TSTP Solution File: ALG211+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% 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 : Wed Aug 30 16:11:37 EDT 2023
% Result : Theorem 5.69s 5.93s
% Output : Proof 5.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 03:27:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 5.69/5.93 SZS status Theorem for theBenchmark.p
% 5.69/5.93 SZS output start Proof for theBenchmark.p
% 5.69/5.93 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
% 5.69/5.93 Clause #1 (by assumption #[]): Eq
% 5.69/5.93 (∀ (S T V : Iota),
% 5.69/5.93 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))
% 5.69/5.93 True
% 5.69/5.93 Clause #2 (by assumption #[]): Eq (∀ (A : Iota), a_vector_space A → Exists fun B => basis_of B A) True
% 5.69/5.93 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), a_vector_subspace_of A B → a_vector_space A) True
% 5.69/5.93 Clause #4 (by assumption #[]): Eq
% 5.69/5.93 (∀ (W V E : Iota),
% 5.69/5.93 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))
% 5.69/5.93 True
% 5.69/5.93 Clause #5 (by assumption #[]): Eq
% 5.69/5.93 (Not
% 5.69/5.93 (∀ (W V : Iota),
% 5.69/5.93 And (a_vector_subspace_of W V) (a_vector_space V) →
% 5.69/5.93 Exists fun E => Exists fun F => And (basis_of (union E F) V) (basis_of E W)))
% 5.69/5.93 True
% 5.69/5.93 Clause #6 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), a_vector_subspace_of a B → a_vector_space a) True
% 5.69/5.93 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (a_vector_subspace_of a a_1 → a_vector_space a) True
% 5.69/5.93 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)
% 5.69/5.93 Clause #9 (by clausification #[2]): ∀ (a : Iota), Eq (a_vector_space a → Exists fun B => basis_of B a) True
% 5.69/5.93 Clause #10 (by clausification #[9]): ∀ (a : Iota), Or (Eq (a_vector_space a) False) (Eq (Exists fun B => basis_of B a) True)
% 5.69/5.93 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)
% 5.69/5.93 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
% 5.69/5.93 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
% 5.69/5.93 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota),
% 5.69/5.93 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)
% 5.69/5.93 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)
% 5.69/5.93 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)
% 5.69/5.93 Clause #17 (by clausification #[4]): ∀ (a : Iota),
% 5.69/5.93 Eq
% 5.69/5.93 (∀ (V E : Iota),
% 5.69/5.93 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))
% 5.69/5.93 True
% 5.69/5.93 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota),
% 5.69/5.93 Eq
% 5.69/5.93 (∀ (E : Iota),
% 5.69/5.93 And (a_vector_subspace_of a a_1) (a_subset_of E (vec_to_class a)) →
% 5.69/5.93 Iff (lin_ind_subset E a) (lin_ind_subset E a_1))
% 5.69/5.93 True
% 5.69/5.93 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota),
% 5.69/5.93 Eq
% 5.69/5.93 (And (a_vector_subspace_of a a_1) (a_subset_of a_2 (vec_to_class a)) →
% 5.69/5.93 Iff (lin_ind_subset a_2 a) (lin_ind_subset a_2 a_1))
% 5.69/5.93 True
% 5.69/5.93 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota),
% 5.69/5.93 Or (Eq (And (a_vector_subspace_of a a_1) (a_subset_of a_2 (vec_to_class a))) False)
% 5.69/5.93 (Eq (Iff (lin_ind_subset a_2 a) (lin_ind_subset a_2 a_1)) True)
% 5.69/5.93 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota),
% 5.69/5.93 Or (Eq (Iff (lin_ind_subset a a_1) (lin_ind_subset a a_2)) True)
% 5.69/5.93 (Or (Eq (a_vector_subspace_of a_1 a_2) False) (Eq (a_subset_of a (vec_to_class a_1)) False))
