%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO226+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 07:48:17 PM UTC 2025 % Result : Theorem 6.98s 7.19s % Output : Proof 7.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEO226+1 : TPTP v9.2.0. Released v3.3.0. % 0.11/0.13 % Command : duper %s % 0.14/0.34 % Computer : n017.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 12:24:08 EDT 2025 % 0.14/0.34 % CPUTime : % 6.98/7.19 SZS status Theorem for theBenchmark.p % 6.98/7.19 SZS output start Proof for theBenchmark.p % 6.98/7.19 Clause #8 (by assumption #[]): Eq (∀ (X Y : Iota), convergent_lines X Y → Not (apart_point_and_line (intersection_point X Y) X)) True % 6.98/7.19 Clause #9 (by assumption #[]): Eq (∀ (X Y : Iota), convergent_lines X Y → Not (apart_point_and_line (intersection_point X Y) Y)) True % 6.98/7.19 Clause #18 (by assumption #[]): Eq % 6.98/7.19 (Not % 6.98/7.19 (∀ (L M : Iota), % 6.98/7.19 And (And (line L) (line M)) (convergent_lines L M) → % 6.98/7.19 Exists fun X => point X → And (Not (apart_point_and_line X L)) (Not (apart_point_and_line X M)))) % 6.98/7.19 True % 6.98/7.19 Clause #56 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (Y : Iota), convergent_lines a Y → Not (apart_point_and_line (intersection_point a Y) Y)) True % 6.98/7.19 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota), Eq (convergent_lines a a_1 → Not (apart_point_and_line (intersection_point a a_1) a_1)) True % 6.98/7.19 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), % 6.98/7.19 Or (Eq (convergent_lines a a_1) False) (Eq (Not (apart_point_and_line (intersection_point a a_1) a_1)) True) % 6.98/7.19 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), % 6.98/7.19 Or (Eq (convergent_lines a a_1) False) (Eq (apart_point_and_line (intersection_point a a_1) a_1) False) % 6.98/7.19 Clause #65 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (Y : Iota), convergent_lines a Y → Not (apart_point_and_line (intersection_point a Y) a)) True % 6.98/7.19 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), Eq (convergent_lines a a_1 → Not (apart_point_and_line (intersection_point a a_1) a)) True % 6.98/7.19 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), % 6.98/7.19 Or (Eq (convergent_lines a a_1) False) (Eq (Not (apart_point_and_line (intersection_point a a_1) a)) True) % 6.98/7.19 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines a a_1) False) (Eq (apart_point_and_line (intersection_point a a_1) a) False) % 6.98/7.19 Clause #98 (by clausification #[18]): Eq % 6.98/7.19 (∀ (L M : Iota), % 6.98/7.19 And (And (line L) (line M)) (convergent_lines L M) → % 6.98/7.19 Exists fun X => point X → And (Not (apart_point_and_line X L)) (Not (apart_point_and_line X M))) % 6.98/7.19 False % 6.98/7.19 Clause #99 (by clausification #[98]): ∀ (a : Iota), % 6.98/7.19 Eq % 6.98/7.19 (Not % 6.98/7.19 (∀ (M : Iota), % 6.98/7.19 And (And (line (skS.0 0 a)) (line M)) (convergent_lines (skS.0 0 a) M) → % 6.98/7.19 Exists fun X => point X → And (Not (apart_point_and_line X (skS.0 0 a))) (Not (apart_point_and_line X M)))) % 6.98/7.19 True % 6.98/7.19 Clause #100 (by clausification #[99]): ∀ (a : Iota), % 6.98/7.19 Eq % 6.98/7.19 (∀ (M : Iota), % 6.98/7.19 And (And (line (skS.0 0 a)) (line M)) (convergent_lines (skS.0 0 a) M) → % 6.98/7.19 Exists fun X => point X → And (Not (apart_point_and_line X (skS.0 0 a))) (Not (apart_point_and_line X M))) % 6.98/7.19 False % 6.98/7.19 Clause #101 (by clausification #[100]): ∀ (a a_1 : Iota), % 6.98/7.19 Eq % 6.98/7.19 (Not % 6.98/7.19 (And (And (line (skS.0 0 a)) (line (skS.0 1 a a_1))) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) → % 6.98/7.19 Exists fun X => % 6.98/7.19 point X → And (Not (apart_point_and_line X (skS.0 0 a))) (Not (apart_point_and_line X (skS.0 1 a a_1))))) % 6.98/7.19 True % 6.98/7.19 Clause #102 (by clausification #[101]): ∀ (a a_1 : Iota), % 6.98/7.19 Eq % 6.98/7.19 (And (And (line (skS.0 0 a)) (line (skS.0 1 a a_1))) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) → % 6.98/7.19 Exists fun X => % 6.98/7.19 point X → And (Not (apart_point_and_line X (skS.0 0 a))) (Not (apart_point_and_line X (skS.0 1 a a_1)))) % 6.98/7.19 False % 6.98/7.19 Clause #103 (by clausification #[102]): ∀ (a a_1 : Iota), % 6.98/7.19 Eq (And (And (line (skS.0 0 a)) (line (skS.0 1 a a_1))) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) True % 6.98/7.19 Clause #104 (by clausification #[102]): ∀ (a a_1 : Iota), % 6.98/7.19 Eq % 6.98/7.19 (Exists fun X => % 6.98/7.19 point X → And (Not (apart_point_and_line X (skS.0 0 a))) (Not (apart_point_and_line X (skS.0 1 a a_1)))) % 6.98/7.19 False % 6.98/7.19 Clause #105 (by clausification #[103]): ∀ (a a_1 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) True % 6.98/7.19 Clause #108 (by superposition #[105, 59]): ∀ (a a_1 : Iota), % 6.98/7.19 Or (Eq True False) (Eq (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 1 a a_1)) False) % 6.98/7.19 Clause #109 (by superposition #[105, 68]): ∀ (a a_1 : Iota), % 7.04/7.21 Or (Eq True False) (Eq (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 0 a)) False) % 7.04/7.21 Clause #120 (by clausification #[104]): ∀ (a a_1 a_2 : Iota), % 7.04/7.21 Eq (point a → And (Not (apart_point_and_line a (skS.0 0 a_1))) (Not (apart_point_and_line a (skS.0 1 a_1 a_2)))) False % 7.04/7.21 Clause #122 (by clausification #[120]): ∀ (a a_1 a_2 : Iota), % 7.04/7.21 Eq (And (Not (apart_point_and_line a (skS.0 0 a_1))) (Not (apart_point_and_line a (skS.0 1 a_1 a_2)))) False % 7.04/7.21 Clause #157 (by clausification #[108]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 1 a a_1)) False % 7.04/7.21 Clause #173 (by clausification #[109]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 0 a)) False % 7.04/7.21 Clause #225 (by clausification #[122]): ∀ (a a_1 a_2 : Iota), % 7.04/7.21 Or (Eq (Not (apart_point_and_line a (skS.0 0 a_1))) False) (Eq (Not (apart_point_and_line a (skS.0 1 a_1 a_2))) False) % 7.04/7.21 Clause #226 (by clausification #[225]): ∀ (a a_1 a_2 : Iota), % 7.04/7.21 Or (Eq (Not (apart_point_and_line a (skS.0 1 a_1 a_2))) False) (Eq (apart_point_and_line a (skS.0 0 a_1)) True) % 7.04/7.21 Clause #227 (by clausification #[226]): ∀ (a a_1 a_2 : Iota), % 7.04/7.21 Or (Eq (apart_point_and_line a (skS.0 0 a_1)) True) (Eq (apart_point_and_line a (skS.0 1 a_1 a_2)) True) % 7.04/7.21 Clause #228 (by superposition #[227, 157]): ∀ (a a_1 : Iota), % 7.04/7.21 Or (Eq (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 0 a)) True) (Eq True False) % 7.04/7.21 Clause #469 (by clausification #[228]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (intersection_point (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 0 a)) True % 7.04/7.21 Clause #470 (by superposition #[469, 173]): Eq True False % 7.04/7.21 Clause #473 (by clausification #[470]): False % 7.04/7.21 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------