%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO178+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 3.97s 4.17s % Output : Proof 4.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO178+1 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.13 % Command : duper %s % 0.13/0.35 % Computer : n010.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 12:46:38 EDT 2025 % 0.13/0.35 % CPUTime : % 3.97/4.17 SZS status Theorem for theBenchmark.p % 3.97/4.17 SZS output start Proof for theBenchmark.p % 3.97/4.17 Clause #6 (by assumption #[]): Eq (∀ (X Y : Iota), distinct_points X Y → Not (apart_point_and_line X (line_connecting X Y))) True % 3.97/4.17 Clause #7 (by assumption #[]): Eq (∀ (X Y : Iota), distinct_points X Y → Not (apart_point_and_line Y (line_connecting X Y))) True % 3.97/4.17 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 % 3.97/4.17 Clause #14 (by assumption #[]): Eq % 3.97/4.17 (Not % 3.97/4.17 (∀ (X Y Z : Iota), % 3.97/4.17 And (distinct_points X Y) (apart_point_and_line Z (line_connecting X Y)) → % 3.97/4.17 And (distinct_points Z X) (distinct_points Z Y))) % 3.97/4.17 True % 3.97/4.17 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 % 3.97/4.17 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 % 3.97/4.17 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 3.97/4.17 Or (Eq (distinct_points a a_1) False) (Eq (Not (apart_point_and_line a_1 (line_connecting a a_1))) True) % 3.97/4.17 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) % 3.97/4.17 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 % 3.97/4.17 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 % 3.97/4.17 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) % 3.97/4.17 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) % 3.97/4.17 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 % 3.97/4.17 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), % 3.97/4.17 Eq (∀ (Z : Iota), apart_point_and_line a a_1 → Or (distinct_points a Z) (apart_point_and_line Z a_1)) True % 3.97/4.17 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 % 3.97/4.17 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 3.97/4.17 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) % 3.97/4.17 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 3.97/4.17 Or (Eq (apart_point_and_line a a_1) False) % 3.97/4.17 (Or (Eq (distinct_points a a_2) True) (Eq (apart_point_and_line a_2 a_1) True)) % 3.97/4.17 Clause #67 (by clausification #[14]): Eq % 3.97/4.17 (∀ (X Y Z : Iota), % 3.97/4.17 And (distinct_points X Y) (apart_point_and_line Z (line_connecting X Y)) → % 3.97/4.17 And (distinct_points Z X) (distinct_points Z Y)) % 3.97/4.17 False % 3.97/4.17 Clause #68 (by clausification #[67]): ∀ (a : Iota), % 3.97/4.17 Eq % 3.97/4.17 (Not % 3.97/4.17 (∀ (Y Z : Iota), % 3.97/4.17 And (distinct_points (skS.0 0 a) Y) (apart_point_and_line Z (line_connecting (skS.0 0 a) Y)) → % 3.97/4.17 And (distinct_points Z (skS.0 0 a)) (distinct_points Z Y))) % 3.97/4.17 True % 3.97/4.17 Clause #69 (by clausification #[68]): ∀ (a : Iota), % 3.97/4.17 Eq % 3.97/4.17 (∀ (Y Z : Iota), % 3.97/4.17 And (distinct_points (skS.0 0 a) Y) (apart_point_and_line Z (line_connecting (skS.0 0 a) Y)) → % 3.97/4.17 And (distinct_points Z (skS.0 0 a)) (distinct_points Z Y)) % 3.97/4.17 False % 3.97/4.17 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota), % 3.97/4.17 Eq % 3.97/4.17 (Not % 3.97/4.17 (∀ (Z : Iota), % 3.97/4.17 And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 3.97/4.17 (apart_point_and_line Z (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) → % 3.97/4.17 And (distinct_points Z (skS.0 0 a)) (distinct_points Z (skS.0 1 a a_1)))) % 3.97/4.17 True % 3.97/4.17 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), % 3.97/4.17 Eq % 3.97/4.17 (∀ (Z : Iota), % 3.97/4.17 And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 3.97/4.17 (apart_point_and_line