%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO176+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 07:48:07 PM UTC 2025 % Result : Theorem 65.07s 65.28s % Output : Proof 65.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO176+1 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.13 % Command : duper %s % 0.13/0.35 % Computer : n014.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 11:19:53 EDT 2025 % 0.13/0.35 % CPUTime : % 65.07/65.28 SZS status Theorem for theBenchmark.p % 65.07/65.28 SZS output start Proof for theBenchmark.p % 65.07/65.28 Clause #8 (by assumption #[]): Eq (∀ (X Y : Iota), convergent_lines X Y → Not (apart_point_and_line (intersection_point X Y) X)) True % 65.07/65.28 Clause #9 (by assumption #[]): Eq (∀ (X Y : Iota), convergent_lines X Y → Not (apart_point_and_line (intersection_point X Y) Y)) True % 65.07/65.28 Clause #11 (by assumption #[]): Eq (∀ (X Y Z : Iota), apart_point_and_line X Y → Or (distinct_points X Z) (apart_point_and_line Z Y)) True % 65.07/65.28 Clause #14 (by assumption #[]): Eq % 65.07/65.28 (Not % 65.07/65.28 (∀ (X Y U V : Iota), % 65.07/65.28 And (And (distinct_points X Y) (convergent_lines U V)) % 65.07/65.28 (Or (apart_point_and_line X U) (apart_point_and_line X V)) → % 65.07/65.28 distinct_points X (intersection_point U V))) % 65.07/65.28 True % 65.07/65.28 Clause #34 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (Y : Iota), convergent_lines a Y → Not (apart_point_and_line (intersection_point a Y) Y)) True % 65.07/65.28 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (convergent_lines a a_1 → Not (apart_point_and_line (intersection_point a a_1) a_1)) True % 65.07/65.28 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 65.07/65.28 Or (Eq (convergent_lines a a_1) False) (Eq (Not (apart_point_and_line (intersection_point a a_1) a_1)) True) % 65.07/65.28 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 65.07/65.28 Or (Eq (convergent_lines a a_1) False) (Eq (apart_point_and_line (intersection_point a a_1) a_1) False) % 65.07/65.28 Clause #38 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (Y : Iota), convergent_lines a Y → Not (apart_point_and_line (intersection_point a Y) a)) True % 65.07/65.28 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (convergent_lines a a_1 → Not (apart_point_and_line (intersection_point a a_1) a)) True % 65.07/65.28 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 65.07/65.28 Or (Eq (convergent_lines a a_1) False) (Eq (Not (apart_point_and_line (intersection_point a a_1) a)) True) % 65.07/65.28 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines a a_1) False) (Eq (apart_point_and_line (intersection_point a a_1) a) False) % 65.07/65.28 Clause #52 (by clausification #[14]): Eq % 65.07/65.28 (∀ (X Y U V : Iota), % 65.07/65.28 And (And (distinct_points X Y) (convergent_lines U V)) (Or (apart_point_and_line X U) (apart_point_and_line X V)) → % 65.07/65.28 distinct_points X (intersection_point U V)) % 65.07/65.28 False % 65.07/65.28 Clause #53 (by clausification #[52]): ∀ (a : Iota), % 65.07/65.28 Eq % 65.07/65.28 (Not % 65.07/65.28 (∀ (Y U V : Iota), % 65.07/65.28 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V)) % 65.07/65.28 (Or (apart_point_and_line (skS.0 0 a) U) (apart_point_and_line (skS.0 0 a) V)) → % 65.07/65.28 distinct_points (skS.0 0 a) (intersection_point U V))) % 65.07/65.28 True % 65.07/65.28 Clause #54 (by clausification #[53]): ∀ (a : Iota), % 65.07/65.28 Eq % 65.07/65.28 (∀ (Y U V : Iota), % 65.07/65.28 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V)) % 65.07/65.28 (Or (apart_point_and_line (skS.0 0 a) U) (apart_point_and_line (skS.0 0 a) V)) → % 65.07/65.28 distinct_points (skS.0 0 a) (intersection_point U V)) % 65.07/65.28 False % 65.07/65.28 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), % 65.07/65.28 Eq % 65.07/65.28 (Not % 65.07/65.28 (∀ (U V : Iota), % 65.07/65.28 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V)) % 