%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO192+2 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 46.17s 46.34s % Output : Proof 46.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO192+2 : TPTP v9.2.0. Released v3.3.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n006.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 11:23:38 EDT 2025 % 0.13/0.34 % CPUTime : % 46.17/46.34 SZS status Theorem for theBenchmark.p % 46.17/46.34 SZS output start Proof for theBenchmark.p % 46.17/46.34 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), Not (distinct_points X X)) True % 46.17/46.34 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), Not (distinct_lines X X)) True % 46.17/46.34 Clause #2 (by assumption #[]): Eq (∀ (X : Iota), Not (convergent_lines X X)) True % 46.17/46.34 Clause #4 (by assumption #[]): Eq (∀ (X Y Z : Iota), distinct_lines X Y → Or (distinct_lines X Z) (distinct_lines Y Z)) True % 46.17/46.34 Clause #5 (by assumption #[]): Eq (∀ (X Y Z : Iota), convergent_lines X Y → Or (convergent_lines X Z) (convergent_lines Y Z)) True % 46.17/46.34 Clause #7 (by assumption #[]): Eq % 46.17/46.34 (∀ (X Y Z : Iota), % 46.17/46.34 convergent_lines X Y → % 46.17/46.34 Or (apart_point_and_line Z X) (apart_point_and_line Z Y) → distinct_points Z (intersection_point X Y)) % 46.17/46.34 True % 46.17/46.34 Clause #10 (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 % 46.17/46.34 Clause #11 (by assumption #[]): Eq (∀ (X Y : Iota), convergent_lines X Y → distinct_lines X Y) True % 46.17/46.34 Clause #12 (by assumption #[]): Eq % 46.17/46.34 (Not % 46.17/46.34 (∀ (X Y Z : Iota), % 46.17/46.34 convergent_lines X Y → % 46.17/46.34 apart_point_and_line (intersection_point X Y) Z → And (distinct_lines X Z) (distinct_lines Y Z))) % 46.17/46.34 True % 46.17/46.34 Clause #13 (by clausification #[2]): ∀ (a : Iota), Eq (Not (convergent_lines a a)) True % 46.17/46.34 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (convergent_lines a a) False % 46.17/46.34 Clause #15 (by clausification #[1]): ∀ (a : Iota), Eq (Not (distinct_lines a a)) True % 46.17/46.34 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (distinct_lines a a) False % 46.17/46.34 Clause #17 (by clausification #[0]): ∀ (a : Iota), Eq (Not (distinct_points a a)) True % 46.17/46.34 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (distinct_points a a) False % 46.17/46.34 Clause #19 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (Y : Iota), convergent_lines a Y → distinct_lines a Y) True % 46.17/46.34 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (convergent_lines a a_1 → distinct_lines a a_1) True % 46.17/46.34 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines a a_1) False) (Eq (distinct_lines a a_1) True) % 46.17/46.34 Clause #22 (by clausification #[7]): ∀ (a : Iota), % 46.17/46.34 Eq % 46.17/46.34 (∀ (Y Z : Iota), % 46.17/46.34 convergent_lines a Y → % 46.17/46.34 Or (apart_point_and_line Z a) (apart_point_and_line Z Y) → distinct_points Z (intersection_point a Y)) % 46.17/46.34 True % 46.17/46.34 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 46.17/46.34 Eq % 46.17/46.34 (∀ (Z : Iota), % 46.17/46.34 convergent_lines a a_1 → % 46.17/46.34 Or (apart_point_and_line Z a) (apart_point_and_line Z a_1) → distinct_points Z (intersection_point a a_1)) % 46.17/46.34 True % 46.17/46.34 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 46.17/46.34 Eq % 46.17/46.34 (convergent_lines a a_1 → % 46.17/46.34 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)) % 46.17/46.34 True % 46.17/46.34 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 46.17/46.34 Or (Eq (convergent_lines a a_1) False) % 46.17/46.34 (Eq % 46.17/46.34 (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)) % 