel_through_point L (skS.0 0 a)) → % 4.06/4.31 left_apart_point (skS.0 0 a) (parallel_through_point L B))) % 4.06/4.31 True % 4.06/4.31 Clause #76 (by clausification #[75]): ∀ (a : Iota), % 4.06/4.31 Eq % 4.06/4.31 (∀ (B L : Iota), % 4.06/4.31 right_apart_point B (parallel_through_point L (skS.0 0 a)) → % 4.06/4.31 left_apart_point (skS.0 0 a) (parallel_through_point L B)) % 4.06/4.31 False % 4.06/4.31 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota), % 4.06/4.31 Eq % 4.06/4.31 (Not % 4.06/4.31 (∀ (L : Iota), % 4.06/4.31 right_apart_point (skS.0 1 a a_1) (parallel_through_point L (skS.0 0 a)) → % 4.06/4.31 left_apart_point (skS.0 0 a) (parallel_through_point L (skS.0 1 a a_1)))) % 4.06/4.31 True % 4.06/4.31 Clause #78 (by clausification #[77]): ∀ (a a_1 : Iota), % 4.06/4.31 Eq % 4.06/4.31 (∀ (L : Iota), % 4.06/4.31 right_apart_point (skS.0 1 a a_1) (parallel_through_point L (skS.0 0 a)) → % 4.06/4.31 left_apart_point (skS.0 0 a) (parallel_through_point L (skS.0 1 a a_1))) % 4.06/4.31 False % 4.06/4.31 Clause #79 (by clausification #[78]): ∀ (a a_1 a_2 : Iota), % 4.06/4.31 Eq % 4.06/4.31 (Not % 4.06/4.31 (right_apart_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a)) → % 4.06/4.31 left_apart_point (skS.0 0 a) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)))) % 4.06/4.31 True % 4.06/4.31 Clause #80 (by clausification #[79]): ∀ (a a_1 a_2 : Iota), % 4.06/4.31 Eq % 4.06/4.31 (right_apart_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a)) → % 4.06/4.31 left_apart_point (skS.0 0 a) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 1 a a_1))) % 4.06/4.31 False % 4.06/4.31 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 : Iota), % 4.06/4.31 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 % 4.06/4.31 Clause #83 (by superposition #[81, 70]): ∀ (a a_1 a_2 : Iota), % 4.06/4.31 Or (Eq True False) % 4.06/4.31 (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) % 4.06/4.31 Clause #189 (by clausification #[19]): ∀ (a : Iota), Eq (∀ (L : Iota), Not (Or (left_apart_point a L) (left_apart_point a (reverse_line L)))) True % 4.06/4.31 Clause #190 (by clausification #[189]): ∀ (a a_1 : Iota), Eq (Not (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1)))) True % 4.06/4.31 Clause #191 (by clausification #[190]): ∀ (a a_1 : Iota), Eq (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1))) False % 4.06/4.31 Clause #193 (by clausification #[191]): ∀ (a a_1 : Iota), Eq (left_apart_point a a_1) False % 4.06/4.31 Clause #411 (by clausification #[83]): ∀ (a a_1 a_2 : Iota), % 4.06/4.31 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 % 4.06/4.31 Clause #412 (by superposition #[411, 193]): Eq True False % 4.06/4.31 Clause #413 (by clausification #[412]): False % 4.06/4.31 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------