% 5.69/5.93 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 : Iota),
% 5.69/5.93 Or (Eq (a_vector_subspace_of a a_1) False)
% 5.69/5.93 (Or (Eq (a_subset_of a_2 (vec_to_class a)) False)
% 5.69/5.93 (Or (Eq (lin_ind_subset a_2 a) False) (Eq (lin_ind_subset a_2 a_1) True)))
% 5.69/5.93 Clause #24 (by clausification #[1]): ∀ (a : Iota),
% 5.69/5.93 Eq
% 5.69/5.93 (∀ (T V : Iota),
% 5.69/5.93 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))
% 5.69/5.93 True
% 5.69/5.93 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota),
% 5.69/5.93 Eq
% 5.69/5.93 (∀ (V : Iota),
% 5.69/5.93 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))
% 5.78/5.96 True
% 5.78/5.96 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota),
% 5.78/5.96 Eq
% 5.78/5.96 (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))
% 5.78/5.96 True
% 5.78/5.96 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota),
% 5.78/5.96 Or (Eq (And (lin_ind_subset a a_1) (basis_of a_2 a_1)) False)
% 5.78/5.96 (Eq (Exists fun U => And (a_subset_of U a_2) (basis_of (union a U) a_1)) True)
% 5.78/5.96 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota),
% 5.78/5.96 Or (Eq (Exists fun U => And (a_subset_of U a) (basis_of (union a_1 U) a_2)) True)
% 5.78/5.96 (Or (Eq (lin_ind_subset a_1 a_2) False) (Eq (basis_of a a_2) False))
% 5.78/5.96 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.78/5.96 Or (Eq (lin_ind_subset a a_1) False)
% 5.78/5.96 (Or (Eq (basis_of a_2 a_1) False)
% 5.78/5.96 (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))
% 5.78/5.96 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.78/5.96 Or (Eq (lin_ind_subset a a_1) False)
% 5.78/5.96 (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))
% 5.78/5.96 Clause #32 (by clausification #[5]): Eq
% 5.78/5.96 (∀ (W V : Iota),
% 5.78/5.96 And (a_vector_subspace_of W V) (a_vector_space V) →
% 5.78/5.96 Exists fun E => Exists fun F => And (basis_of (union E F) V) (basis_of E W))
% 5.78/5.96 False
% 5.78/5.96 Clause #33 (by clausification #[32]): ∀ (a : Iota),
% 5.78/5.96 Eq
% 5.78/5.96 (Not
% 5.78/5.96 (∀ (V : Iota),
% 5.78/5.96 And (a_vector_subspace_of (skS.0 2 a) V) (a_vector_space V) →
% 5.78/5.96 Exists fun E => Exists fun F => And (basis_of (union E F) V) (basis_of E (skS.0 2 a))))
% 5.78/5.96 True
% 5.78/5.96 Clause #34 (by clausification #[33]): ∀ (a : Iota),
% 5.78/5.96 Eq
% 5.78/5.96 (∀ (V : Iota),
% 5.78/5.96 And (a_vector_subspace_of (skS.0 2 a) V) (a_vector_space V) →
% 5.78/5.96 Exists fun E => Exists fun F => And (basis_of (union E F) V) (basis_of E (skS.0 2 a)))
% 5.78/5.96 False
% 5.78/5.96 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota),
% 5.78/5.96 Eq
% 5.78/5.96 (Not
% 5.78/5.96 (And (a_vector_subspace_of (skS.0 2 a) (skS.0 3 a a_1)) (a_vector_space (skS.0 3 a a_1)) →
% 5.78/5.96 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))))
% 5.78/5.96 True
% 5.78/5.96 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota),
% 5.78/5.96 Eq
% 5.78/5.96 (And (a_vector_subspace_of (skS.0 2 a) (skS.0 3 a a_1)) (a_vector_space (skS.0 3 a a_1)) →
% 5.78/5.96 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)))
% 5.78/5.96 False
% 5.78/5.96 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
% 5.78/5.96 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota),
% 5.78/5.96 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
% 5.78/5.96 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (a_vector_space (skS.0 3 a a_1)) True
% 5.78/5.96 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