46.17/46.34 True) % 46.17/46.34 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 46.17/46.34 Or (Eq (convergent_lines a a_1) False) % 46.17/46.34 (Or (Eq (Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1)) False) % 46.17/46.34 (Eq (distinct_points a_2 (intersection_point a a_1)) True)) % 46.17/46.34 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 46.17/46.34 Or (Eq (convergent_lines a a_1) False) % 46.17/46.34 (Or (Eq (distinct_points a_2 (intersection_point a a_1)) True) (Eq (apart_point_and_line a_2 a_1) False)) % 46.17/46.34 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 46.17/46.34 Or (Eq (convergent_lines a a_1) False) % 46.17/46.34 (Or (Eq (distinct_points a_2 (intersection_point a a_1)) True) (Eq (apart_point_and_line a_2 a) False)) % 46.17/46.34 Clause #39 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), convergent_lines a Y → Or (convergent_lines a Z) (convergent_lines Y Z)) True % 46.17/46.34 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), convergent_lines a a_1 → Or (convergent_lines a Z) (convergent_lines a_1 Z)) True % 46.17/46.34 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines a a_1 → Or (convergent_lines a a_2) (convergent_lines a_1 a_2)) True % 46.17/46.36 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 46.17/46.36 Or (Eq (convergent_lines a a_1) False) (Eq (Or (convergent_lines a a_2) (convergent_lines a_1 a_2)) True) % 46.17/46.36 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 46.17/46.36 Or (Eq (convergent_lines a a_1) False) (Or (Eq (convergent_lines a a_2) True) (Eq (convergent_lines a_1 a_2) True)) % 46.17/46.36 Clause #44 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), distinct_lines a Y → Or (distinct_lines a Z) (distinct_lines Y Z)) True % 46.17/46.36 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), distinct_lines a a_1 → Or (distinct_lines a Z) (distinct_lines a_1 Z)) True % 46.17/46.36 Clause #46 (by clausification #[45]): ∀ (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 % 46.17/46.36 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), % 46.17/46.36 Or (Eq (distinct_lines a a_1) False) (Eq (Or (distinct_lines a a_2) (distinct_lines a_1 a_2)) True) % 46.17/46.36 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), % 46.17/46.36 Or (Eq (distinct_lines a a_1) False) (Or (Eq (distinct_lines a a_2) True) (Eq (distinct_lines a_1 a_2) True)) % 46.17/46.36 Clause #49 (by clausification #[10]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), apart_point_and_line a Y → Or (distinct_lines Y Z) (apart_point_and_line a Z)) True % 46.17/46.36 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 46.17/46.36 Eq (∀ (Z : Iota), apart_point_and_line a a_1 → Or (distinct_lines a_1 Z) (apart_point_and_line a Z)) True % 46.17/46.36 Clause #51 (by clausification #[50]): ∀ (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 % 46.17/46.36 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 46.17/46.36 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) % 46.17/46.36 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), % 46.17/46.36 Or (Eq (apart_point_and_line a a_1) False) % 46.17/46.36 (Or (Eq (distinct_lines a_1 a_2) True) (Eq (apart_point_and_line a a_2) True)) % 46.17/46.36 Clause #70 (by clausification #[12]): Eq % 46.17/46.36 (∀ (X Y Z : Iota), % 46.17/46.36 convergent_lines X Y → % 46.17/46.36 apart_point_and_line (intersection_point X Y) Z → And (distinct_lines X Z) (distinct_lines Y Z)) % 46.17/46.36 False % 46.17/46.36 Clause #71 (by clausification #[70]): ∀ (a : Iota), % 46.17/46.36 Eq % 46.17/46.36 (Not % 46.17/46.36 (∀ (Y Z : Iota), % 46.17/46.36 convergent_lines (skS.0 0 a) Y → % 46.17/46.36 apart_point_and_line (intersection_point (skS.0 0 a) Y) Z → % 46.17/46.36 And (distinct_lines (skS.0 0 a) Z) (distinct_lines Y Z))) % 46.17/46.36 True % 46.17/46.36 Clause #72 (by clausification #[71]): ∀ (a : Iota), % 46.17/46.36 Eq % 46.17/46.36 (∀ (Y Z : Iota), % 46.17/46.36 convergent_lines (skS.0 0 a) Y → % 46.17/46.36 apart_point_and_line (intersection_point (skS.0 0 a) Y) Z → % 46.17/46.36 And (distinct_lines (skS.0 0 a) Z) (distinct_lines Y Z)) % 46.17/46.36 False % 46.17/46.36 Clause #73 (by clausification #[72]): ∀ (a a_1 : Iota), % 46.17/46.36 Eq % 46.17/46.36 (Not % 46.17/46.36 (∀ (Z : Iota), % 46.17/46.36 convergent_lines (skS.0 0 a) (skS.0 1 a a_1) → % 46.17/46.36 apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) Z → % 46.17/46.36 And (distinct_lines (skS.0 0 a) Z) (distinct_lines (skS.0 1 a a_1) Z))) % 46.17/46.36 True % 46.17/46.36 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota), % 46.17/46.36 Eq % 46.17/46.36 (∀ (Z : Iota), % 46.17/46.36 convergent_lines (skS.0 0 a) (skS.0 1 a a_1) → % 46.17/46.36 apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) Z → % 46.17/46.36 And (distinct_lines (skS.0 0 a) Z) (distinct_lines (skS.0 1 a a_1) Z)) % 46.17/46.36 False % 46.17/46.36 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota), % 46.17/46.36 Eq % 46.17/46.36 (Not % 46.17/46.36 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1) → % 46.17/46.36 apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2) → % 46.17/46.36 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)))) % 46.17/46.36 True % 46.17/46.36 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), % 46.17/46.36 Eq % 46.17/46.36 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1) → % 46.17/46.36 apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2) → % 46.21/46.38 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))) % 46.21/46.38 False % 46.21/46.38 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) True % 46.21/46.38 Clause #78 (by clausification #[76]): ∀ (a a_1 a_2 : Iota), % 46.21/46.38 Eq % 46.21/46.38 (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2) → % 46.21/46.38 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))) % 46.21/46.38 False % 46.21/46.38 Clause #80 (by superposition #[77, 27]): ∀ (a a_1 a_2 : Iota), % 46.21/46.38 Or (Eq True False) % 46.21/46.38 (Or (Eq (distinct_points a (intersection_point (skS.0 0 a_1) (skS.0 1 a_1 a_2))) True) % 46.21/46.38 (Eq (apart_point_and_line a (skS.0 1 a_1 a_2)) False)) % 46.21/46.38 Clause #81 (by superposition #[77, 43]): ∀ (a a_1 a_2 : Iota), % 46.21/46.38 Or (Eq True False) (Or (Eq (convergent_lines (skS.0 0 a) a_1) True) (Eq (convergent_lines (skS.0 1 a a_2) a_1) True)) % 46.21/46.38 Clause #82 (by superposition #[28, 77]): ∀ (a a_1 a_2 : Iota), % 46.21/46.38 Or (Eq True False) % 46.21/46.38 (Or (Eq (distinct_points a (intersection_point (skS.0 0 a_1) (skS.0 1 a_1 a_2))) True) % 46.21/46.38 (Eq (apart_point_and_line a (skS.0 0 a_1)) False)) % 46.21/46.38 Clause #85 (by clausification #[81]): ∀ (a a_1 a_2 : Iota), Or (Eq (convergent_lines (skS.0 0 a) a_1) True) (Eq (convergent_lines (skS.0 1 a a_2) a_1) True) % 46.21/46.38 Clause #89 (by superposition #[85, 43]): ∀ (a a_1 a_2 a_3 : Iota), % 46.21/46.38 Or (Eq (convergent_lines (skS.0 0 a) a_1) True) % 46.21/46.38 (Or (Eq True False) (Or (Eq (convergent_lines (skS.0 1 a a_2) a_3) True) (Eq (convergent_lines a_1 a_3) True))) % 46.21/46.38 Clause #91 (by clausification #[78]): ∀ (a a_1 a_2 : Iota), % 46.21/46.38 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 % 46.21/46.38 Clause #92 (by clausification #[78]): ∀ (a a_1 a_2 : Iota), % 46.21/46.38 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 % 46.21/46.38 Clause #94 (by superposition #[91, 53]): ∀ (a a_1 a_2 a_3 : Iota), % 46.21/46.38 Or (Eq True False) % 46.21/46.38 (Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) a_3) True) % 46.21/46.38 (Eq (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) a_3) True)) % 46.21/46.38 Clause #108 (by clausification #[80]): ∀ (a a_1 a_2 : Iota), % 46.21/46.38 Or (Eq (distinct_points a (intersection_point (skS.0 0 a_1) (skS.0 1 a_1 a_2))) True) % 46.21/46.38 (Eq (apart_point_and_line a (skS.0 1 a_1 a_2)) False) % 46.21/46.38 Clause #112 (by clausification #[89]): ∀ (a a_1 a_2 a_3 : Iota), % 46.21/46.38 Or (Eq (convergent_lines (skS.0 0 a) a_1) True) % 46.21/46.38 (Or (Eq (convergent_lines (skS.0 1 a a_2) a_3) True) (Eq (convergent_lines a_1 a_3) True)) % 46.21/46.38 Clause #114 (by superposition #[112, 21]): ∀ (a a_1 a_2 a_3 : Iota), % 46.21/46.38 Or (Eq (convergent_lines (skS.0 1 a a_1) a_2) True) % 46.21/46.38 (Or (Eq (convergent_lines a_3 a_2) True) (Or (Eq True False) (Eq (distinct_lines (skS.0 0 a) a_3) True))) % 46.21/46.38 Clause #129 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), % 46.21/46.38 Or (Eq (distinct_points a (intersection_point (skS.0 0 a_1) (skS.0 1 a_1 a_2))) True) % 46.21/46.38 (Eq (apart_point_and_line a (skS.0 0 a_1)) False) % 46.21/46.38 Clause #138 (by clausification #[114]): ∀ (a a_1 a_2 a_3 : Iota), % 46.21/46.38 Or (Eq (convergent_lines (skS.0 1 a a_1) a_2) True) % 46.21/46.38 (Or (Eq (convergent_lines a_3 a_2) True) (Eq (distinct_lines (skS.0 0 a) a_3) True)) % 46.21/46.38 Clause #140 (by superposition #[138, 21]): ∀ (a a_1 a_2 a_3 : Iota), % 46.21/46.38 Or (Eq (convergent_lines a a_1) True) % 46.21/46.38 (Or (Eq (distinct_lines (skS.0 0 a_2) a) True) % 46.21/46.38 (Or (Eq True False) (Eq (distinct_lines (skS.0 1 a_2 a_3) a_1) True))) % 46.21/46.38 Clause #173 (by clausification #[140]): ∀ (a a_1 a_2 a_3 : Iota), % 46.21/46.38 Or (Eq (convergent_lines a a_1) True) % 46.21/46.38 (Or (Eq (distinct_lines (skS.0 0 a_2) a) True) (Eq (distinct_lines (skS.0 1 a_2 a_3) a_1) True)) % 46.21/46.38 Clause #182 (by clausification #[92]): ∀ (a a_1 a_2 : Iota), % 46.21/46.38 Or (Eq (distinct_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) False) % 46.21/46.38 (Eq (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False) % 46.21/46.38 Clause #186 (by superposition #[182, 173]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 46.21/46.38 Or (Eq (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False) % 46.21/46.38 (Or (Eq (convergent_lines (skS.0 2 a a_1 a_2) a_3) True) % 46.21/46.41 (Or (Eq False True) (Eq (distinct_lines (skS.0 1 a a_4) a_3) True))) % 46.21/46.41 Clause #233 (by clausification #[94]): ∀ (a a_1 a_2 a_3 : Iota), % 46.21/46.41 Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) a_3) True) % 46.21/46.41 (Eq (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) a_3) True) % 46.21/46.41 Clause #235 (by superposition #[233, 108]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 46.21/46.41 Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) (skS.0 1 a_3 a_4)) True) % 46.21/46.41 (Or % 46.21/46.41 (Eq % 46.21/46.41 (distinct_points (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) % 46.21/46.41 (intersection_point (skS.0 0 a_3) (skS.0 1 a_3 a_4))) % 46.21/46.41 True) % 46.21/46.41 (Eq True False)) % 46.21/46.41 Clause #236 (by superposition #[233, 129]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 46.21/46.41 Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) (skS.0 0 a_3)) True) % 46.21/46.41 (Or % 46.21/46.41 (Eq % 46.21/46.41 (distinct_points (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) % 46.21/46.41 (intersection_point (skS.0 0 a_3) (skS.0 1 a_3 a_4))) % 46.21/46.41 True) % 46.21/46.41 (Eq True False)) % 46.21/46.41 Clause #1438 (by clausification #[186]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 46.21/46.41 Or (Eq (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False) % 46.21/46.41 (Or (Eq (convergent_lines (skS.0 2 a a_1 a_2) a_3) True) (Eq (distinct_lines (skS.0 1 a a_4) a_3) True)) % 46.21/46.41 Clause #3444 (by clausification #[235]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 46.21/46.41 Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) (skS.0 1 a_3 a_4)) True) % 46.21/46.41 (Eq % 46.21/46.41 (distinct_points (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) % 46.21/46.41 (intersection_point (skS.0 0 a_3) (skS.0 1 a_3 a_4))) % 46.21/46.41 True) % 46.21/46.41 Clause #3447 (by superposition #[3444, 18]): ∀ (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) % 46.21/46.41 Clause #3452 (by clausification #[3447]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True % 46.21/46.41 Clause #3453 (by superposition #[3452, 48]): ∀ (a a_1 a_2 a_3 : Iota), % 46.21/46.41 Or (Eq True False) % 46.21/46.41 (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)) % 46.21/46.41 Clause #3455 (by clausification #[3453]): ∀ (a a_1 a_2 a_3 : Iota), % 46.21/46.41 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) % 46.21/46.41 Clause #3456 (by superposition #[3455, 16]): ∀ (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) % 46.21/46.41 Clause #3459 (by clausification #[3456]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True % 46.21/46.41 Clause #3463 (by superposition #[3459, 1438]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 46.21/46.41 Or (Eq True False) % 46.21/46.41 (Or (Eq (convergent_lines (skS.0 2 a a_1 a_2) a_3) True) (Eq (distinct_lines (skS.0 1 a a_4) a_3) True)) % 46.21/46.41 Clause #3471 (by clausification #[3463]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 46.21/46.41 Or (Eq (convergent_lines (skS.0 2 a a_1 a_2) a_3) True) (Eq (distinct_lines (skS.0 1 a a_4) a_3) True) % 46.21/46.41 Clause #3472 (by superposition #[3471, 14]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_2 a_3)) True) (Eq True False) % 46.21/46.41 Clause #3487 (by clausification #[236]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 46.21/46.41 Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) (skS.0 0 a_3)) True) % 46.21/46.41 (Eq % 46.21/46.41 (distinct_points (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) % 46.21/46.41 (intersection_point (skS.0 0 a_3) (skS.0 1 a_3 a_4))) % 46.21/46.41 True) % 46.21/46.41 Clause #3490 (by superposition #[3487, 18]): ∀ (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) % 46.21/46.41 Clause #3495 (by clausification #[3490]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines (skS.0 2 a a_1 a_2) (skS.0 0 a)) True % 46.21/46.41 Clause #3496 (by superposition #[3495, 48]): ∀ (a a_1 a_2 a_3 : Iota), % 46.21/46.41 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)) % 46.21/46.41 Clause #3506 (by clausification #[3472]): ∀ (a a_1 a_2 a_3 : Iota), Eq (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_2 a_3)) True % 46.21/46.41 Clause #3508 (by clausification #[3496]): ∀ (a a_1 a_2 a_3 : Iota), % 46.21/46.41 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) % 46.21/46.41 Clause #3509 (by superposition #[3508, 16]): ∀ (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) % 46.30/46.48 Clause #3519 (by clausification #[3509]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) True % 46.30/46.48 Clause #3520 (by backward demodulation #[3519, 182]): ∀ (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) % 46.30/46.48 Clause #3523 (by clausification #[3520]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False % 46.30/46.48 Clause #3524 (by superposition #[3523, 3506]): Eq False True % 46.30/46.48 Clause #3655 (by clausification #[3524]): False % 46.30/46.48 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------