%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO225+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 07:48:17 PM UTC 2025 % Result : Theorem 3.71s 3.88s % Output : Proof 3.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO225+1 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.14 % Command : duper %s % 0.14/0.35 % Computer : n020.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 11:53:23 EDT 2025 % 0.14/0.35 % CPUTime : % 3.71/3.88 SZS status Theorem for theBenchmark.p % 3.71/3.88 SZS output start Proof for theBenchmark.p % 3.71/3.88 Clause #6 (by assumption #[]): Eq (∀ (X Y : Iota), distinct_points X Y → Not (apart_point_and_line X (line_connecting X Y))) True % 3.71/3.88 Clause #7 (by assumption #[]): Eq (∀ (X Y : Iota), distinct_points X Y → Not (apart_point_and_line Y (line_connecting X Y))) True % 3.71/3.88 Clause #18 (by assumption #[]): Eq % 3.71/3.88 (Not % 3.71/3.88 (∀ (A B : Iota), % 3.71/3.88 And (And (point A) (point B)) (distinct_points A B) → % 3.71/3.88 Exists fun X => line X → And (Not (apart_point_and_line A X)) (Not (apart_point_and_line B X)))) % 3.71/3.88 True % 3.71/3.88 Clause #48 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (Y : Iota), distinct_points a Y → Not (apart_point_and_line Y (line_connecting a Y))) True % 3.71/3.88 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), Eq (distinct_points a a_1 → Not (apart_point_and_line a_1 (line_connecting a a_1))) True % 3.71/3.88 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 3.71/3.88 Or (Eq (distinct_points a a_1) False) (Eq (Not (apart_point_and_line a_1 (line_connecting a a_1))) True) % 3.71/3.88 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), Or (Eq (distinct_points a a_1) False) (Eq (apart_point_and_line a_1 (line_connecting a a_1)) False) % 3.71/3.88 Clause #52 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (Y : Iota), distinct_points a Y → Not (apart_point_and_line a (line_connecting a Y))) True % 3.71/3.88 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (distinct_points a a_1 → Not (apart_point_and_line a (line_connecting a a_1))) True % 3.71/3.88 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), Or (Eq (distinct_points a a_1) False) (Eq (Not (apart_point_and_line a (line_connecting a a_1))) True) % 3.71/3.88 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), Or (Eq (distinct_points a a_1) False) (Eq (apart_point_and_line a (line_connecting a a_1)) False) % 3.71/3.88 Clause #98 (by clausification #[18]): Eq % 3.71/3.88 (∀ (A B : Iota), % 3.71/3.88 And (And (point A) (point B)) (distinct_points A B) → % 3.71/3.88 Exists fun X => line X → And (Not (apart_point_and_line A X)) (Not (apart_point_and_line B X))) % 3.71/3.88 False % 3.71/3.88 Clause #99 (by clausification #[98]): ∀ (a : Iota), % 3.71/3.88 Eq % 3.71/3.88 (Not % 3.71/3.88 (∀ (B : Iota), % 3.71/3.88 And (And (point (skS.0 0 a)) (point B)) (distinct_points (skS.0 0 a) B) → % 3.71/3.88 Exists fun X => line X → And (Not (apart_point_and_line (skS.0 0 a) X)) (Not (apart_point_and_line B X)))) % 3.71/3.88 True % 3.71/3.88 Clause #100 (by clausification #[99]): ∀ (a : Iota), % 3.71/3.88 Eq % 3.71/3.88 (∀ (B : Iota), % 3.71/3.88 And (And (point (skS.0 0 a)) (point B)) (distinct_points (skS.0 0 a) B) → % 3.71/3.88 Exists fun X => line X → And (Not (apart_point_and_line (skS.0 0 a) X)) (Not (apart_point_and_line B