65.07/65.28 (Or (apart_point_and_line (skS.0 0 a) U) (apart_point_and_line (skS.0 0 a) V)) → % 65.07/65.28 distinct_points (skS.0 0 a) (intersection_point U V))) % 65.07/65.28 True % 65.07/65.28 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), % 65.07/65.28 Eq % 65.07/65.28 (∀ (U V : Iota), % 65.07/65.28 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V)) % 65.07/65.28 (Or (apart_point_and_line (skS.0 0 a) U) (apart_point_and_line (skS.0 0 a) V)) → % 65.07/65.28 distinct_points (skS.0 0 a) (intersection_point U V)) % 65.07/65.28 False % 65.07/65.28 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), % 65.07/65.28 Eq % 65.07/65.28 (Not % 65.07/65.28 (∀ (V : Iota), % 65.07/65.28 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines (skS.0 2 a a_1 a_2) V)) % 65.07/65.28 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) (apart_point_and_line (skS.0 0 a) V)) → % 65.07/65.28 distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) V))) % 65.07/65.28 True % 65.07/65.28 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), % 65.07/65.30 Eq % 65.07/65.30 (∀ (V : Iota), % 65.07/65.30 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines (skS.0 2 a a_1 a_2) V)) % 65.07/65.30 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) (apart_point_and_line (skS.0 0 a) V)) → % 65.07/65.30 distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) V)) % 65.07/65.30 False % 65.07/65.30 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota), % 65.07/65.30 Eq % 65.07/65.30 (Not % 65.07/65.30 (And % 65.07/65.30 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 65.07/65.30 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 65.07/65.30 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 65.07/65.30 (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) → % 65.07/65.30 distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))) % 65.07/65.30 True % 65.07/65.30 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota), % 65.07/65.30 Eq % 65.07/65.30 (And % 65.07/65.30 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 65.07/65.30 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 65.07/65.30 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 65.07/65.30 (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) → % 65.07/65.30 distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 65.07/65.30 False % 65.07/65.30 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 a_3 : Iota), % 65.07/65.30 Eq % 65.07/65.30 (And % 65.07/65.30 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 65.07/65.30 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 65.07/65.30 (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)))) % 65.07/65.30 True % 65.07/65.30 Clause #62 (by clausification #[60]): ∀ (a a_1 a_2 a_3 : Iota), % 65.07/65.30 Eq (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) False % 65.07/65.30 Clause #63 (by clausification #[61]): ∀ (a a_1 a_2 a_3 : Iota), % 65.07/65.30 Eq % 65.07/65.30 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 65.07/65.30 (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) % 65.07/65.30 True % 65.07/65.30 Clause #64 (by clausification #[61]): ∀ (a a_1 a_2 a_3 : Iota), % 65.07/65.30 Eq (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 65.07/65.30 True % 65.07/65.30 Clause #65 (by clausification #[63]): ∀ (a a_1 a_2 a_3 : Iota), % 65.07/65.30 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 65.07/65.30 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)) True) % 65.07/65.30 Clause #72 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), apart_point_and_line a Y → Or (distinct_points a Z) (apart_point_and_line Z Y)) True % 65.07/65.30 Clause #73 (by clausification #[72]): ∀ (a a_1 : Iota), % 65.07/65.30 Eq (∀ (Z : Iota), apart_point_and_line a a_1 → Or (distinct_points a Z) (apart_point_and_line Z a_1)) True % 65.07/65.30 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), Eq (apart_point_and_line a a_1 → Or (distinct_points a a_2) (apart_point_and_line a_2 a_1)) True % 65.07/65.30 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota), % 65.07/65.30 Or (Eq (apart_point_and_line a a_1) False) (Eq (Or (distinct_points a a_2) (apart_point_and_line a_2 a_1)) True) % 65.07/65.30 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), % 65.07/65.30 Or (Eq (apart_point_and_line a a_1) False) % 65.07/65.30 (Or (Eq (distinct_points a a_2) True) (Eq (apart_point_and_line a_2 a_1) True)) % 65.07/65.30 Clause #77 (by superposition #[76, 65]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 65.07/65.30 Or (Eq (distinct_points (skS.0 0 a) a_1) True) % 65.07/65.30 (Or (Eq (apart_point_and_line a_1 (skS.0 3 a a_2 a_3 a_4)) True) % 65.07/65.30 (Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_2 a_3)) True) (Eq False True))) % 65.07/65.30 Clause #92 (by clausification #[64]): ∀ (a a_1 a_2 a_3 : Iota), Eq (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) True % 65.07/65.30 Clause #94 (by superposition #[92, 37]): ∀ (a a_1 a_2 a_3 : Iota), % 65.07/65.30 Or (Eq True False) % 65.07/65.30 (Eq (apart_point_and_line (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 3 a a_1 a_2 a_3)) % 65.07/65.30 False) % 65.07/65.30 Clause #95 (by superposition #[92, 41]): ∀ (a a_1 a_2 a_3 : Iota), % 65.07/65.30 Or (Eq True False) % 65.07/65.30 (Eq (apart_point_and_line (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 2 a a_1 a_2)) % 65.23/65.40 False) % 65.23/65.40 Clause #115 (by clausification #[77]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 65.23/65.40 Or (Eq (distinct_points (skS.0 0 a) a_1) True) % 65.23/65.40 (Or (Eq (apart_point_and_line a_1 (skS.0 3 a a_2 a_3 a_4)) True) % 65.23/65.40 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_2 a_3)) True)) % 65.23/65.40 Clause #146 (by clausification #[94]): ∀ (a a_1 a_2 a_3 : Iota), % 65.23/65.40 Eq (apart_point_and_line (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 3 a a_1 a_2 a_3)) % 65.23/65.40 False % 65.23/65.40 Clause #147 (by superposition #[146, 115]): ∀ (a a_1 a_2 a_3 : Iota), % 65.23/65.40 Or (Eq (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) True) % 65.23/65.40 (Or (Eq False True) (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)) % 65.23/65.40 Clause #153 (by clausification #[95]): ∀ (a a_1 a_2 a_3 : Iota), % 65.23/65.40 Eq (apart_point_and_line (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 2 a a_1 a_2)) False % 65.23/65.40 Clause #911 (by clausification #[147]): ∀ (a a_1 a_2 a_3 : Iota), % 65.23/65.40 Or (Eq (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) True) % 65.23/65.40 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 65.23/65.40 Clause #912 (by superposition #[911, 62]): ∀ (a a_1 a_2 : Iota), Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) (Eq True False) % 65.23/65.40 Clause #917 (by clausification #[912]): ∀ (a a_1 a_2 : Iota), Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True % 65.23/65.40 Clause #921 (by superposition #[917, 76]): ∀ (a a_1 a_2 a_3 : Iota), % 65.23/65.40 Or (Eq True False) % 65.23/65.40 (Or (Eq (distinct_points (skS.0 0 a) a_1) True) (Eq (apart_point_and_line a_1 (skS.0 2 a a_2 a_3)) True)) % 65.23/65.40 Clause #922 (by clausification #[921]): ∀ (a a_1 a_2 a_3 : Iota), % 65.23/65.40 Or (Eq (distinct_points (skS.0 0 a) a_1) True) (Eq (apart_point_and_line a_1 (skS.0 2 a a_2 a_3)) True) % 65.23/65.40 Clause #923 (by superposition #[922, 153]): ∀ (a a_1 a_2 a_3 : Iota), % 65.23/65.40 Or (Eq (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) True) % 65.23/65.40 (Eq True False) % 65.23/65.40 Clause #8390 (by clausification #[923]): ∀ (a a_1 a_2 a_3 : Iota), % 65.23/65.40 Eq (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) True % 65.23/65.40 Clause #8391 (by superposition #[8390, 62]): Eq True False % 65.23/65.40 Clause #8396 (by clausification #[8391]): False % 65.23/65.40 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------