% 5.78/5.96 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)
% 5.78/5.96 Clause #42 (by superposition #[40, 8]): ∀ (a : Iota), Or (Eq True False) (Eq (a_vector_space (skS.0 2 a)) True)
% 5.78/5.96 Clause #44 (by superposition #[40, 23]): ∀ (a a_1 a_2 : Iota),
% 5.78/5.96 Or (Eq True False)
% 5.78/5.96 (Or (Eq (a_subset_of a (vec_to_class (skS.0 2 a_1))) False)
% 5.78/5.96 (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)))
% 5.78/5.96 Clause #45 (by clausification #[42]): ∀ (a : Iota), Eq (a_vector_space (skS.0 2 a)) True
% 5.78/5.96 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)
% 5.78/5.96 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
% 5.78/5.96 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
% 5.78/5.99 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)
% 5.78/5.99 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
% 5.78/5.99 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)
% 5.78/5.99 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)
% 5.78/5.99 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
% 5.78/5.99 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
% 5.78/5.99 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
% 5.78/5.99 Clause #66 (by clausification #[44]): ∀ (a a_1 a_2 : Iota),
% 5.78/5.99 Or (Eq (a_subset_of a (vec_to_class (skS.0 2 a_1))) False)
% 5.78/5.99 (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))
% 5.78/5.99 Clause #67 (by superposition #[66, 56]): ∀ (a a_1 a_2 : Iota),
% 5.78/5.99 Or (Eq (lin_ind_subset (skS.0 0 (skS.0 2 a) a_1) (skS.0 2 a)) False)
% 5.78/5.99 (Or (Eq (lin_ind_subset (skS.0 0 (skS.0 2 a) a_1) (skS.0 3 a a_2)) True) (Eq False True))
% 5.78/5.99 Clause #70 (by clausification #[67]): ∀ (a a_1 a_2 : Iota),
% 5.78/5.99 Or (Eq (lin_ind_subset (skS.0 0 (skS.0 2 a) a_1) (skS.0 2 a)) False)
% 5.78/5.99 (Eq (lin_ind_subset (skS.0 0 (skS.0 2 a) a_1) (skS.0 3 a a_2)) True)
% 5.78/5.99 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)
% 5.78/5.99 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
% 5.78/5.99 Clause #73 (by superposition #[72, 30]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.78/5.99 Or (Eq True False)
% 5.78/5.99 (Or (Eq (basis_of a (skS.0 3 a_1 a_2)) False)
% 5.78/5.99 (Eq
% 5.78/5.99 (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))
% 5.78/5.99 (skS.0 3 a_1 a_2))
% 5.78/5.99 True))
% 5.78/5.99 Clause #99 (by clausification #[73]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.78/5.99 Or (Eq (basis_of a (skS.0 3 a_1 a_2)) False)
% 5.78/5.99 (Eq
% 5.78/5.99 (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))
% 5.78/5.99 (skS.0 3 a_1 a_2))
% 5.78/5.99 True)
% 5.78/5.99 Clause #100 (by superposition #[99, 57]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.78/5.99 Or
% 5.78/5.99 (Eq
% 5.78/5.99 (basis_of
% 5.78/5.99 (union (skS.0 0 (skS.0 2 a) a_1)
% 5.78/5.99 (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))
% 5.78/5.99 (skS.0 3 a a_2))
% 5.78/5.99 True)
% 5.78/5.99 (Eq False True)
% 5.78/5.99 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.78/5.99 Eq
% 5.78/5.99 (basis_of
% 5.78/5.99 (union (skS.0 0 (skS.0 2 a) a_1)
% 5.78/5.99 (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))
% 5.78/5.99 (skS.0 3 a a_2))
% 5.78/5.99 True
% 5.78/5.99 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)
% 5.78/5.99 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
% 5.78/5.99 Clause #111 (by superposition #[110, 50]): Eq False True
% 5.78/5.99 Clause #112 (by clausification #[111]): False
% 5.78/5.99 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------