%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO174+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 5.00s 5.18s % Output : Proof 5.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO174+1 : TPTP v9.2.0. Released v3.3.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n009.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 12:11:38 EDT 2025 % 0.13/0.34 % CPUTime : % 5.00/5.18 SZS status Theorem for theBenchmark.p % 5.00/5.18 SZS output start Proof for theBenchmark.p % 5.00/5.18 Clause #6 (by assumption #[]): Eq (∀ (X Y : Iota), distinct_points X Y → Not (apart_point_and_line X (line_connecting X Y))) True % 5.00/5.18 Clause #7 (by assumption #[]): Eq (∀ (X Y : Iota), distinct_points X Y → Not (apart_point_and_line Y (line_connecting X Y))) True % 5.00/5.18 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 % 5.00/5.18 Clause #14 (by assumption #[]): Eq % 5.00/5.18 (Not % 5.00/5.18 (∀ (X Y U V : Iota), % 5.00/5.18 And (And (distinct_points X Y) (convergent_lines U V)) % 5.00/5.18 (Or (apart_point_and_line X U) (apart_point_and_line Y U)) → % 5.00/5.18 distinct_lines U (line_connecting X Y))) % 5.00/5.18 True % 5.00/5.18 Clause #21 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (Y : Iota), distinct_points a Y → Not (apart_point_and_line Y (line_connecting a Y))) True % 5.00/5.18 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (distinct_points a a_1 → Not (apart_point_and_line a_1 (line_connecting a a_1))) True % 5.00/5.18 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 5.00/5.18 Or (Eq (distinct_points a a_1) False) (Eq (Not (apart_point_and_line a_1 (line_connecting a a_1))) True) % 5.00/5.18 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (distinct_points a a_1) False) (Eq (apart_point_and_line a_1 (line_connecting a a_1)) False) % 5.00/5.18 Clause #25 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (Y : Iota), distinct_points a Y → Not (apart_point_and_line a (line_connecting a Y))) True % 5.00/5.18 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (distinct_points a a_1 → Not (apart_point_and_line a (line_connecting a a_1))) True % 5.00/5.18 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (distinct_points a a_1) False) (Eq (Not (apart_point_and_line a (line_connecting a a_1))) True) % 5.00/5.18 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (distinct_points a a_1) False) (Eq (apart_point_and_line a (line_connecting a a_1)) False) % 5.00/5.18 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 % 5.00/5.18 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), % 5.00/5.18 Eq (∀ (Z : Iota), apart_point_and_line a a_1 → Or (distinct_lines a_1 Z) (apart_point_and_line a Z)) True % 5.00/5.18 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 % 5.00/5.18 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), % 5.00/5.18 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) % 5.00/5.18 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 5.00/5.18 Or (Eq (apart_point_and_line a a_1) False) % 5.00/5.18 (Or (Eq (distinct_lines a_1 a_2) True) (Eq (apart_point_and_line a a_2) True)) % 5.00/5.18 Clause #52 (by clausification #[14]): Eq % 5.00/5.18 (∀ (X Y U V : Iota), % 5.00/5.18 And (And (distinct_points X Y) (convergent_lines U V)) (Or (apart_point_and_line X U) (apart_point_and_line Y U)) → % 5.00/5.18 distinct_lines U (line_connecting X Y)) % 5.00/5.18 False % 5.00/5.18 Clause #53 (by clausification #[52]): ∀ (a : Iota), % 5.00/5.18 Eq % 5.00/5.18 (Not % 5.00/5.18 (∀ (Y U V : Iota), % 5.00/5.18 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V)) % 5.00/5.18 (Or (apart_point_and_line (skS.0 0 a) U) (apart_point_and_line Y U)) → % 5.00/5.18 distinct_lines U (line_connecting (skS.0 0 a) Y))) % 5.00/5.18 True % 5.00/5.18 Clause #54 (by clausification #[53]): ∀ (a : Iota), % 5.00/5.18 Eq % 5.00/5.18 (∀ (Y U V : Iota), % 5.00/5.18 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V)) % 5.00/5.18 (Or (apart_point_and_line (skS.0 0 a) U) (apart_point_and_line Y U)) → % 5.00/5.18 distinct_lines U (line_connecting (skS.0 0 a) Y)) % 5.00/5.18 False % 5.00/5.18 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), % 5.00/5.18 Eq % 5.00/5.18 (Not % 5.00/5.18 (∀ (U V : Iota), % 5.00/5.18 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V)) % 5.00/5.18 (Or (apart_point_and_line (skS.0 0 a) U) (apart_point_and_line (skS.0 1 a a_1) U)) → % 5.00/5.18 distinct_lines U (line_connecting (skS.0 0 a) (skS.0 1 a a_1)))) % 5.00/5.18 True % 5.00/5.18 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), % 5.00/5.20 Eq % 5.00/5.20 (∀ (U V : Iota), % 5.00/5.20 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V)) % 5.00/5.20 (Or (apart_point_and_line (skS.0 0 a) U) (apart_point_and_line (skS.0 1 a a_1) U)) → % 5.00/5.20 distinct_lines U (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) % 5.00/5.20 False % 5.00/5.20 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), % 5.00/5.20 Eq % 5.00/5.20 (Not % 5.00/5.20 (∀ (V : Iota), % 5.00/5.20 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)) % 5.00/5.20 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 5.00/5.20 (apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) → % 5.00/5.20 distinct_lines (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1)))) % 