%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO185+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 108.85s 109.35s % Output : Proof 108.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : GEO185+1 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.14 % Command : duper %s % 0.13/0.36 % Computer : n011.cluster.edu % 0.13/0.36 % Model : x86_64 x86_64 % 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.36 % Memory : 8042.1875MB % 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.36 % CPULimit : 300 % 0.13/0.36 % WCLimit : 300 % 0.13/0.36 % DateTime : Fri Oct 3 11:26:08 EDT 2025 % 0.13/0.36 % CPUTime : % 108.85/109.35 SZS status Theorem for theBenchmark.p % 108.85/109.35 SZS output start Proof for theBenchmark.p % 108.85/109.35 Clause #8 (by assumption #[]): Eq (∀ (X Y : Iota), convergent_lines X Y → Not (apart_point_and_line (intersection_point X Y) X)) True % 108.85/109.35 Clause #9 (by assumption #[]): Eq (∀ (X Y : Iota), convergent_lines X Y → Not (apart_point_and_line (intersection_point X Y) Y)) True % 108.85/109.35 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 % 108.85/109.35 Clause #14 (by assumption #[]): Eq % 108.85/109.35 (Not % 108.85/109.35 (∀ (X Y U V : Iota), % 108.85/109.35 And (And (distinct_points X Y) (convergent_lines U V)) (Not (distinct_points X (intersection_point U V))) → % 108.85/109.35 And (Not (apart_point_and_line X U)) (Not (apart_point_and_line X V)))) % 108.85/109.35 True % 108.85/109.35 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 % 108.85/109.35 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 % 108.85/109.35 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 108.85/109.35 Or (Eq (convergent_lines a a_1) False) (Eq (Not (apart_point_and_line (intersection_point a a_1) a_1)) True) % 108.85/109.35 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 108.85/109.35 Or (Eq (convergent_lines a a_1) False) (Eq (apart_point_and_line (intersection_point a a_1) a_1) False) % 108.85/109.35 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 % 108.85/109.35 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 % 108.85/109.35 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 108.85/109.35 Or (Eq (convergent_lines a a_1) False) (Eq (Not (apart_point_and_line (intersection_point a a_1) a)) True) % 108.85/109.35 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) % 108.85/109.35 Clause #52 (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 % 108.85/109.35 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), % 108.85/109.35 Eq (∀ (Z : Iota), apart_point_and_line a a_1 → Or (distinct_points a Z) (apart_point_and_line Z a_1)) True % 108.85/109.35 Clause #54 (by clausification #[53]): ∀ (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 % 108.85/109.35 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 108.85/109.35 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) % 108.85/109.35 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 108.85/109.35 Or (Eq (apart_point_and_line a a_1) False) % 108.85/109.35 (Or (Eq (distinct_points a a_2) True) (Eq (apart_point_and_line a_2 a_1) True)) % 108.85/109.35 Clause #67 (by clausification #[14]): Eq % 108.85/109.35 (∀ (X Y U V : Iota), % 108.85/109.35 And (And (distinct_points X Y) (convergent_lines U V)) (Not (distinct_points X (intersection_point U V))) → % 108.85/109.36 And (Not (apart_point_and_line X U)) (Not (apart_point_and_line X V))) % 108.85/109.36 False % 108.85/109.36 Clause #68 (by clausification #[67]): ∀ (a : Iota), % 108.85/109.36 Eq % 108.85/109.36 (Not % 108.85/109.36 (∀ (Y U V : Iota), % 108.85/109.36 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V)) % 108.85/109.36 (Not (distinct_points (skS.0 0 a) (intersection_point U V))) → % 108.85/109.36 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 0 a) V)))) % 108.85/109.36 True % 108.85/109.36 Clause #69 (by clausification #[68]): ∀ (a : Iota), % 108.85/109.36 Eq % 108.85/109.36 (∀ (Y U V : Iota), % 108.85/109.36 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V)) % 108.85/109.36 (Not (distinct_points (skS.0 0 a) (intersection_point U V))) → % 108.85/109.36 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 0 a) V))) % 108.85/109.36 False % 108.85/109.36 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota), % 108.85/109.36 Eq % 108.85/109.36 (Not % 108.85/109.36 (∀ (U V : Iota), % 108.85/109.36 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V)) % 108.85/109.36 (Not (distinct_points (skS.0 0 a) (intersection_point U V))) → % 108.85/109.38 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 0 a) V)))) % 108.85/109.38 True % 108.85/109.38 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), % 108.85/109.38 Eq % 108.85/109.38 (∀ (U V : Iota), % 108.85/109.38 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V)) % 108.85/109.38 (Not (distinct_points (skS.0 0 a) (intersection_point U V))) → % 108.85/109.38 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 0 a) V))) % 108.85/109.38 False % 108.85/109.38 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), % 108.85/109.38 Eq % 108.85/109.38 (Not % 108.85/109.38 (∀ (V : Iota), % 108.85/109.38 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)) % 108.85/109.38 (Not (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) V))) → % 108.85/109.38 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)))) % 108.85/109.38 True % 108.85/109.38 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), % 108.85/109.38 Eq % 108.85/109.38 (∀ (V : Iota), % 108.85/109.38 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)) % 108.85/109.38 (Not (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) V))) → % 108.85/109.38 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))) % 108.85/109.38 False % 108.85/109.38 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 