%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO179+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 07:48:08 PM UTC 2025 % Result : Theorem 108.78s 109.00s % Output : Proof 109.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : GEO179+1 : TPTP v9.2.0. Released v3.3.0. % 0.11/0.13 % Command : duper %s % 0.12/0.34 % Computer : n005.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 12:47:08 EDT 2025 % 0.12/0.34 % CPUTime : % 108.78/109.00 SZS status Theorem for theBenchmark.p % 108.78/109.00 SZS output start Proof for theBenchmark.p % 108.78/109.00 Clause #6 (by assumption #[]): Eq (∀ (X Y : Iota), distinct_points X Y → Not (apart_point_and_line X (line_connecting X Y))) True % 108.78/109.00 Clause #7 (by assumption #[]): Eq (∀ (X Y : Iota), distinct_points X Y → Not (apart_point_and_line Y (line_connecting X Y))) True % 108.78/109.00 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 % 108.78/109.00 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 % 108.78/109.00 Clause #14 (by assumption #[]): Eq % 108.78/109.00 (Not % 108.78/109.00 (∀ (X Y Z : Iota), % 108.78/109.00 And (distinct_points X Y) (apart_point_and_line Z (line_connecting X Y)) → % 108.78/109.00 And (distinct_lines (line_connecting X Y) (line_connecting Z X)) % 108.78/109.00 (distinct_lines (line_connecting X Y) (line_connecting Z Y)))) % 108.78/109.00 True % 108.78/109.00 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 % 108.78/109.00 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 % 108.78/109.00 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 108.78/109.00 Or (Eq (distinct_points a a_1) False) (Eq (Not (apart_point_and_line a_1 (line_connecting a a_1))) True) % 108.78/109.00 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) % 108.78/109.00 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 % 108.78/109.00 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 % 108.78/109.00 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) % 108.78/109.00 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) % 108.78/109.00 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 % 108.78/109.00 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), % 108.78/109.00 Eq (∀ (Z : Iota), apart_point_and_line a a_1 → Or (distinct_lines a_1 Z) (apart_point_and_line a Z)) True % 108.78/109.00 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 % 108.78/109.00 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), % 108.78/109.00 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) % 108.78/109.00 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 108.78/109.00 Or (Eq (apart_point_and_line a a_1) False) % 108.78/109.00 (Or (Eq (distinct_lines a_1 a_2) True) (Eq (apart_point_and_line a a_2) True)) % 108.78/109.00 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 % 108.78/109.00 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), % 108.78/109.00 Eq (∀ (Z : Iota), apart_point_and_line a a_1 → Or (distinct_points a Z) (apart_point_and_line Z a_1)) True % 108.78/109.00 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 % 108.78/109.00 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 108.78/109.00 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) % 108.78/109.00 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 108.78/109.00 Or (Eq (apart_point_and_line a a_1) False) % 108.78/109.00 (Or (Eq (distinct_points a a_2) True) (Eq (apart_point_and_line a_2 a_1) True)) % 108.78/109.00 Clause #76 (by clausification #[14]): Eq % 108.78/109.00 (∀ (X Y Z : Iota), % 108.78/109.00 And (distinct_points X Y) (apart_point_and_line Z (line_connecting X Y)) → % 108.78/109.00 And (distinct_lines (line_connecting X Y) (line_connecting Z X)) % 108.87/109.02 (distinct_lines (line_connecting X Y) (line_connecting Z Y))) % 108.87/109.02 False % 108.87/109.02 Clause #77 (by clausification #[76]): ∀ (a : Iota), % 108.87/109.02 Eq % 108.87/109.02 (Not % 108.87/109.02 (∀ (Y Z : Iota), % 108.87/109.02 And (distinct_points (skS.0 0 a) Y) (apart_point_and_line Z (line_connecting (skS.0 0 a) Y)) → % 108.87/109.02 And (distinct_lines (line_connecting (skS.0 0 a) Y) (line_connecting Z (skS.0 0 a))) % 108.87/109.02 (distinct_lines (line_connecting (skS.0 0 a) Y) (line_connecting Z Y)))) % 108.87/109.02 True % 108.87/109.02 Clause #78 (by clausification #[77]): ∀ (a : Iota), % 108.87/109.02 Eq % 108.87/109.02 (∀ (Y Z : Iota), % 108.87/109.02 And (distinct_points (skS.0 0 a) Y) (apart_point_and_line Z (line_connecting (skS.0 0 a) Y)) → % 108.87/109.02 And (distinct_lines (line_connecting (skS.0 0 a) Y) (line_connecting Z (skS.0 0 a))) % 108.87/109.02 (distinct_lines (line_connecting (skS.0 0 a) Y) (line_connecting Z Y))) % 108.87/109.02 False % 108.87/109.02 Clause #79 (by clausification #[78]): ∀ (a a_1 : Iota), % 108.87/109.02 Eq % 108.87/109.02 (Not % 108.87/109.02 (∀ (Z : Iota), % 108.87/109.02 And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 108.87/109.02 (apart_point_and_line Z (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) → % 108.87/109.02 And (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) (line_connecting Z (skS.0 0 a))) % 108.87/109.02 (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) (line_connecting Z (skS.0 1 a a_1))))) % 108.87/109.02 True % 108.87/109.02 Clause #80 (by clausification #[79]): ∀ (a a_1 : Iota), % 108.87/109.02 Eq % 108.87/109.02 (∀ (Z : Iota), % 108.87/109.02 And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 108.87/109.02 (apart_point_and_line Z (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) → % 108.87/109.02 And (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) (line_connecting Z (skS.0 0 a))) % 108.87/109.02 (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) (line_connecting Z (skS.0 1 a a_1)))) % 108.87/109.02 False % 108.87/109.02 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 : Iota), % 108.87/109.02 Eq % 108.87/109.02 (Not % 108.87/109.02 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 108.87/109.02 (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) → % 108.87/109.02 And % 108.87/109.02 (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) % 108.87/109.02 (line_connecting (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 108.87/109.02 (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) % 108.87/109.02 (line_connecting (skS.0 2 a a_1 a_2) (skS.0 1 a a_1))))) % 108.87/109.02 True % 108.87/109.02 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 : Iota), % 108.87/109.02 Eq % 108.87/109.02 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 108.87/109.02 (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) → % 108.87/109.02 And % 108.87/109.02 (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) (line_connecting (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 108.87/109.02 (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) % 108.87/109.02 (line_connecting (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)))) % 108.87/109.02 False % 108.87/109.02 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), % 108.87/109.02 Eq % 108.87/109.02 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 108.87/109.02 (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1)))) % 108.87/109.02 True % 108.87/109.02 Clause #84 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), % 108.87/109.02 Eq % 108.87/109.02 (And % 108.87/109.02 (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) (line_connecting (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 108.87/109.02 (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) % 108.87/109.02 (line_connecting (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)))) % 108.87/109.02 False % 108.87/109.02 Clause #85 (by clausification #[83]): ∀ (a a_1 a_2 : Iota), Eq (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True % 108.87/109.02 Clause #86 (by clausification #[83]): ∀ (a a_1 : Iota), Eq (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) True % 108.87/109.02 Clause #87 (by superposition #[85, 51]): ∀ (a a_1 a_2 a_3 : Iota), % 108.87/109.02 Or (Eq True False) % 108.87/109.02 (Or (Eq (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) a_2) True) % 108.87/109.02 (Eq (apart_point_and_line (skS.0 2 a a_1 a_3) a_2) True)) % 108.87/109.02 Clause #88 (by superposition #[85, 56]): ∀ (a a_1 a_2 a_3 : Iota), % 108.87/109.02 Or (Eq True False) % 108.87/109.02 (Or (Eq (distinct_points (skS.0 2 a a_1 a_2) a_3) True) % 108.87/109.02 (Eq (apart_point_and_line a_3 (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True)) % 108.87/109.05 Clause #89 (by superposition #[86, 24]): ∀ (a a_1 : Iota), % 108.87/109.05 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) % 108.87/109.05 Clause #90 (by superposition #[86, 28]): ∀ (a a_1 : Iota), % 108.87/109.05 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) % 108.87/109.05 Clause #99 (by clausification #[84]): ∀ (a a_1 a_2 : Iota), % 108.87/109.05 Or % 108.87/109.05 (Eq (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) (line_connecting (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 