%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO220+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 07:48:16 PM UTC 2025 % Result : Theorem 7.32s 7.48s % Output : Proof 7.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.10 % Problem : GEO220+1 : TPTP v9.2.0. Released v3.3.0. % 0.02/0.11 % Command : duper %s % 0.10/0.31 % Computer : n009.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.31 % CPULimit : 300 % 0.16/0.31 % WCLimit : 300 % 0.16/0.31 % DateTime : Fri Oct 3 11:48:23 EDT 2025 % 0.16/0.31 % CPUTime : % 7.32/7.48 SZS status Theorem for theBenchmark.p % 7.32/7.48 SZS output start Proof for theBenchmark.p % 7.32/7.48 Clause #16 (by assumption #[]): Eq (∀ (L M N : Iota), And (Not (unorthogonal_lines L M)) (Not (unorthogonal_lines L N)) → Not (convergent_lines M N)) % 7.32/7.48 True % 7.32/7.48 Clause #17 (by assumption #[]): Eq % 7.32/7.48 (Not % 7.32/7.48 (∀ (L M N : Iota), And (Not (unorthogonal_lines L M)) (Not (unorthogonal_lines L N)) → Not (convergent_lines M N))) % 7.32/7.48 True % 7.32/7.48 Clause #24 (by clausification #[16]): ∀ (a : Iota), % 7.32/7.48 Eq (∀ (M N : Iota), And (Not (unorthogonal_lines a M)) (Not (unorthogonal_lines a N)) → Not (convergent_lines M N)) % 7.32/7.48 True % 7.32/7.48 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), % 7.32/7.48 Eq (∀ (N : Iota), And (Not (unorthogonal_lines a a_1)) (Not (unorthogonal_lines a N)) → Not (convergent_lines a_1 N)) % 7.32/7.48 True % 7.32/7.48 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 7.32/7.48 Eq (And (Not (unorthogonal_lines a a_1)) (Not (unorthogonal_lines a a_2)) → Not (convergent_lines a_1 a_2)) True % 7.32/7.48 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 7.32/7.48 Or (Eq (And (Not (unorthogonal_lines a a_1)) (Not (unorthogonal_lines a a_2))) False) % 7.32/7.48 (Eq (Not (convergent_lines a_1 a_2)) True) % 7.32/7.48 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 7.32/7.48 Or (Eq (Not (convergent_lines a a_1)) True) % 7.32/7.48 (Or (Eq (Not (unorthogonal_lines a_2 a)) False) (Eq (Not (unorthogonal_lines a_2 a_1)) False)) % 7.32/7.48 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), % 7.32/7.48 Or (Eq (Not (unorthogonal_lines a a_1)) False) % 7.32/7.48 (Or (Eq (Not (unorthogonal_lines a a_2)) False) (Eq (convergent_lines a_1 a_2) False)) % 7.32/7.48 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), % 7.32/7.48 Or (Eq (Not (unorthogonal_lines a a_1)) False) % 7.32/7.48 (Or (Eq (convergent_lines a_2 a_1) False) (Eq (unorthogonal_lines a a_2) True)) % 7.32/7.48 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), % 7.32/7.48 Or (Eq (convergent_lines a a_1) False) % 7.32/7.48 (Or (Eq (unorthogonal_lines a_2 a) True) (Eq (unorthogonal_lines a_2 a_1) True)) % 7.32/7.48 Clause #32 (by clausification #[17]): Eq (∀ (L M N : Iota), And (Not (unorthogonal_lines L M)) (Not (unorthogonal_lines L N)) → Not (convergent_lines M N)) % 7.32/7.48 False % 7.32/7.48 Clause #33 (by clausification #[32]): ∀ (a : Iota), % 7.32/7.48 Eq % 7.32/7.48 (Not % 7.32/7.48 (∀ (M N : Iota), % 7.32/7.48 And (Not (unorthogonal_lines (skS.0 0 a) M)) (Not (unorthogonal_lines (skS.0 0 a) N)) → % 7.32/7.48 Not (convergent_lines M N))) % 7.32/7.48 True % 7.32/7.48 Clause #34 (by clausification #[33]): ∀ (a : Iota), % 7.32/7.48 Eq % 7.32/7.48 (∀ (M N : Iota), % 7.32/7.48 And (Not (unorthogonal_lines (skS.0 0 a) M)) (Not (unorthogonal_lines (skS.0 0 a) N)) → % 7.32/7.48 Not (convergent_lines M N)) % 7.32/7.48 False % 7.32/7.48 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), % 7.32/7.48 Eq % 7.32/7.48 (Not % 7.32/7.48 (∀ (N : Iota), % 7.32/7.48 And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) (Not (unorthogonal_lines (skS.0 0 a) N)) → % 7.32/7.48 Not (convergent_lines (skS.0 1 a a_1) N))) % 7.32/7.48 True % 7.32/7.48 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 7.32/7.48 Eq % 7.32/7.48 (∀ (N : Iota), % 7.32/7.48 And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) (Not (unorthogonal_lines (skS.0 0 a) N)) → % 7.32/7.48 Not (convergent_lines (skS.0 1 a a_1) N)) % 7.32/7.48 False % 7.32/7.48 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 7.32/7.48 Eq % 7.32/7.48 (Not % 7.32/7.48 (And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) % 7.32/7.48 (Not (unorthogonal_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) → % 7.32/7.48 Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 7.32/7.48 True % 7.32/7.48 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 7.32/7.48 Eq % 7.32/7.48 (And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) % 7.32/7.48 (Not (unorthogonal_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) → % 7.32/7.48 Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 7.32/7.48 False % 7.32/7.48 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 7.32/7.48 Eq % 7.32/7.48 (And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) % 7.32/7.48 (Not (unorthogonal_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)))) % 7.32/7.48 True % 7.32/7.48 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Eq (Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) False % 7.32/7.48 Clause #41 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), Eq (Not (unorthogonal_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) True % 7.32/7.50 Clause #42 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) True % 7.32/7.50 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Eq (unorthogonal_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) False % 7.32/7.50 Clause #120 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)) False % 7.32/7.50 Clause #140 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True % 7.32/7.50 Clause #141 (by superposition #[140, 31]): ∀ (a a_1 a_2 a_3 : Iota), % 7.32/7.50 Or (Eq True False) % 7.32/7.50 (Or (Eq (unorthogonal_lines a (skS.0 1 a_1 a_2)) True) (Eq (unorthogonal_lines a (skS.0 2 a_1 a_2 a_3)) True)) % 7.32/7.50 Clause #302 (by clausification #[141]): ∀ (a a_1 a_2 a_3 : Iota), % 7.32/7.50 Or (Eq (unorthogonal_lines a (skS.0 1 a_1 a_2)) True) (Eq (unorthogonal_lines a (skS.0 2 a_1 a_2 a_3)) True) % 7.32/7.50 Clause #303 (by superposition #[302, 43]): ∀ (a a_1 : Iota), Or (Eq (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False) % 7.32/7.50 Clause #304 (by clausification #[303]): ∀ (a a_1 : Iota), Eq (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)) True % 7.32/7.50 Clause #305 (by superposition #[304, 120]): Eq True False % 7.32/7.50 Clause #306 (by clausification #[305]): False % 7.32/7.50 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------