%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO183+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 21.04s 21.29s % Output : Proof 21.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : GEO183+1 : TPTP v9.2.0. Released v3.3.0. % 0.10/0.13 % Command : duper %s % 0.13/0.34 % Computer : n005.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 12:24:23 EDT 2025 % 0.13/0.34 % CPUTime : % 21.04/21.29 SZS status Theorem for theBenchmark.p % 21.04/21.29 SZS output start Proof for theBenchmark.p % 21.04/21.29 Clause #6 (by assumption #[]): Eq (∀ (X Y : Iota), distinct_points X Y → Not (apart_point_and_line X (line_connecting X Y))) True % 21.04/21.29 Clause #7 (by assumption #[]): Eq (∀ (X Y : Iota), distinct_points X Y → Not (apart_point_and_line Y (line_connecting X Y))) True % 21.04/21.29 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 % 21.04/21.29 Clause #14 (by assumption #[]): Eq % 21.04/21.29 (Not % 21.04/21.29 (∀ (X Y U V : Iota), % 21.04/21.29 And (And (distinct_points X Y) (convergent_lines U V)) (Not (distinct_lines U (line_connecting X Y))) → % 21.04/21.29 And (Not (apart_point_and_line X U)) (Not (apart_point_and_line Y U)))) % 21.04/21.29 True % 21.04/21.29 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 % 21.04/21.29 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 % 21.04/21.29 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 21.04/21.29 Or (Eq (distinct_points a a_1) False) (Eq (Not (apart_point_and_line a_1 (line_connecting a a_1))) True) % 21.04/21.29 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) % 21.04/21.29 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 % 21.04/21.29 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 % 21.04/21.29 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) % 21.04/21.29 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) % 21.04/21.29 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 % 21.04/21.29 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), % 21.04/21.29 Eq (∀ (Z : Iota), apart_point_and_line a a_1 → Or (distinct_lines a_1 Z) (apart_point_and_line a Z)) True % 21.04/21.29 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 % 21.04/21.29 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), % 21.04/21.29 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) % 21.04/21.29 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 21.04/21.29 Or (Eq (apart_point_and_line a a_1) False) % 21.04/21.29 (Or (Eq (distinct_lines a_1 a_2) True) (Eq (apart_point_and_line a a_2) True)) % 21.04/21.29 Clause #67 (by clausification #[14]): Eq % 21.04/21.29 (∀ (X Y U V : Iota), % 21.04/21.29 And (And (distinct_points X Y) (convergent_lines U V)) (Not (distinct_lines U (line_connecting X Y))) → % 21.04/21.29 And (Not (apart_point_and_line X U)) (Not (apart_point_and_line Y U))) % 21.12/21.29 False % 21.12/21.29 Clause #68 (by clausification #[67]): ∀ (a : Iota), % 21.12/21.29 Eq % 21.12/21.29 (Not % 21.12/21.29 (∀ (Y U V : Iota), % 21.12/21.29 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V)) % 21.12/21.29 (Not (distinct_lines U (line_connecting (skS.0 0 a) Y))) → % 21.12/21.29 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line Y U)))) % 21.12/21.29 True % 21.12/21.29 Clause #69 (by clausification #[68]): ∀ (a : Iota), % 21.12/21.29 Eq % 21.12/21.29 (∀ (Y U V : Iota), % 21.12/21.29 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V)) % 21.12/21.29 (Not (distinct_lines U (line_connecting (skS.0 0 a) Y))) → % 21.12/21.29 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line Y U))) % 21.12/21.29 False % 21.12/21.29 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota), % 21.12/21.29 Eq % 21.12/21.29 (Not % 21.12/21.29 (∀ (U V : Iota), % 21.12/21.29 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V)) % 21.12/21.29 (Not (distinct_lines U (line_connecting (skS.0 0 a) (skS.0 1 a a_1)))) → % 21.12/21.29 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 1 a a_1) U)))) % 21.12/21.32 True % 21.12/21.32 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), % 21.12/21.32 Eq % 21.12/21.32 (∀ (U V : Iota), % 21.12/21.32 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V)) % 21.12/21.32 (Not (distinct_lines U (line_connecting (skS.0 0 a) (skS.0 1 a a_1)))) → % 21.12/21.32 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 1 a a_1) U))) % 21.12/21.32 False % 21.12/21.32 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), % 21.12/21.32 Eq % 21.12/21.32 (Not % 21.12/21.32 (∀ (V : Iota), % 21.12/21.32 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)) % 21.12/21.32 (Not (distinct_lines (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1)))) → % 21.12/21.32 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 21.12/21.32 (Not (apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))))) % 21.12/21.32 True % 21.12/21.32 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), % 21.12/21.32 Eq % 21.12/21.32 (∀ (V : Iota), % 21.12/21.32 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)) % 21.12/21.32 (Not (distinct_lines (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1)))) → % 21.12/21.32 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 21.12/21.32 (Not (apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 21.12/21.32 False % 21.12/21.32 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 