%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO264+3 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 4.08s 4.28s % Output : Proof 4.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO264+3 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.12/0.34 % Computer : n018.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 11:25:53 EDT 2025 % 0.12/0.34 % CPUTime : % 4.08/4.28 SZS status Theorem for theBenchmark.p % 4.08/4.28 SZS output start Proof for theBenchmark.p % 4.08/4.28 Clause #19 (by assumption #[]): Eq (∀ (A L : Iota), Not (Or (left_apart_point A L) (left_apart_point A (reverse_line L)))) True % 4.08/4.28 Clause #36 (by assumption #[]): Eq % 4.08/4.28 (Not % 4.08/4.28 (∀ (A B C D : Iota), % 4.08/4.28 left_apart_point C (line_connecting A B) → % 4.08/4.28 And (right_apart_point D (line_connecting B C)) (right_apart_point D (line_connecting C A)) → % 4.08/4.28 left_apart_point D (line_connecting A B))) % 4.08/4.28 True % 4.08/4.28 Clause #163 (by clausification #[19]): ∀ (a : Iota), Eq (∀ (L : Iota), Not (Or (left_apart_point a L) (left_apart_point a (reverse_line L)))) True % 4.08/4.28 Clause #164 (by clausification #[163]): ∀ (a a_1 : Iota), Eq (Not (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1)))) True % 4.08/4.28 Clause #165 (by clausification #[164]): ∀ (a a_1 : Iota), Eq (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1))) False % 4.08/4.28 Clause #167 (by clausification #[165]): ∀ (a a_1 : Iota), Eq (left_apart_point a a_1) False % 4.08/4.28 Clause #296 (by clausification #[36]): Eq % 4.08/4.28 (∀ (A B C D : Iota), % 4.08/4.28 left_apart_point C (line_connecting A B) → % 4.08/4.28 And (right_apart_point D (line_connecting B C)) (right_apart_point D (line_connecting C A)) → % 4.08/4.28 left_apart_point D (line_connecting A B)) % 4.08/4.28 False % 4.08/4.28 Clause #297 (by clausification #[296]): ∀ (a : Iota), % 4.08/4.28 Eq % 4.08/4.28 (Not % 4.08/4.28 (∀ (B C D : Iota), % 4.08/4.28 left_apart_point C (line_connecting (skS.0 0 a) B) → % 4.08/4.28 And (right_apart_point D (line_connecting B C)) (right_apart_point D (line_connecting C (skS.0 0 a))) → % 4.08/4.28 left_apart_point D (line_connecting (skS.0 0 a) B))) % 4.08/4.28 True % 4.08/4.28 Clause #298 (by clausification #[297]): ∀ (a : Iota), % 4.08/4.28 Eq % 4.08/4.28 (∀ (B C D : Iota), % 4.08/4.28 left_apart_point C (line_connecting (skS.0 0 a) B) → % 4.08/4.28 And (right_apart_point D (line_connecting B C)) (right_apart_point D (line_connecting C (skS.0 0 a))) → % 4.08/4.28 left_apart_point D (line_connecting (skS.0 0 a) B)) % 4.08/4.28 False % 4.08/4.28 Clause #299 (by clausification #[298]): ∀ (a a_1 : Iota), % 4.08/4.28 Eq % 4.08/4.28 (Not % 4.08/4.28 (∀ (C D : Iota), % 4.08/4.28 left_apart_point C (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) → % 4.08/4.28 And (right_apart_point D (line_connecting (skS.0 1 a a_1) C)) % 4.08/4.28 (right_apart_point D (line_connecting C (skS.0 0 a))) → % 4.08/4.28 left_apart_point D (line_connecting (skS.0 0 a) (skS.0 1 a a_1)))) % 4.08/4.28 True % 4.08/4.28 Clause #300 (by clausification #[299]): ∀ (a a_1 : Iota), % 4.08/4.28 Eq % 4.08/4.28 (∀ (C D : Iota), % 4.08/4.28 left_apart_point C (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) → % 4.08/4.28 And (right_apart_point D (line_connecting (skS.0 1 a a_1) C)) % 4.08/4.28 (right_apart_point D (line_connecting C (skS.0 0 a))) → % 4.08/4.28 left_apart_point D (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) % 4.08/4.28 False % 4.08/4.28 Clause #301 (by clausification #[300]): ∀ (a a_1 a_2 : Iota), % 4.08/4.28 Eq % 4.08/4.28 (Not % 4.08/4.28 (∀ (D : Iota), % 4.08/4.28 left_apart_point (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) → % 4.08/4.28 And (right_apart_point D (line_connecting (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.08/4.28 (right_apart_point D (line_connecting (skS.0 2 a a_1 a_2) (skS.0 0 a))) → % 4.08/4.28 left_apart_point D (line_connecting (skS.0 0 a) (skS.0 1 a a_1)))) % 4.08/4.28 True % 4.08/4.28 Clause #302 (by clausification #[301]): ∀ (a a_1 a_2 : Iota), % 4.08/4.28 Eq % 4.08/4.28 (∀ (D : Iota), % 4.08/4.28 left_apart_point (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) → % 4.08/4.28 And (right_apart_point D (line_connecting (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.08/4.28 (right_apart_point D (line_connecting (skS.0 2 a a_1 a_2) (skS.0 0 a))) → % 4.08/4.28 left_apart_point D (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) % 4.08/4.28 False % 4.08/4.28 Clause #303 (by clausification #[302]): ∀ (a a_1 a_2 a_3 : Iota), % 4.08/4.28 Eq % 4.08/4.28 (Not % 4.08/4.28 (left_apart_point (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) → % 4.08/4.28 And (right_apart_point (skS.0 3 a a_1 a_2 a_3) (line_connecting (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.08/4.28 (right_apart_point (skS.0 3 a a_1 a_2 a_3) (line_connecting (skS.0 2 a a_1 a_2) (skS.0 0 a))) → % 4.08/4.28 left_apart_point (skS.0 3 a a_1 a_2 a_3) (line_connecting (skS.0 0 a) (skS.0 1 a a_1)))) % 4.08/4.29 True % 4.08/4.29 Clause #304 (by clausification #[303]): ∀ (a a_1 a_2 a_3 : Iota), % 4.08/4.29 Eq % 4.08/4.29 (left_apart_point (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) → % 4.08/4.29 And (right_apart_point (skS.0 3 a a_1 a_2 a_3) (line_connecting (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.08/4.29 (right_apart_point (skS.0 3 a a_1 a_2 a_3) (line_connecting (skS.0 2 a a_1 a_2) (skS.0 0 a))) → % 4.08/4.29 left_apart_point (skS.0 3 a a_1 a_2 a_3) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) % 4.08/4.29 False % 4.08/4.29 Clause #305 (by clausification #[304]): ∀ (a a_1 a_2 : Iota), Eq (left_apart_point (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True % 4.08/4.29 Clause #307 (by superposition #[305, 167]): Eq True False % 4.08/4.29 Clause #329 (by clausification #[307]): False % 4.08/4.29 SZS output end Proof for theBenchmark.p 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