%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO192+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 07:48:10 PM UTC 2025 % Result : Theorem 5.05s 5.24s % Output : Proof 5.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : GEO192+1 : TPTP v9.2.0. Released v3.3.0. % 0.12/0.14 % Command : duper %s % 0.14/0.36 % Computer : n025.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Fri Oct 3 11:43:38 EDT 2025 % 0.14/0.36 % CPUTime : % 5.05/5.24 SZS status Theorem for theBenchmark.p % 5.05/5.24 SZS output start Proof for theBenchmark.p % 5.05/5.24 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), Not (distinct_lines X X)) True % 5.05/5.24 Clause #4 (by assumption #[]): Eq (∀ (X Y Z : Iota), distinct_lines X Y → Or (distinct_lines X Z) (distinct_lines Y Z)) True % 5.05/5.24 Clause #8 (by assumption #[]): Eq (∀ (X Y : Iota), convergent_lines X Y → Not (apart_point_and_line (intersection_point X Y) X)) True % 5.05/5.24 Clause #9 (by assumption #[]): Eq (∀ (X Y : Iota), convergent_lines X Y → Not (apart_point_and_line (intersection_point X Y) Y)) True % 5.05/5.24 Clause #12 (by assumption #[]): Eq (∀ (X Y Z : Iota), apart_point_and_line X Y → Or (distinct_lines Y Z) (apart_point_and_line X Z)) True % 5.05/5.24 Clause #14 (by assumption #[]): Eq % 5.05/5.24 (Not % 5.05/5.24 (∀ (X Y Z : Iota), % 5.05/5.24 convergent_lines X Y → % 5.05/5.24 apart_point_and_line (intersection_point X Y) Z → And (distinct_lines X Z) (distinct_lines Y Z))) % 5.05/5.24 True % 5.05/5.24 Clause #17 (by clausification #[1]): ∀ (a : Iota), Eq (Not (distinct_lines a a)) True % 5.05/5.24 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (distinct_lines a a) False % 5.05/5.24 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 % 5.05/5.24 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 % 5.05/5.24 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 5.05/5.24 Or (Eq (convergent_lines a a_1) False) (Eq (Not (apart_point_and_line (intersection_point a a_1) a_1)) True) % 5.05/5.24 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 5.05/5.24 Or (Eq (convergent_lines a a_1) False) (Eq (apart_point_and_line (intersection_point a a_1) a_1) False) % 5.05/5.24 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 % 5.05/5.24 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 % 5.05/5.24 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 5.05/5.24 Or (Eq (convergent_lines a a_1) False) (Eq (Not (apart_point_and_line (intersection_point a a_1) a)) True) % 5.05/5.24 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) % 5.05/5.24 Clause #47 (by clausification #[12]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), apart_point_and_line a Y → Or (distinct_lines Y Z) (apart_point_and_line a Z)) True % 5.05/5.24 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), % 5.05/5.24 Eq (∀ (Z : Iota), apart_point_and_line a a_1 → Or (distinct_lines a_1 Z) (apart_point_and_line a Z)) True % 5.05/5.24 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), Eq (apart_point_and_line a a_1 → Or (distinct_lines a_1 a_2) (apart_point_and_line a a_2)) True % 5.05/5.24 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), % 5.05/5.24 Or (Eq (apart_point_and_line a a_1) False) (Eq (Or (distinct_lines a_1 a_2) (apart_point_and_line a a_2)) True) % 5.05/5.24 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 5.05/5.24 Or (Eq (apart_point_and_line a a_1) False) % 5.05/5.24 (Or (Eq (distinct_lines a_1 a_2) True) (Eq (apart_point_and_line a a_2) True)) % 5.05/5.24 Clause #57 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), distinct_lines a Y → Or (distinct_lines a Z) (distinct_lines Y Z)) True % 5.05/5.24 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), distinct_lines a a_1 → Or (distinct_lines a Z) (distinct_lines a_1 Z)) True % 5.05/5.24 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines a a_1 → Or (distinct_lines a a_2) (distinct_lines a_1 a_2)) True % 5.05/5.24 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), % 5.05/5.24 Or (Eq (distinct_lines a a_1) False) (Eq (Or (distinct_lines a a_2) (distinct_lines a_1 a_2)) True) % 5.05/5.24 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), % 5.05/5.24 Or (Eq (distinct_lines a a_1) False) (Or (Eq (distinct_lines a a_2) True) (Eq (distinct_lines a_1 a_2) True)) % 5.05/5.24 Clause #67 (by clausification #[14]): Eq % 5.05/5.24 (∀ (X Y Z : Iota), % 5.05/5.24 convergent_lines X Y → % 5.05/5.26 apart_point_and_line (intersection_point X Y) Z → And (distinct_lines X Z) (distinct_lines Y Z)) % 5.05/5.26 False % 5.05/5.26 Clause #68 (by clausification #[67]): ∀ (a : Iota), % 5.05/5.26 Eq % 5.05/5.26 (Not % 5.05/5.26 (∀ (Y Z : Iota), % 5.05/5.26 convergent_lines (skS.0 0 a) Y → % 5.05/5.26 apart_point_and_line (intersection_point (skS.0 0 a) Y) Z → % 5.05/5.26 And (distinct_lines (skS.0 0 a) Z) (distinct_lines Y Z))) % 5.05/5.26 True % 5.05/5.26 Clause #69 (by clausification #[68]): ∀ (a : Iota), % 5.05/5.26 Eq % 5.05/5.26 (∀ (Y Z : Iota), % 5.05/5.26 convergent_lines (skS.0 0 a) Y → % 5.05/5.26 apart_point_and_line (intersection_point (skS.0 0 a) Y) Z → % 5.05/5.26 And (distinct_lines (skS.0 0 a) Z) (distinct_lines Y Z)) % 5.05/5.26 False % 5.05/5.26 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota), % 5.05/5.26 Eq % 5.05/5.26 (Not % 5.05/5.26 (∀ (Z : Iota), % 5.05/5.26 convergent_lines (skS.0 0 a) (skS.0 1 a a_1) → % 5.05/5.26 apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) Z → % 5.05/5.26 And (distinct_lines (skS.0 0 a) Z) (distinct_lines (skS.0 1 a a_1) Z))) % 5.05/5.26 True % 5.05/5.26 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), % 5.05/5.26 Eq % 5.05/5.26 (∀ (Z : Iota), % 5.05/5.26 convergent_lines (skS.0 0 a) (skS.0 1 a a_1) → % 5.05/5.26 apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) Z → % 5.05/5.26 And (distinct_lines (skS.0 0 a) Z) (distinct_lines (skS.0 1 a a_1) Z)) % 5.05/5.26 False % 5.05/5.26 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), % 5.05/5.26 Eq % 5.05/5.26 (Not % 5.05/5.26 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1) → % 5.05/5.26 apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2) → % 5.05/5.26 And (distinct_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 5.05/5.26 True % 5.05/5.26 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), % 5.05/5.26 Eq % 5.05/5.26 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1) → % 5.05/5.26 apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2) → % 5.05/5.26 And (distinct_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 5.05/5.26 False % 5.05/5.26 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) True % 5.05/5.26 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), % 5.05/5.26 Eq % 5.05/5.26 (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2) → % 5.05/5.26 And (distinct_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 5.05/5.26 False % 5.05/5.26 Clause #76 (by superposition #[74, 37]): ∀ (a a_1 : Iota), % 5.05/5.26 Or (Eq True False) (Eq (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 1 a a_1)) False) % 5.05/5.26 Clause #77 (by superposition #[74, 41]): ∀ (a a_1 : Iota), % 5.05/5.26 Or (Eq True False) (Eq (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 0 a)) False) % 5.05/5.26 Clause #95 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), % 5.05/5.26 Eq (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)) True % 5.05/5.26 Clause #96 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), % 5.05/5.26 Eq (And (distinct_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) False % 5.05/5.26 Clause #97 (by superposition #[95, 51]): ∀ (a a_1 a_2 a_3 : Iota), % 5.05/5.26 Or (Eq True False) % 5.05/5.26 (Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) a_3) True) % 5.05/5.26 (Eq (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) a_3) True)) % 5.05/5.26 Clause #102 (by clausification #[77]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 0 a)) False % 5.05/5.26 Clause #120 (by clausification #[76]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 1 a a_1)) False % 5.05/5.26 Clause #190 (by clausification #[96]): ∀ (a a_1 a_2 : Iota), % 5.05/5.26 Or (Eq (distinct_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) False) % 5.05/5.26 (Eq (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False) % 5.05/5.26 Clause #211 (by clausification #[97]): ∀ (a a_1 a_2 a_3 : Iota), % 5.05/5.26 Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) a_3) True) % 5.05/5.26 (Eq (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) a_3) True) % 5.05/5.27 Clause #214 (by superposition #[211, 102]): ∀ (a a_1 a_2 : Iota), Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) (skS.0 0 a)) True) (Eq True False) % 5.05/5.27 Clause #215 (by superposition #[211, 120]): ∀ (a a_1 a_2 : Iota), Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True) (Eq True False) % 5.05/5.27 Clause #220 (by clausification #[214]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines (skS.0 2 a a_1 a_2) (skS.0 0 a)) True % 5.05/5.27 Clause #221 (by superposition #[220, 61]): ∀ (a a_1 a_2 a_3 : Iota), % 5.05/5.27 Or (Eq True False) (Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) a_3) True) (Eq (distinct_lines (skS.0 0 a) a_3) True)) % 5.05/5.27 Clause #222 (by clausification #[215]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True % 5.05/5.27 Clause #223 (by superposition #[222, 61]): ∀ (a a_1 a_2 a_3 : Iota), % 5.05/5.27 Or (Eq True False) % 5.05/5.27 (Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) a_3) True) (Eq (distinct_lines (skS.0 1 a a_1) a_3) True)) % 5.05/5.27 Clause #224 (by clausification #[221]): ∀ (a a_1 a_2 a_3 : Iota), % 5.05/5.27 Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) a_3) True) (Eq (distinct_lines (skS.0 0 a) a_3) True) % 5.05/5.27 Clause #225 (by superposition #[224, 18]): ∀ (a a_1 a_2 : Iota), Or (Eq (distinct_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) (Eq True False) % 5.05/5.27 Clause #227 (by clausification #[225]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) True % 5.05/5.27 Clause #228 (by backward demodulation #[227, 190]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False) % 5.05/5.27 Clause #230 (by clausification #[228]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False % 5.05/5.27 Clause #276 (by clausification #[223]): ∀ (a a_1 a_2 a_3 : Iota), % 5.05/5.27 Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) a_3) True) (Eq (distinct_lines (skS.0 1 a a_1) a_3) True) % 5.05/5.27 Clause #277 (by superposition #[276, 18]): ∀ (a a_1 a_2 : Iota), Or (Eq (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True) (Eq True False) % 5.05/5.27 Clause #281 (by clausification #[277]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True % 5.05/5.27 Clause #282 (by superposition #[281, 230]): Eq True False % 5.05/5.27 Clause #284 (by clausification #[282]): False % 5.05/5.27 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------