Z (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) → % 4.01/4.19 And (distinct_points Z (skS.0 0 a)) (distinct_points Z (skS.0 1 a a_1))) % 4.01/4.19 False % 4.01/4.19 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), % 4.01/4.19 Eq % 4.01/4.19 (Not % 4.01/4.19 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 4.01/4.19 (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) → % 4.01/4.19 And (distinct_points (skS.0 2 a a_1 a_2) (skS.0 0 a)) (distinct_points (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)))) % 4.01/4.19 True % 4.01/4.19 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), % 4.01/4.19 Eq % 4.01/4.19 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 4.01/4.19 (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) → % 4.01/4.19 And (distinct_points (skS.0 2 a a_1 a_2) (skS.0 0 a)) (distinct_points (skS.0 2 a a_1 a_2) (skS.0 1 a a_1))) % 4.01/4.19 False % 4.01/4.19 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), % 4.01/4.19 Eq % 4.01/4.19 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) % 4.01/4.19 (apart_point_and_line (skS.0 2 a a_1 a_2) (line_connecting (skS.0 0 a) (skS.0 1 a a_1)))) % 4.01/4.19 True % 4.01/4.19 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), % 4.01/4.19 Eq (And (distinct_points (skS.0 2 a a_1 a_2) (skS.0 0 a)) (distinct_points (skS.0 2 a a_1 a_2) (skS.0 1 a a_1))) False % 4.01/4.19 Clause #76 (by clausification #[74]): ∀ (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 % 4.01/4.19 Clause #77 (by clausification #[74]): ∀ (a a_1 : Iota), Eq (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) True % 4.01/4.19 Clause #79 (by superposition #[76, 56]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.19 Or (Eq True False) % 4.01/4.19 (Or (Eq (distinct_points (skS.0 2 a a_1 a_2) a_3) True) % 4.01/4.19 (Eq (apart_point_and_line a_3 (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True)) % 4.01/4.19 Clause #80 (by superposition #[77, 24]): ∀ (a a_1 : Iota), % 4.01/4.19 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) % 4.01/4.19 Clause #81 (by superposition #[77, 28]): ∀ (a a_1 : Iota), % 4.01/4.19 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) % 4.01/4.19 Clause #99 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), % 4.01/4.19 Or (Eq (distinct_points (skS.0 2 a a_1 a_2) (skS.0 0 a)) False) % 4.01/4.19 (Eq (distinct_points (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) False) % 4.01/4.19 Clause #101 (by clausification #[81]): ∀ (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 % 4.01/4.19 Clause #135 (by clausification #[80]): ∀ (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 % 4.01/4.19 Clause #136 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota), % 4.01/4.19 Or (Eq (distinct_points (skS.0 2 a a_1 a_2) a_3) True) % 4.01/4.19 (Eq (apart_point_and_line a_3 (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True) % 4.01/4.19 Clause #142 (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) % 4.01/4.19 Clause #143 (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) % 4.01/4.19 Clause #147 (by clausification #[142]): ∀ (a a_1 a_2 : Iota), Eq (distinct_points (skS.0 2 a a_1 a_2) (skS.0 0 a)) True % 4.01/4.19 Clause #148 (by backward demodulation #[147, 99]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (distinct_points (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) False) % 4.01/4.19 Clause #153 (by clausification #[143]): ∀ (a a_1 a_2 : Iota), Eq (distinct_points (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True % 4.01/4.19 Clause #158 (by clausification #[148]): ∀ (a a_1 a_2 : Iota), Eq (distinct_points (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) False % 4.01/4.19 Clause #159 (by superposition #[158, 153]): Eq False True % 4.01/4.19 Clause #163 (by clausification #[159]): False % 4.01/4.19 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------