%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO237+1 : TPTP v9.2.0. Bugfixed v6.4.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 07:48:19 PM UTC 2025 % Result : Theorem 5.72s 5.91s % Output : Proof 5.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GEO237+1 : TPTP v9.2.0. Bugfixed v6.4.0. % 0.04/0.13 % Command : duper %s % 0.13/0.34 % Computer : n004.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 11:47:23 EDT 2025 % 0.13/0.34 % CPUTime : % 5.72/5.91 SZS status Theorem for theBenchmark.p % 5.72/5.91 SZS output start Proof for theBenchmark.p % 5.72/5.91 Clause #2 (by assumption #[]): Eq % 5.72/5.91 (∀ (A B L : Iota), % 5.72/5.91 Iff (divides_points L A B) % 5.72/5.91 (Or (And (left_apart_point A L) (left_apart_point B (reverse_line L))) % 5.72/5.91 (And (left_apart_point A (reverse_line L)) (left_apart_point B L)))) % 5.72/5.91 True % 5.72/5.91 Clause #14 (by assumption #[]): Eq (∀ (A L : Iota), Not (Or (left_apart_point A L) (left_apart_point A (reverse_line L)))) True % 5.72/5.91 Clause #31 (by assumption #[]): Eq % 5.72/5.91 (Not % 5.72/5.91 (∀ (A B C L : Iota), % 5.72/5.91 apart_point_and_line C L → divides_points L A B → Or (divides_points L A C) (divides_points L B C))) % 5.72/5.91 True % 5.72/5.91 Clause #79 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (L : Iota), Not (Or (left_apart_point a L) (left_apart_point a (reverse_line L)))) True % 5.72/5.91 Clause #80 (by clausification #[79]): ∀ (a a_1 : Iota), Eq (Not (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1)))) True % 5.72/5.91 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota), Eq (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1))) False % 5.72/5.91 Clause #83 (by clausification #[81]): ∀ (a a_1 : Iota), Eq (left_apart_point a a_1) False % 5.72/5.91 Clause #85 (by clausification #[2]): ∀ (a : Iota), % 5.72/5.91 Eq % 5.72/5.91 (∀ (B L : Iota), % 5.72/5.91 Iff (divides_points L a B) % 5.72/5.91 (Or (And (left_apart_point a L) (left_apart_point B (reverse_line L))) % 5.72/5.91 (And (left_apart_point a (reverse_line L)) (left_apart_point B L)))) % 5.72/5.91 True % 5.72/5.91 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota), % 5.72/5.91 Eq % 5.72/5.91 (∀ (L : Iota), % 5.72/5.91 Iff (divides_points L a a_1) % 5.72/5.91 (Or (And (left_apart_point a L) (left_apart_point a_1 (reverse_line L))) % 5.72/5.91 (And (left_apart_point a (reverse_line L)) (left_apart_point a_1 L)))) % 5.72/5.91 True % 5.72/5.91 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota), % 5.72/5.91 Eq % 5.72/5.91 (Iff (divides_points a a_1 a_2) % 5.72/5.91 (Or (And (left_apart_point a_1 a) (left_apart_point a_2 (reverse_line a))) % 5.72/5.91 (And (left_apart_point a_1 (reverse_line a)) (left_apart_point a_2 a)))) % 5.72/5.91 True % 5.72/5.91 Clause #89 (by clausification #[87]): ∀ (a a_1 a_2 : Iota), % 5.72/5.91 Or (Eq (divides_points a a_1 a_2) False) % 5.72/5.91 (Eq % 5.72/5.91 (Or (And (left_apart_point a_1 a) (left_apart_point a_2 (reverse_line a))) % 5.72/5.91 (And (left_apart_point a_1 (reverse_line a)) (left_apart_point a_2 a))) % 5.72/5.91 True) % 5.72/5.91 Clause #231 (by clausification #[31]): Eq % 5.72/5.91 (∀ (A B C L : Iota), % 5.72/5.91 apart_point_and_line C L → divides_points L A B → Or (divides_points L A C) (divides_points L B C)) % 5.72/5.91 False % 5.72/5.91 Clause #232 (by clausification #[231]): ∀ (a : Iota), % 5.72/5.91 Eq % 5.72/5.91 (Not % 5.72/5.91 (∀ (B C L : Iota), % 5.72/5.91 apart_point_and_line C L → % 5.72/5.91 divides_points L (skS.0 0 a) B → Or (divides_points L (skS.0 0 a) C) (divides_points L B C))) % 5.72/5.91 True % 5.72/5.91 Clause #233 (by clausification #[232]): ∀ (a : Iota), % 5.72/5.91 Eq % 5.72/5.91 (∀ (B C L : Iota), % 5.72/5.91 apart_point_and_line C L → % 5.72/5.91 divides_points L (skS.0 0 a) B → Or (divides_points L (skS.0 0 a) C) (divides_points L B C)) % 5.72/5.91 False % 5.72/5.91 Clause #234 (by clausification #[233]): ∀ (a a_1 : Iota), % 5.72/5.91 Eq % 5.72/5.91 (Not % 5.72/5.91 (∀ (C L : Iota), % 5.72/5.91 apart_point_and_line C L → % 5.72/5.91 divides_points L (skS.0 0 a) (skS.0 1 a a_1) → % 5.72/5.91 Or (divides_points L (skS.0 0 a) C) (divides_points