a_3 : Iota), % 108.85/109.38 Eq % 108.85/109.38 (Not % 108.85/109.38 (And % 108.85/109.38 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 108.85/109.38 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 108.85/109.38 (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)))) → % 108.85/109.38 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 108.85/109.38 (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))))) % 108.85/109.38 True % 108.85/109.38 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 a_3 : Iota), % 108.85/109.38 Eq % 108.85/109.38 (And % 108.85/109.38 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 108.85/109.38 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 108.85/109.38 (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)))) → % 108.85/109.38 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 108.85/109.38 (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)))) % 108.85/109.38 False % 108.85/109.38 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 a_3 : Iota), % 108.85/109.38 Eq % 108.85/109.38 (And % 108.85/109.38 (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))) % 108.85/109.38 (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))))) % 108.85/109.38 True % 108.85/109.38 Clause #77 (by clausification #[75]): ∀ (a a_1 a_2 a_3 : Iota), % 108.85/109.38 Eq % 108.85/109.38 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 108.85/109.38 (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)))) % 108.85/109.38 False % 108.85/109.38 Clause #78 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota), % 108.85/109.38 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 % 108.85/109.38 Clause #79 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota), % 108.85/109.38 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))) % 108.85/109.38 True % 108.85/109.38 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota), % 108.85/109.38 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 % 108.85/109.38 Clause #90 (by clausification #[79]): ∀ (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 % 108.85/109.38 Clause #92 (by superposition #[90, 37]): ∀ (a a_1 a_2 a_3 : Iota), % 108.85/109.38 Or (Eq True False) % 108.85/109.38 (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)) % 108.85/109.38 False) % 108.85/109.38 Clause #93 (by superposition #[90, 41]): ∀ (a a_1 a_2 a_3 : Iota), % 108.85/109.38 Or (Eq True False) % 108.85/109.38 (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)) % 108.85/109.38 False) % 108.85/109.38 Clause #100 (by clausification #[77]): ∀ (a a_1 a_2 a_3 : Iota), % 108.85/109.38 Or (Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) False) % 108.98/109.52 (Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) False) % 108.98/109.52 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 a_3 : Iota), % 108.98/109.52 Or (Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) False) % 108.98/109.52 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 108.98/109.52 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 a_3 : Iota), % 108.98/109.52 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 108.98/109.52 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)) True) % 108.98/109.52 Clause #104 (by superposition #[102, 56]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 108.98/109.52 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 108.98/109.52 (Or (Eq True False) % 108.98/109.52 (Or (Eq (distinct_points (skS.0 0 a) a_3) True) (Eq (apart_point_and_line a_3 (skS.0 3 a a_1 a_2 a_4)) True))) % 108.98/109.52 Clause #132 (by clausification #[92]): ∀ (a a_1 a_2 a_3 : Iota), % 108.98/109.52 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)) % 108.98/109.52 False % 108.98/109.52 Clause #141 (by clausification #[93]): ∀ (a a_1 a_2 a_3 : Iota), % 108.98/109.52 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 % 108.98/109.52 Clause #282 (by clausification #[104]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 108.98/109.52 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 108.98/109.52 (Or (Eq (distinct_points (skS.0 0 a) a_3) True) (Eq (apart_point_and_line a_3 (skS.0 3 a a_1 a_2 a_4)) True)) % 108.98/109.52 Clause #285 (by superposition #[282, 132]): ∀ (a a_1 a_2 a_3 : Iota), % 108.98/109.52 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 108.98/109.52 (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) % 108.98/109.52 (Eq True False)) % 108.98/109.52 Clause #2531 (by clausification #[285]): ∀ (a a_1 a_2 a_3 : Iota), % 108.98/109.52 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 108.98/109.52 (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) % 108.98/109.52 Clause #2532 (by superposition #[2531, 80]): ∀ (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) % 108.98/109.52 Clause #2537 (by clausification #[2532]): ∀ (a a_1 a_2 : Iota), Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True % 108.98/109.52 Clause #2541 (by superposition #[2537, 56]): ∀ (a a_1 a_2 a_3 : Iota), % 108.98/109.52 Or (Eq True False) % 108.98/109.52 (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)) % 108.98/109.52 Clause #2542 (by clausification #[2541]): ∀ (a a_1 a_2 a_3 : Iota), % 108.98/109.52 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) % 108.98/109.52 Clause #2543 (by superposition #[2542, 141]): ∀ (a a_1 a_2 a_3 : Iota), % 108.98/109.52 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) % 108.98/109.52 (Eq True False) % 108.98/109.52 Clause #11328 (by clausification #[2543]): ∀ (a a_1 a_2 a_3 : Iota), % 108.98/109.52 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 % 108.98/109.52 Clause #11329 (by superposition #[11328, 80]): Eq True False % 108.98/109.52 Clause #11370 (by clausification #[11329]): False % 108.98/109.52 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------