%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ALG211+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 07:44:07 PM UTC 2025 % Result : Theorem 5.25s 5.45s % Output : Proof 5.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG211+1 : TPTP v9.2.0. Released v3.1.0. % 0.12/0.13 % Command : duper %s % 0.12/0.34 % Computer : n022.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 09:38:38 EDT 2025 % 0.12/0.34 % CPUTime : % 5.25/5.45 SZS status Theorem for theBenchmark.p % 5.25/5.45 SZS output start Proof for theBenchmark.p % 5.25/5.45 Clause #0 (by assumption #[]): Eq (∀ (B V : Iota), basis_of B V → And (lin_ind_subset B V) (a_subset_of B (vec_to_class V))) True % 5.25/5.45 Clause #1 (by assumption #[]): Eq % 5.25/5.45 (∀ (S T V : Iota), % 5.25/5.45 And (lin_ind_subset S V) (basis_of T V) → Exists fun U => And (a_subset_of U T) (basis_of (union S U) V)) % 5.25/5.45 True % 5.25/5.45 Clause #2 (by assumption #[]): Eq (∀ (A : Iota), a_vector_space A → Exists fun B => basis_of B A) True % 5.25/5.45 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), a_vector_subspace_of A B → a_vector_space A) True % 5.25/5.45 Clause #4 (by assumption #[]): Eq % 5.25/5.45 (∀ (W V E : Iota), % 5.25/5.45 And (a_vector_subspace_of W V) (a_subset_of E (vec_to_class W)) → Iff (lin_ind_subset E W) (lin_ind_subset E V)) % 5.25/5.45 True % 5.25/5.45 Clause #5 (by assumption #[]): Eq % 5.25/5.45 (Not % 5.25/5.45 (∀ (W V : Iota), % 5.25/5.45 And (a_vector_subspace_of W V) (a_vector_space V) → % 5.25/5.45 Exists fun E => Exists fun F => And (basis_of (union E F) V) (basis_of E W))) % 5.25/5.45 True % 5.25/5.45 Clause #6 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), a_vector_subspace_of a B → a_vector_space a) True % 5.25/5.45 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (a_vector_subspace_of a a_1 → a_vector_space a) True % 5.25/5.45 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (a_vector_subspace_of a a_1) False) (Eq (a_vector_space a) True) % 5.25/5.45 Clause #9 (by clausification #[2]): ∀ (a : Iota), Eq (a_vector_space a → Exists fun B => basis_of B a) True % 5.25/5.45 Clause #10 (by clausification #[9]): ∀ (a : Iota), Or (Eq (a_vector_space a) False) (Eq (Exists fun B => basis_of B a) True) % 5.25/5.45 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (a_vector_space a) False) (Eq (basis_of (skS.0 0 a a_1) a) True) % 5.25/5.45 Clause #12 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (V : Iota), basis_of a V → And (lin_ind_subset a V) (a_subset_of a (vec_to_class V))) True % 5.25/5.45 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (basis_of a a_1 → And (lin_ind_subset a a_1) (a_subset_of a (vec_to_class a_1))) True % 5.25/5.45 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), % 5.25/5.45 Or (Eq (basis_of a a_1) False) (Eq (And (lin_ind_subset a a_1) (a_subset_of a (vec_to_class a_1))) True) % 5.25/5.45 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (basis_of a a_1) False) (Eq (a_subset_of a (vec_to_class a_1)) True) % 5.25/5.45 Clause #16 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (basis_of a a_1) False) (Eq (lin_ind_subset a a_1) True) % 5.25/5.45 Clause #17 (by clausification #[4]): ∀ (a : Iota), % 5.25/5.45 Eq % 5.25/5.45 (∀ (V E : Iota), % 5.25/5.45 And (a_vector_subspace_of a V) (a_subset_of E (vec_to_class a)) → Iff (lin_ind_subset E a) (lin_ind_subset E V)) % 5.25/5.45 True % 5.25/5.45 