5.00/5.20 True % 5.00/5.20 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), % 5.00/5.20 Eq % 5.00/5.20 (∀ (V : Iota), % 5.00/5.20 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)) % 5.00/5.20 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 5.00/5.20 (apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) → % 5.00/5.20 distinct_lines (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) % 5.00/5.20 False % 5.00/5.20 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota), % 5.00/5.20 Eq % 5.00/5.20 (Not % 5.00/5.20 (And % 5.00/5.20 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 5.00/5.20 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 5.00/5.20 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 5.00/5.20 (apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) → % 5.00/5.20 distinct_lines (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1)))) % 5.00/5.20 True % 5.00/5.20 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota), % 5.00/5.20 Eq % 5.00/5.20 (And % 5.00/5.20 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 5.00/5.20 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 5.00/5.20 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 5.00/5.20 (apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) → % 5.00/5.20 distinct_lines (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) % 5.00/5.20 False % 5.00/5.20 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 a_3 : Iota), % 5.00/5.20 Eq % 5.00/5.20 (And % 5.00/5.20 (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))) % 5.00/5.20 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 5.00/5.20 (apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 5.00/5.20 True % 5.00/5.20 Clause #62 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) False % 5.00/5.20 Clause #63 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), % 5.00/5.20 Eq % 5.00/5.20 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 5.00/5.20 (apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 5.00/5.20 True % 5.00/5.20 Clause #64 (by clausification #[61]): ∀ (a a_1 a_2 a_3 : Iota), % 5.00/5.20 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))) % 5.00/5.20 True % 5.00/5.20 Clause #65 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 5.00/5.20 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 5.00/5.20 (Eq (apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True) % 5.00/5.20 Clause #66 (by superposition #[65, 51]): ∀ (a a_1 a_2 a_3 : Iota), % 5.00/5.20 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 5.00/5.20 (Or (Eq True False) % 5.00/5.20 (Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) a_3) True) (Eq (apart_point_and_line (skS.0 1 a a_1) a_3) True))) % 5.00/5.20 Clause #93 (by clausification #[64]): ∀ (a a_1 : Iota), Eq (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) True % 5.00/5.20 Clause #98 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota), % 5.00/5.20 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 5.00/5.20 (Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) a_3) True) (Eq (apart_point_and_line (skS.0 1 a a_1) a_3) True)) % 5.00/5.20 Clause #101 (by superposition #[98, 62]): ∀ (a a_1 a_2 : Iota), % 5.00/5.20 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 5.00/5.20 (Or (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True) (Eq True False)) % 5.00/5.21 Clause #104 (by superposition #[93, 24]): ∀ (a a_1 : Iota), % 5.00/5.21 Or (Eq True False) (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) False) % 5.00/5.21 Clause #105 (by superposition #[93, 28]): ∀ (a a_1 : Iota), % 5.00/5.21 Or (Eq True False) (Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) False) % 5.00/5.21 Clause #115 (by clausification #[105]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) False % 5.00/5.21 Clause #148 (by clausification #[104]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) False % 5.00/5.21 Clause #259 (by clausification #[101]): ∀ (a a_1 a_2 : Iota), % 5.00/5.21 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 5.00/5.21 (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True) % 5.00/5.21 Clause #262 (by superposition #[259, 148]): ∀ (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) % 5.00/5.21 Clause #267 (by clausification #[262]): ∀ (a a_1 a_2 : Iota), Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True % 5.00/5.21 Clause #269 (by superposition #[267, 51]): ∀ (a a_1 a_2 a_3 : Iota), % 5.00/5.21 Or (Eq True False) % 5.00/5.21 (Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) a_3) True) (Eq (apart_point_and_line (skS.0 0 a) a_3) True)) % 5.00/5.21 Clause #278 (by clausification #[269]): ∀ (a a_1 a_2 a_3 : Iota), % 5.00/5.21 Or (Eq (distinct_lines (skS.0 2 a a_1 a_2) a_3) True) (Eq (apart_point_and_line (skS.0 0 a) a_3) True) % 5.00/5.21 Clause #279 (by superposition #[278, 62]): ∀ (a a_1 : Iota), % 5.00/5.21 Or (Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True) (Eq True False) % 5.00/5.21 Clause #285 (by clausification #[279]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True % 5.00/5.21 Clause #286 (by superposition #[285, 115]): Eq True False % 5.00/5.21 Clause #291 (by clausification #[286]): False % 5.00/5.21 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------