108.87/109.05 False) % 108.87/109.05 (Eq % 108.87/109.05 (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) % 108.87/109.05 (line_connecting (skS.0 2 a a_1 a_2) (skS.0 1 a a_1))) % 108.87/109.05 False) % 108.87/109.05 Clause #101 (by clausification #[90]): ∀ (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 % 108.87/109.05 Clause #119 (by clausification #[87]): ∀ (a a_1 a_2 a_3 : Iota), % 108.87/109.05 Or (Eq (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) a_2) True) % 108.87/109.05 (Eq (apart_point_and_line (skS.0 2 a a_1 a_3) a_2) True) % 108.87/109.05 Clause #120 (by superposition #[119, 99]): ∀ (a a_1 a_2 a_3 : Iota), % 108.87/109.05 Or (Eq (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 2 a a_1 a_3) (skS.0 0 a))) True) % 108.87/109.05 (Or (Eq True False) % 108.87/109.05 (Eq % 108.87/109.05 (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) % 108.87/109.05 (line_connecting (skS.0 2 a a_1 a_3) (skS.0 1 a a_1))) % 108.87/109.05 False)) % 108.87/109.05 Clause #135 (by clausification #[89]): ∀ (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 % 108.87/109.05 Clause #136 (by clausification #[88]): ∀ (a a_1 a_2 a_3 : Iota), % 108.87/109.05 Or (Eq (distinct_points (skS.0 2 a a_1 a_2) a_3) True) % 108.87/109.05 (Eq (apart_point_and_line a_3 (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True) % 108.87/109.05 Clause #141 (by superposition #[136, 101]): ∀ (a a_1 a_2 : Iota), Or (Eq (distinct_points (skS.0 2 a a_1 a_2) (skS.0 0 a)) True) (Eq True False) % 108.87/109.05 Clause #142 (by superposition #[136, 135]): ∀ (a a_1 a_2 : Iota), Or (Eq (distinct_points (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True) (Eq True False) % 108.87/109.05 Clause #146 (by clausification #[141]): ∀ (a a_1 a_2 : Iota), Eq (distinct_points (skS.0 2 a a_1 a_2) (skS.0 0 a)) True % 108.87/109.05 Clause #148 (by superposition #[146, 28]): ∀ (a a_1 a_2 : Iota), % 108.87/109.05 Or (Eq True False) % 108.87/109.05 (Eq (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 2 a a_1 a_2) (skS.0 0 a))) False) % 108.87/109.05 Clause #151 (by clausification #[142]): ∀ (a a_1 a_2 : Iota), Eq (distinct_points (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True % 108.87/109.05 Clause #153 (by superposition #[151, 28]): ∀ (a a_1 a_2 : Iota), % 108.87/109.05 Or (Eq True False) % 108.87/109.05 (Eq (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 2 a a_1 a_2) (skS.0 1 a a_1))) False) % 108.87/109.05 Clause #434 (by clausification #[120]): ∀ (a a_1 a_2 a_3 : Iota), % 108.87/109.05 Or (Eq (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 2 a a_1 a_3) (skS.0 0 a))) True) % 108.87/109.05 (Eq % 108.87/109.05 (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) % 108.87/109.05 (line_connecting (skS.0 2 a a_1 a_3) (skS.0 1 a a_1))) % 108.87/109.05 False) % 108.87/109.05 Clause #435 (by superposition #[434, 119]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 108.87/109.05 Or (Eq (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 2 a a_1 a_3) (skS.0 0 a))) True) % 108.87/109.05 (Or (Eq False True) % 108.87/109.05 (Eq (apart_point_and_line (skS.0 2 a a_1 a_4) (line_connecting (skS.0 2 a a_1 a_3) (skS.0 1 a a_1))) True)) % 108.87/109.05 Clause #1087 (by clausification #[148]): ∀ (a a_1 a_2 : Iota), % 108.87/109.05 Eq (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 2 a a_1 a_2) (skS.0 0 a))) False % 108.87/109.05 Clause #1179 (by clausification #[153]): ∀ (a a_1 a_2 : Iota), % 108.87/109.05 Eq (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 2 a a_1 a_2) (skS.0 1 a a_1))) False % 108.87/109.05 Clause #9553 (by clausification #[435]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 108.87/109.05 Or (Eq (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 2 a a_1 a_3) (skS.0 0 a))) True) % 108.87/109.05 (Eq (apart_point_and_line (skS.0 2 a a_1 a_4) (line_connecting (skS.0 2 a a_1 a_3) (skS.0 1 a a_1))) True) % 108.87/109.05 Clause #9629 (by superposition #[9553, 1179]): ∀ (a a_1 a_2 a_3 : Iota), % 109.04/109.21 Or (Eq (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 2 a a_1 a_3) (skS.0 0 a))) True) % 109.04/109.21 (Eq True False) % 109.04/109.21 Clause #9709 (by clausification #[9629]): ∀ (a a_1 a_2 a_3 : Iota), % 109.04/109.21 Eq (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 2 a a_1 a_3) (skS.0 0 a))) True % 109.04/109.21 Clause #9711 (by superposition #[9709, 1087]): Eq True False % 109.04/109.21 Clause #9780 (by clausification #[9711]): False % 109.04/109.21 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------