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), % 5.25/5.45 Eq % 5.25/5.45 (∀ (E : Iota), % 5.25/5.45 And (a_vector_subspace_of a a_1) (a_subset_of E (vec_to_class a)) → % 5.25/5.45 Iff (lin_ind_subset E a) (lin_ind_subset E a_1)) % 5.25/5.45 True % 5.25/5.45 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), % 5.25/5.45 Eq % 5.25/5.45 (And (a_vector_subspace_of a a_1) (a_subset_of a_2 (vec_to_class a)) → % 5.25/5.45 Iff (lin_ind_subset a_2 a) (lin_ind_subset a_2 a_1)) % 5.25/5.45 True % 5.25/5.45 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), % 5.25/5.45 Or (Eq (And (a_vector_subspace_of a a_1) (a_subset_of a_2 (vec_to_class a))) False) % 5.25/5.45 (Eq (Iff (lin_ind_subset a_2 a) (lin_ind_subset a_2 a_1)) True) % 5.25/5.45 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), % 5.25/5.45 Or (Eq (Iff (lin_ind_subset a a_1) (lin_ind_subset a a_2)) True) % 5.25/5.45 (Or (Eq (a_vector_subspace_of a_1 a_2) False) (Eq (a_subset_of a (vec_to_class a_1)) False)) % 5.25/5.45 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), % 5.25/5.45 Or (Eq (a_vector_subspace_of a a_1) False) % 5.25/5.45 (Or (Eq (a_subset_of a_2 (vec_to_class a)) False) % 5.25/5.45 (Or (Eq (lin_ind_subset a_2 a) False) (Eq (lin_ind_subset a_2 a_1) True))) % 5.25/5.45 Clause #24 (by clausification #[1]): ∀ (a : Iota), % 5.25/5.45 Eq % 5.25/5.45 (∀ (T V : Iota), % 5.25/5.45 And (lin_ind_subset a V) (basis_of T V) → Exists fun U => And (a_subset_of U T) (basis_of (union a U) V)) % 5.25/5.45 True % 5.25/5.45 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), % 5.25/5.45 Eq % 5.25/5.45 (∀ (V : Iota), % 5.25/5.45 And (lin_ind_subset a V) (basis_of a_1 V) → Exists fun U => And (a_subset_of U a_1) (basis_of (union a U) V)) % 5.25/5.47 True % 5.25/5.47 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 5.25/5.47 Eq % 5.25/5.47 (And (lin_ind_subset a a_1) (basis_of a_2 a_1) → Exists fun U => And (a_subset_of U a_2) (basis_of (union a U) a_1)) % 5.25/5.47 True % 5.25/5.47 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 5.25/5.47 Or (Eq (And (lin_ind_subset a a_1) (basis_of a_2 a_1)) False) % 5.25/5.47 (Eq (Exists fun U => And (a_subset_of U a_2) (basis_of (union a U) a_1)) True) % 5.25/5.47 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 5.25/5.47 Or (Eq (Exists fun U => And (a_subset_of U a) (basis_of (union a_1 U) a_2)) True) % 5.25/5.47 (Or (Eq (lin_ind_subset a_1 a_2) False) (Eq (basis_of a a_2) False)) % 5.25/5.47 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 a_3 : Iota), % 5.25/5.47 Or (Eq (lin_ind_subset a a_1) False) % 5.25/5.47 (Or (Eq (basis_of a_2 a_1) False) % 5.25/5.47 (Eq (And (a_subset_of (skS.0 1 a_2 a a_1 a_3) a_2) (basis_of (union a (skS.0 1 a_2 a a_1 a_3)) a_1)) True)) % 5.25/5.47 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 a_3 : Iota), % 5.25/5.47 Or (Eq (lin_ind_subset a a_1) False) % 5.25/5.47 (Or (Eq (basis_of a_2 a_1) False) (Eq (basis_of (union a (skS.0 1 a_2 a a_1 a_3)) a_1) True)) % 5.25/5.47 Clause #32 (by clausification #[5]): Eq % 5.25/5.47 (∀ (W V : Iota), % 5.25/5.47 And (a_vector_subspace_of W V) (a_vector_space V) → % 5.25/5.47 Exists fun E => Exists fun F => And (basis_of (union E F) V) (basis_of E W)) % 5.25/5.47 False % 5.25/5.47 Clause #33 (by clausification #[32]): ∀ (a : Iota), % 5.25/5.47 Eq % 5.25/5.47 (Not % 5.25/5.47 (∀ (V : Iota), % 5.25/5.47 And (a_vector_subspace_of (skS.0 2 