X))) % 3.71/3.88 False % 3.71/3.88 Clause #101 (by clausification #[100]): ∀ (a a_1 : Iota), % 3.71/3.88 Eq % 3.71/3.88 (Not % 3.71/3.88 (And (And (point (skS.0 0 a)) (point (skS.0 1 a a_1))) (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) → % 3.71/3.88 Exists fun X => % 3.71/3.88 line X → And (Not (apart_point_and_line (skS.0 0 a) X)) (Not (apart_point_and_line (skS.0 1 a a_1) X)))) % 3.71/3.88 True % 3.71/3.88 Clause #102 (by clausification #[101]): ∀ (a a_1 : Iota), % 3.71/3.88 Eq % 3.71/3.88 (And (And (point (skS.0 0 a)) (point (skS.0 1 a a_1))) (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) → % 3.71/3.88 Exists fun X => % 3.71/3.88 line X → And (Not (apart_point_and_line (skS.0 0 a) X)) (Not (apart_point_and_line (skS.0 1 a a_1) X))) % 3.71/3.88 False % 3.71/3.88 Clause #103 (by clausification #[102]): ∀ (a a_1 : Iota), % 3.71/3.88 Eq (And (And (point (skS.0 0 a)) (point (skS.0 1 a a_1))) (distinct_points (skS.0 0 a) (skS.0 1 a a_1))) True % 3.71/3.88 Clause #104 (by clausification #[102]): ∀ (a a_1 : Iota), % 3.71/3.88 Eq % 3.71/3.88 (Exists fun X => % 3.71/3.88 line X → And (Not (apart_point_and_line (skS.0 0 a) X)) (Not (apart_point_and_line (skS.0 1 a a_1) X))) % 3.71/3.88 False % 3.71/3.88 Clause #105 (by clausification #[103]): ∀ (a a_1 : Iota), Eq (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) True % 3.71/3.88 Clause #109 (by superposition #[105, 51]): ∀ (a a_1 : Iota), % 3.71/3.88 Or (Eq True False) (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) False) % 3.71/3.88 Clause #110 (by superposition #[105, 55]): ∀ (a a_1 : Iota), % 3.71/3.88 Or (Eq True False) (Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) False) % 3.71/3.89 Clause #121 (by clausification #[104]): ∀ (a a_1 a_2 : Iota), % 3.71/3.89 Eq (line a → And (Not (apart_point_and_line (skS.0 0 a_1) a)) (Not (apart_point_and_line (skS.0 1 a_1 a_2) a))) False % 3.71/3.89 Clause #123 (by clausification #[121]): ∀ (a a_1 a_2 : Iota), % 3.71/3.89 Eq (And (Not (apart_point_and_line (skS.0 0 a) a_1)) (Not (apart_point_and_line (skS.0 1 a a_2) a_1))) False % 3.71/3.89 Clause #132 (by clausification #[123]): ∀ (a a_1 a_2 : Iota), % 3.71/3.89 Or (Eq (Not (apart_point_and_line (skS.0 0 a) a_1)) False) (Eq (Not (apart_point_and_line (skS.0 1 a a_2) a_1)) False) % 3.71/3.89 Clause #133 (by clausification #[132]): ∀ (a a_1 a_2 : Iota), % 3.71/3.89 Or (Eq (Not (apart_point_and_line (skS.0 1 a a_1) a_2)) False) (Eq (apart_point_and_line (skS.0 0 a) a_2) True) % 3.71/3.89 Clause #134 (by clausification #[133]): ∀ (a a_1 a_2 : Iota), % 3.71/3.89 Or (Eq (apart_point_and_line (skS.0 0 a) a_1) True) (Eq (apart_point_and_line (skS.0 1 a a_2) a_1) True) % 3.71/3.89 Clause #144 (by clausification #[110]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) False % 3.71/3.89 Clause #168 (by clausification #[109]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) False % 3.71/3.89 Clause #169 (by superposition #[168, 134]): ∀ (a a_1 : Iota), % 3.71/3.89 Or (Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True) (Eq False True) % 3.71/3.89 Clause #172 (by clausification #[169]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True % 3.71/3.89 Clause #173 (by superposition #[172, 144]): Eq True False % 3.71/3.89 Clause #177 (by clausification #[173]): False % 3.71/3.89 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------