%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO185+2 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 07:48:09 PM UTC 2025 % Result : Theorem 35.43s 35.61s % Output : Proof 35.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO185+2 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.13 % Command : duper %s % 0.13/0.35 % Computer : n022.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 12:15:08 EDT 2025 % 0.13/0.35 % CPUTime : % 35.43/35.61 SZS status Theorem for theBenchmark.p % 35.43/35.61 SZS output start Proof for theBenchmark.p % 35.43/35.61 Clause #7 (by assumption #[]): Eq % 35.43/35.61 (∀ (X Y Z : Iota), % 35.43/35.61 convergent_lines X Y → % 35.43/35.61 Or (apart_point_and_line Z X) (apart_point_and_line Z Y) → distinct_points Z (intersection_point X Y)) % 35.43/35.61 True % 35.43/35.61 Clause #12 (by assumption #[]): Eq % 35.43/35.61 (Not % 35.43/35.61 (∀ (X Y U V : Iota), % 35.43/35.61 And (And (distinct_points X Y) (convergent_lines U V)) (Not (distinct_points X (intersection_point U V))) → % 35.43/35.61 And (Not (apart_point_and_line X U)) (Not (apart_point_and_line X V)))) % 35.43/35.61 True % 35.43/35.61 Clause #22 (by clausification #[7]): ∀ (a : Iota), % 35.43/35.61 Eq % 35.43/35.61 (∀ (Y Z : Iota), % 35.43/35.61 convergent_lines a Y → % 35.43/35.61 Or (apart_point_and_line Z a) (apart_point_and_line Z Y) → distinct_points Z (intersection_point a Y)) % 35.43/35.61 True % 35.43/35.61 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 35.43/35.61 Eq % 35.43/35.61 (∀ (Z : Iota), % 35.43/35.61 convergent_lines a a_1 → % 35.43/35.61 Or (apart_point_and_line Z a) (apart_point_and_line Z a_1) → distinct_points Z (intersection_point a a_1)) % 35.43/35.61 True % 35.43/35.61 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 35.43/35.61 Eq % 35.43/35.61 (convergent_lines a a_1 → % 35.43/35.61 Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1) → distinct_points a_2 (intersection_point a a_1)) % 35.43/35.61 True % 35.43/35.61 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 35.43/35.61 Or (Eq (convergent_lines a a_1) False) % 35.43/35.61 (Eq % 35.43/35.61 (Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1) → distinct_points a_2 (intersection_point a a_1)) % 35.43/35.61 True) % 35.43/35.61 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 35.43/35.61 Or (Eq (convergent_lines a a_1) False) % 35.43/35.61 (Or (Eq (Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1)) False) % 35.43/35.61 (Eq (distinct_points a_2 (intersection_point a a_1)) True)) % 35.43/35.61 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 35.43/35.61 Or (Eq (convergent_lines a a_1) False) % 35.43/35.61 (Or (Eq (distinct_points a_2 (intersection_point a a_1)) True) (Eq (apart_point_and_line a_2 a_1) False)) % 35.43/35.61 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 35.43/35.61 Or (Eq (convergent_lines a a_1) False) % 35.43/35.61 (Or (Eq (distinct_points a_2 (intersection_point a a_1)) True) (Eq (apart_point_and_line a_2 a) False)) % 35.43/35.61 Clause #70 (by clausification #[12]): Eq % 35.43/35.61 (∀ (X Y U V : Iota), % 35.43/35.61 And (And (distinct_points X Y) (convergent_lines U V)) (Not (distinct_points X (intersection_point U V))) → % 35.43/35.61 And (Not (apart_point_and_line X U)) (Not (apart_point_and_line X V))) % 35.43/35.61 False % 35.43/35.61 Clause #71 (by clausification #[70]): ∀ (a : Iota), % 35.43/35.61 Eq % 35.43/35.61 (Not % 35.43/35.61 (∀ (Y U V : Iota), % 35.43/35.61 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V)) % 35.43/35.61 (Not (distinct_points (skS.0 0 a) (intersection_point U V))) → % 35.43/35.61 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 0 a) V)))) % 35.43/35.61 True % 35.43/35.61 Clause #72 (by clausification #[71]): ∀ (a : Iota), % 35.43/35.61 Eq % 35.43/35.61 (∀ (Y U V : Iota), % 35.43/35.61 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V)) % 35.43/35.61 (Not (distinct_points (skS.0 0 a) (intersection_point U V))) → % 35.43/35.61 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 0 a) V))) % 35.43/35.61 False % 35.43/35.61 Clause #73 (by clausification #[72]): ∀ (a a_1 : Iota), % 35.43/35.61 Eq % 35.43/35.61 (Not % 35.43/35.61 (∀ (U V : Iota), % 35.43/35.61 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V)) % 35.43/35.61 (Not (distinct_points (skS.0 0 a) (intersection_point U V))) → % 35.43/35.61 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 0 a) V)))) % 35.43/35.61 True % 35.43/35.61 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota), % 35.43/35.61 Eq % 35.43/35.61 (∀ (U V : Iota), % 35.43/35.61 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V)) % 35.43/35.61 (Not (distinct_points (skS.0 0 a) (intersection_point U V))) → % 35.43/35.61 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 0 a) V))) % 35.43/35.61 False % 35.43/35.61 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota), % 35.43/35.61 Eq % 35.43/35.61 (Not % 35.43/35.61 (∀ (V : Iota), % 35.43/35.61 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)) % 35.43/35.61 (Not (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) V))) → % 35.43/35.63 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) (Not (apart_point_and_line (skS.0 0 a) V)))) % 35.43/35.63 True % 35.43/35.63 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), % 35.43/35.63 Eq % 35.43/35.63 (∀ (V : Iota), % 35.43/35.63 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)) % 35.43/35.63 (Not (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) V))) → % 35.43/35.63 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) (Not (apart_point_and_line (skS.0 0 a) V))) % 35.43/35.63 False % 35.43/35.63 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota), % 35.43/35.63 Eq % 35.43/35.63 (Not % 35.43/35.63 (And % 35.43/35.63 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 35.43/35.63 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 35.43/35.63 (Not (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)))) → % 35.43/35.63 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 35.43/35.63 (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))))) % 35.43/35.63 True % 35.43/35.63 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 a_3 : Iota), % 35.43/35.63 Eq % 35.43/35.63 (And % 35.43/35.63 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 35.43/35.63 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 35.43/35.63 (Not (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)))) → % 35.43/35.63 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 35.43/35.63 (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)))) % 35.43/35.63 False % 35.43/35.63 Clause #79 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota), % 35.43/35.63 Eq % 35.43/35.63 (And % 35.43/35.63 (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))) % 35.43/35.63 (Not (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))))) % 35.43/35.63 True % 35.43/35.63 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota), % 35.43/35.63 Eq % 35.43/35.63 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 35.43/35.63 (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)))) % 35.43/35.63 False % 35.43/35.63 Clause #81 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota), % 35.43/35.63 Eq (Not (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 % 35.43/35.63 Clause #82 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota), % 35.43/35.63 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))) % 35.43/35.63 True % 35.43/35.63 Clause #83 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota), % 35.43/35.63 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 % 35.43/35.63 Clause #84 (by clausification #[82]): ∀ (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 % 35.43/35.63 Clause #87 (by superposition #[84, 27]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 35.43/35.63 Or (Eq True False) % 35.43/35.63 (Or (Eq (distinct_points a (intersection_point (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4))) True) % 35.43/35.63 (Eq (apart_point_and_line a (skS.0 3 a_1 a_2 a_3 a_4)) False)) % 35.43/35.63 Clause #89 (by superposition #[84, 28]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 35.43/35.63 Or (Eq True False) % 35.43/35.63 (Or (Eq (distinct_points a (intersection_point (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4))) True) % 35.43/35.63 (Eq (apart_point_and_line a (skS.0 2 a_1 a_2 a_3)) False)) % 35.43/35.63 Clause #94 (by clausification #[80]): ∀ (a a_1 a_2 a_3 : Iota), % 35.43/35.63 Or (Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) False) % 35.43/35.63 (Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) False) % 35.43/35.63 Clause #95 (by clausification #[94]): ∀ (a a_1 a_2 a_3 : Iota), % 35.43/35.63 Or (Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) False) % 35.43/35.63 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 35.43/35.63 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 a_3 : Iota), % 35.43/35.63 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 35.43/35.63 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)) True) % 35.43/35.63 Clause #126 (by clausification #[87]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 35.43/35.63 Or (Eq (distinct_points a (intersection_point (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4))) True) % 35.48/35.69 (Eq (apart_point_and_line a (skS.0 3 a_1 a_2 a_3 a_4)) False) % 35.48/35.69 Clause #127 (by superposition #[126, 96]): ∀ (a a_1 a_2 a_3 : Iota), % 35.48/35.69 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) % 35.48/35.69 (Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) (Eq False True)) % 35.48/35.69 Clause #151 (by clausification #[89]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 35.48/35.69 Or (Eq (distinct_points a (intersection_point (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4))) True) % 35.48/35.69 (Eq (apart_point_and_line a (skS.0 2 a_1 a_2 a_3)) False) % 35.48/35.69 Clause #800 (by clausification #[127]): ∀ (a a_1 a_2 a_3 : Iota), % 35.48/35.69 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) % 35.48/35.69 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 35.48/35.69 Clause #801 (by superposition #[800, 83]): ∀ (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) % 35.48/35.69 Clause #806 (by clausification #[801]): ∀ (a a_1 a_2 : Iota), Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True % 35.48/35.69 Clause #809 (by superposition #[806, 151]): ∀ (a a_1 a_2 a_3 : Iota), % 35.48/35.69 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) % 35.48/35.69 (Eq True False) % 35.48/35.69 Clause #4920 (by clausification #[809]): ∀ (a a_1 a_2 a_3 : Iota), % 35.48/35.69 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 % 35.48/35.69 Clause #4921 (by superposition #[4920, 83]): Eq True False % 35.48/35.69 Clause #4926 (by clausification #[4921]): False % 35.48/35.69 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------