a) V) (a_vector_space V) → % 5.25/5.47 Exists fun E => Exists fun F => And (basis_of (union E F) V) (basis_of E (skS.0 2 a)))) % 5.25/5.47 True % 5.25/5.47 Clause #34 (by clausification #[33]): ∀ (a : Iota), % 5.25/5.47 Eq % 5.25/5.47 (∀ (V : Iota), % 5.25/5.47 And (a_vector_subspace_of (skS.0 2 a) V) (a_vector_space V) → % 5.25/5.47 Exists fun E => Exists fun F => And (basis_of (union E F) V) (basis_of E (skS.0 2 a))) % 5.25/5.47 False % 5.25/5.47 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), % 5.25/5.47 Eq % 5.25/5.47 (Not % 5.25/5.47 (And (a_vector_subspace_of (skS.0 2 a) (skS.0 3 a a_1)) (a_vector_space (skS.0 3 a a_1)) → % 5.25/5.47 Exists fun E => Exists fun F => And (basis_of (union E F) (skS.0 3 a a_1)) (basis_of E (skS.0 2 a)))) % 5.25/5.47 True % 5.25/5.47 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 5.25/5.47 Eq % 5.25/5.47 (And (a_vector_subspace_of (skS.0 2 a) (skS.0 3 a a_1)) (a_vector_space (skS.0 3 a a_1)) → % 5.25/5.47 Exists fun E => Exists fun F => And (basis_of (union E F) (skS.0 3 a a_1)) (basis_of E (skS.0 2 a))) % 5.25/5.47 False % 5.25/5.47 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (And (a_vector_subspace_of (skS.0 2 a) (skS.0 3 a a_1)) (a_vector_space (skS.0 3 a a_1))) True % 5.25/5.47 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), % 5.25/5.47 Eq (Exists fun E => Exists fun F => And (basis_of (union E F) (skS.0 3 a a_1)) (basis_of E (skS.0 2 a))) False % 5.25/5.47 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (a_vector_space (skS.0 3 a a_1)) True % 5.25/5.47 Clause #40 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (a_vector_subspace_of (skS.0 2 a) (skS.0 3 a a_1)) True % 5.25/5.47 Clause #41 (by superposition #[39, 11]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (basis_of (skS.0 0 (skS.0 3 a a_1) a_2) (skS.0 3 a a_1)) True) % 5.25/5.47 Clause #42 (by superposition #[40, 8]): ∀ (a : Iota), Or (Eq True False) (Eq (a_vector_space (skS.0 2 a)) True) % 5.25/5.47 Clause #44 (by superposition #[40, 23]): ∀ (a a_1 a_2 : Iota), % 5.25/5.47 Or (Eq True False) % 5.25/5.47 (Or (Eq (a_subset_of a (vec_to_class (skS.0 2 a_1))) False) % 5.25/5.47 (Or (Eq (lin_ind_subset a (skS.0 2 a_1)) False) (Eq (lin_ind_subset a (skS.0 3 a_1 a_2)) True))) % 5.25/5.47 Clause #45 (by clausification #[42]): ∀ (a : Iota), Eq (a_vector_space (skS.0 2 a)) True % 5.25/5.47 Clause #46 (by superposition #[45, 11]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (basis_of (skS.0 0 (skS.0 2 a) a_1) (skS.0 2 a)) True) % 5.25/5.47 Clause #47 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Eq (Exists fun F => And (basis_of (union a F) (skS.0 3 a_1 a_2)) (basis_of a (skS.0 2 a_1))) False % 5.25/5.47 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota), Eq (And (basis_of (union a a_1) (skS.0 3 a_2 a_3)) (basis_of a (skS.0 2 a_2))) False % 5.35/5.50 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (basis_of (union a a_1) (skS.0 3 a_2 a_3)) False) (Eq (basis_of a (skS.0 2 a_2)) False) % 5.35/5.50 Clause #50 (by clausification #[46]): ∀ (a a_1 : Iota), Eq (basis_of (skS.0 0 (skS.0 2 a) a_1) (skS.0 2 a)) True % 5.35/5.50 Clause #51 (by superposition #[50, 15]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (a_subset_of (skS.0 0 (skS.0 2 a) a_1) (vec_to_class (skS.0 2 a))) True) % 5.35/5.50 Clause #52 (by superposition #[50, 16]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (lin_ind_subset (skS.0 0 (skS.0 2 a) a_1) (skS.0 2 a)) True) % 5.35/5.50 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (lin_ind_subset (skS.0 0 (skS.0 2 a) a_1) (skS.0 2 a)) True % 5.35/5.50 Clause #56 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (a_subset_of (skS.0 0 (skS.0 2 a) a_1) (vec_to_class (skS.0 2 a))) True % 5.35/5.50 Clause #57 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Eq (basis_of (skS.0 0 (skS.0 3 a a_1) a_2) (skS.0 3 a a_1)) True % 5.35/5.50 Clause #66 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), % 5.35/5.50 Or (Eq (a_subset_of a (vec_to_class (skS.0 2 a_1))) False) % 5.35/5.50 (Or (Eq (lin_ind_subset a (skS.0 2 a_1)) False) (Eq (lin_ind_subset a (skS.0 3 a_1 a_2)) True)) % 5.35/5.50 Clause #67 (by superposition #[66, 56]): ∀ (a a_1 a_2 : Iota), % 5.35/5.50 Or (Eq (lin_ind_subset (skS.0 0 (skS.0 2 a) a_1) (skS.0 2 a)) False) % 5.35/5.50 (Or (Eq (lin_ind_subset (skS.0 0 (skS.0 2 a) a_1) (skS.0 3 a a_2)) True) (Eq False True)) % 5.35/5.50 Clause #70 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), % 5.35/5.50 Or (Eq (lin_ind_subset (skS.0 0 (skS.0 2 a) a_1) (skS.0 2 a)) False) % 5.35/5.50 (Eq (lin_ind_subset (skS.0 0 (skS.0 2 a) a_1) (skS.0 3 a a_2)) True) % 5.35/5.50 Clause #71 (by forward demodulation #[70, 53]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (lin_ind_subset (skS.0 0 (skS.0 2 a) a_1) (skS.0 3 a a_2)) True) % 5.35/5.50 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), Eq (lin_ind_subset (skS.0 0 (skS.0 2 a) a_1) (skS.0 3 a a_2)) True % 5.35/5.50 Clause #73 (by superposition #[72, 30]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.35/5.50 Or (Eq True False) % 5.35/5.50 (Or (Eq (basis_of a (skS.0 3 a_1 a_2)) False) % 5.35/5.50 (Eq % 5.35/5.50 (basis_of (union (skS.0 0 (skS.0 2 a_1) a_3) (skS.0 1 a (skS.0 0 (skS.0 2 a_1) a_3) (skS.0 3 a_1 a_2) a_4)) % 5.35/5.50 (skS.0 3 a_1 a_2)) % 5.35/5.50 True)) % 5.35/5.50 Clause #99 (by clausification #[73]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.35/5.50 Or (Eq (basis_of a (skS.0 3 a_1 a_2)) False) % 5.35/5.50 (Eq % 5.35/5.50 (basis_of (union (skS.0 0 (skS.0 2 a_1) a_3) (skS.0 1 a (skS.0 0 (skS.0 2 a_1) a_3) (skS.0 3 a_1 a_2) a_4)) % 5.35/5.50 (skS.0 3 a_1 a_2)) % 5.35/5.50 True) % 5.35/5.50 Clause #100 (by superposition #[99, 57]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.35/5.50 Or % 5.35/5.50 (Eq % 5.35/5.50 (basis_of % 5.35/5.50 (union (skS.0 0 (skS.0 2 a) a_1) % 5.35/5.50 (skS.0 1 (skS.0 0 (skS.0 3 a a_2) a_3) (skS.0 0 (skS.0 2 a) a_1) (skS.0 3 a a_2) a_4)) % 5.35/5.50 (skS.0 3 a a_2)) % 5.35/5.50 True) % 5.35/5.50 (Eq False True) % 5.35/5.50 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.35/5.50 Eq % 5.35/5.50 (basis_of % 5.35/5.50 (union (skS.0 0 (skS.0 2 a) a_1) % 5.35/5.50 (skS.0 1 (skS.0 0 (skS.0 3 a a_2) a_3) (skS.0 0 (skS.0 2 a) a_1) (skS.0 3 a a_2) a_4)) % 5.35/5.50 (skS.0 3 a a_2)) % 5.35/5.50 True % 5.35/5.50 Clause #102 (by superposition #[101, 49]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (basis_of (skS.0 0 (skS.0 2 a) a_1) (skS.0 2 a)) False) % 5.35/5.50 Clause #110 (by clausification #[102]): ∀ (a a_1 : Iota), Eq (basis_of (skS.0 0 (skS.0 2 a) a_1) (skS.0 2 a)) False % 5.35/5.50 Clause #111 (by superposition #[110, 50]): Eq False True % 5.35/5.50 Clause #112 (by clausification #[111]): False % 5.35/5.50 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------