a_3 : Iota), % 21.12/21.32 Eq % 21.12/21.32 (Not % 21.12/21.32 (And % 21.12/21.32 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 21.12/21.32 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 21.12/21.32 (Not (distinct_lines (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1)))) → % 21.12/21.32 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 21.12/21.32 (Not (apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))))) % 21.12/21.32 True % 21.12/21.32 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 a_3 : Iota), % 21.12/21.32 Eq % 21.12/21.32 (And % 21.12/21.32 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 21.12/21.32 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 21.12/21.32 (Not (distinct_lines (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1)))) → % 21.12/21.32 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 21.12/21.32 (Not (apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 21.12/21.32 False % 21.12/21.32 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 a_3 : Iota), % 21.12/21.32 Eq % 21.12/21.32 (And % 21.12/21.32 (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))) % 21.12/21.32 (Not (distinct_lines (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))))) % 21.12/21.32 True % 21.12/21.32 Clause #77 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), % 21.12/21.32 Eq % 21.12/21.32 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 21.12/21.32 (Not (apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 21.12/21.32 False % 21.12/21.32 Clause #78 (by clausification #[76]): ∀ (a a_1 a_2 : Iota), Eq (Not (distinct_lines (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1)))) True % 21.12/21.32 Clause #79 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota), % 21.12/21.32 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))) % 21.12/21.32 True % 21.12/21.32 Clause #80 (by clausification #[78]): ∀ (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 % 21.12/21.32 Clause #91 (by clausification #[79]): ∀ (a a_1 : Iota), Eq (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) True % 21.12/21.32 Clause #96 (by superposition #[91, 24]): ∀ (a a_1 : Iota), % 21.12/21.32 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) % 21.12/21.32 Clause #97 (by superposition #[91, 28]): ∀ (a a_1 : Iota), % 21.12/21.32 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) % 21.12/21.32 Clause #100 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), % 21.12/21.32 Or (Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) False) % 21.12/21.32 (Eq (Not (apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) False) % 21.12/21.32 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), % 21.12/21.35 Or (Eq (Not (apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) False) % 21.12/21.35 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 21.12/21.35 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 : Iota), % 21.12/21.35 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 21.12/21.35 (Eq (apart_point_and_line (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True) % 21.12/21.35 Clause #103 (by superposition #[102, 51]): ∀ (a a_1 a_2 a_3 : Iota), % 21.12/21.35 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 21.12/21.35 (Or (Eq True False) % 21.12/21.35 (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))) % 21.12/21.35 Clause #112 (by clausification #[97]): ∀ (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 % 21.12/21.35 Clause #140 (by clausification #[96]): ∀ (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 % 21.12/21.35 Clause #235 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota), % 21.12/21.35 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 21.12/21.35 (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)) % 21.12/21.35 Clause #238 (by superposition #[235, 80]): ∀ (a a_1 a_2 : Iota), % 21.12/21.35 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 21.12/21.35 (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)) % 21.12/21.35 Clause #1707 (by clausification #[238]): ∀ (a a_1 a_2 : Iota), % 21.12/21.35 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 21.12/21.35 (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True) % 21.12/21.35 Clause #1710 (by superposition #[1707, 140]): ∀ (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) % 21.12/21.35 Clause #1762 (by clausification #[1710]): ∀ (a a_1 a_2 : Iota), Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True % 21.12/21.35 Clause #1764 (by superposition #[1762, 51]): ∀ (a a_1 a_2 a_3 : Iota), % 21.12/21.35 Or (Eq True False) % 21.12/21.35 (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)) % 21.12/21.35 Clause #1773 (by clausification #[1764]): ∀ (a a_1 a_2 a_3 : Iota), % 21.12/21.35 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) % 21.12/21.35 Clause #1774 (by superposition #[1773, 80]): ∀ (a a_1 : Iota), % 21.12/21.35 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) % 21.12/21.35 Clause #1791 (by clausification #[1774]): ∀ (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 % 21.12/21.35 Clause #1792 (by superposition #[1791, 112]): Eq True False % 21.12/21.35 Clause #1838 (by clausification #[1792]): False % 21.12/21.35 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------