L (skS.0 1 a a_1) C))) % 5.72/5.91 True % 5.72/5.91 Clause #235 (by clausification #[234]): ∀ (a a_1 : Iota), % 5.72/5.91 Eq % 5.72/5.91 (∀ (C L : Iota), % 5.72/5.91 apart_point_and_line C L → % 5.72/5.91 divides_points L (skS.0 0 a) (skS.0 1 a a_1) → % 5.72/5.91 Or (divides_points L (skS.0 0 a) C) (divides_points L (skS.0 1 a a_1) C)) % 5.72/5.91 False % 5.72/5.91 Clause #236 (by clausification #[235]): ∀ (a a_1 a_2 : Iota), % 5.72/5.91 Eq % 5.72/5.91 (Not % 5.72/5.91 (∀ (L : Iota), % 5.72/5.91 apart_point_and_line (skS.0 2 a a_1 a_2) L → % 5.72/5.91 divides_points L (skS.0 0 a) (skS.0 1 a a_1) → % 5.72/5.91 Or (divides_points L (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 5.72/5.91 (divides_points L (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 5.72/5.91 True % 5.72/5.91 Clause #237 (by clausification #[236]): ∀ (a a_1 a_2 : Iota), % 5.72/5.91 Eq % 5.72/5.91 (∀ (L : Iota), % 5.72/5.91 apart_point_and_line (skS.0 2 a a_1 a_2) L → % 5.72/5.91 divides_points L (skS.0 0 a) (skS.0 1 a a_1) → % 5.72/5.91 Or (divides_points L (skS.0 0 a) (skS.0 2 a a_1 a_2)) (divides_points L (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 5.76/5.94 False % 5.76/5.94 Clause #238 (by clausification #[237]): ∀ (a a_1 a_2 a_3 : Iota), % 5.76/5.94 Eq % 5.76/5.94 (Not % 5.76/5.94 (apart_point_and_line (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) → % 5.76/5.94 divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) (skS.0 1 a a_1) → % 5.76/5.94 Or (divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 5.76/5.94 (divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 5.76/5.94 True % 5.76/5.94 Clause #239 (by clausification #[238]): ∀ (a a_1 a_2 a_3 : Iota), % 5.76/5.94 Eq % 5.76/5.94 (apart_point_and_line (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) → % 5.76/5.94 divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) (skS.0 1 a a_1) → % 5.76/5.94 Or (divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 5.76/5.94 (divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 5.76/5.94 False % 5.76/5.94 Clause #241 (by clausification #[239]): ∀ (a a_1 a_2 a_3 : Iota), % 5.76/5.94 Eq % 5.76/5.94 (divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) (skS.0 1 a a_1) → % 5.76/5.94 Or (divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 5.76/5.94 (divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 5.76/5.94 False % 5.76/5.94 Clause #245 (by clausification #[89]): ∀ (a a_1 a_2 : Iota), % 5.76/5.94 Or (Eq (divides_points a a_1 a_2) False) % 5.76/5.94 (Or (Eq (And (left_apart_point a_1 a) (left_apart_point a_2 (reverse_line a))) True) % 5.76/5.94 (Eq (And (left_apart_point a_1 (reverse_line a)) (left_apart_point a_2 a)) True)) % 5.76/5.94 Clause #246 (by clausification #[245]): ∀ (a a_1 a_2 : Iota), % 5.76/5.94 Or (Eq (divides_points a a_1 a_2) False) % 5.76/5.94 (Or (Eq (And (left_apart_point a_1 (reverse_line a)) (left_apart_point a_2 a)) True) % 5.76/5.94 (Eq (left_apart_point a_2 (reverse_line a)) True)) % 5.76/5.94 Clause #248 (by clausification #[246]): ∀ (a a_1 a_2 : Iota), % 5.76/5.94 Or (Eq (divides_points a a_1 a_2) False) % 5.76/5.94 (Or (Eq (left_apart_point a_2 (reverse_line a)) True) (Eq (left_apart_point a_2 a) True)) % 5.76/5.94 Clause #250 (by forward demodulation #[248, 83]): ∀ (a a_1 a_2 : Iota), Or (Eq (divides_points a a_1 a_2) False) (Or (Eq False True) (Eq (left_apart_point a_2 a) True)) % 5.76/5.94 Clause #251 (by clausification #[250]): ∀ (a a_1 a_2 : Iota), Or (Eq (divides_points a a_1 a_2) False) (Eq (left_apart_point a_2 a) True) % 5.76/5.94 Clause #252 (by forward demodulation #[251, 83]): ∀ (a a_1 a_2 : Iota), Or (Eq (divides_points a a_1 a_2) False) (Eq False True) % 5.76/5.94 Clause #253 (by clausification #[252]): ∀ (a a_1 a_2 : Iota), Eq (divides_points a a_1 a_2) False % 5.76/5.94 Clause #266 (by clausification #[241]): ∀ (a a_1 a_2 a_3 : Iota), Eq (divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) (skS.0 1 a a_1)) True % 5.76/5.94 Clause #268 (by superposition #[266, 253]): Eq True False % 5.76/5.94 Clause #269 (by clausification #[268]): False % 5.76/5.94 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------