%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:07:09 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 19:44:06 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.27 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.27
% 0.20/0.27 % SZS status Theorem
% 0.20/0.27
% 0.20/0.30 % SZS output start Proof
% 0.20/0.30 Axiom 1 (bg_2_4_3): a_vector_space(v) = true.
% 0.20/0.30 Axiom 2 (bg_2_4_3_1): a_vector_subspace_of(w, v) = true.
% 0.20/0.30 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.20/0.30 Axiom 4 (bg_2_4_a): ifeq(a_vector_subspace_of(X, Y), true, a_vector_space(X), true) = true.
% 0.20/0.30 Axiom 5 (bg_remark_63_a): ifeq(a_vector_space(X), true, basis_of(b(X), X), true) = true.
% 0.20/0.30 Axiom 6 (basis_of): ifeq(basis_of(X, Y), true, lin_ind_subset(X, Y), true) = true.
% 0.20/0.30 Axiom 7 (basis_of_1): ifeq(basis_of(X, Y), true, a_subset_of(X, vec_to_class(Y)), true) = true.
% 0.20/0.30 Axiom 8 (bg_2_2_5): ifeq(lin_ind_subset(X, Y), true, ifeq(basis_of(Z, Y), true, basis_of(union(X, u(X, Z, Y)), Y), true), true) = true.
% 0.20/0.30 Axiom 9 (bg_2_4_2): ifeq(a_vector_subspace_of(X, Y), true, ifeq(a_subset_of(Z, vec_to_class(X)), true, ifeq(lin_ind_subset(Z, X), true, lin_ind_subset(Z, Y), true), true), true) = true.
% 0.20/0.30
% 0.20/0.30 Goal 1 (bg_2_4_3_2): tuple(basis_of(X, w), basis_of(union(X, Y), v)) = tuple(true, true).
% 0.20/0.30 The goal is true when:
% 0.20/0.30 X = b(w)
% 0.20/0.30 Y = u(b(w), b(v), v)
% 0.20/0.30
% 0.20/0.30 Proof:
% 0.20/0.30 tuple(basis_of(b(w), w), basis_of(union(b(w), u(b(w), b(v), v)), v))
% 0.20/0.30 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.30 tuple(basis_of(b(w), w), ifeq(true, true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.30 = { by axiom 9 (bg_2_4_2) R->L }
% 0.20/0.30 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, ifeq(a_subset_of(b(w), vec_to_class(w)), true, ifeq(lin_ind_subset(b(w), w), true, lin_ind_subset(b(w), v), true), true), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.30 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.30 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, ifeq(ifeq(true, true, a_subset_of(b(w), vec_to_class(w)), true), true, ifeq(lin_ind_subset(b(w), w), true, lin_ind_subset(b(w), v), true), true), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.30 = { by axiom 5 (bg_remark_63_a) R->L }
% 0.20/0.30 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, ifeq(ifeq(ifeq(a_vector_space(w), true, basis_of(b(w), w), true), true, a_subset_of(b(w), vec_to_class(w)), true), true, ifeq(lin_ind_subset(b(w), w), true, lin_ind_subset(b(w), v), true), true), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.30 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.30 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, ifeq(ifeq(ifeq(ifeq(true, true, a_vector_space(w), true), true, basis_of(b(w), w), true), true, a_subset_of(b(w), vec_to_class(w)), true), true, ifeq(lin_ind_subset(b(w), w), true, lin_ind_subset(b(w), v), true), true), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.30 = { by axiom 2 (bg_2_4_3_1) R->L }
% 0.20/0.30 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, ifeq(ifeq(ifeq(ifeq(a_vector_subspace_of(w, v), true, a_vector_space(w), true), true, basis_of(b(w), w), true), true, a_subset_of(b(w), vec_to_class(w)), true), true, ifeq(lin_ind_subset(b(w), w), true, lin_ind_subset(b(w), v), true), true), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.30 = { by axiom 4 (bg_2_4_a) }
% 0.20/0.30 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, ifeq(ifeq(ifeq(true, true, basis_of(b(w), w), true), true, a_subset_of(b(w), vec_to_class(w)), true), true, ifeq(lin_ind_subset(b(w), w), true, lin_ind_subset(b(w), v), true), true), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.30 = { by axiom 3 (ifeq_axiom) }
% 0.20/0.30 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, ifeq(ifeq(basis_of(b(w), w), true, a_subset_of(b(w), vec_to_class(w)), true), true, ifeq(lin_ind_subset(b(w), w), true, lin_ind_subset(b(w), v), true), true), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.30 = { by axiom 7 (basis_of_1) }
% 0.20/0.30 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, ifeq(true, true, ifeq(lin_ind_subset(b(w), w), true, lin_ind_subset(b(w), v), true), true), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.30 = { by axiom 3 (ifeq_axiom) }
% 0.20/0.30 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, ifeq(lin_ind_subset(b(w), w), true, lin_ind_subset(b(w), v), true), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.30 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.30 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, ifeq(ifeq(true, true, lin_ind_subset(b(w), w), true), true, lin_ind_subset(b(w), v), true), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.30 = { by axiom 5 (bg_remark_63_a) R->L }
% 0.20/0.30 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, ifeq(ifeq(ifeq(a_vector_space(w), true, basis_of(b(w), w), true), true, lin_ind_subset(b(w), w), true), true, lin_ind_subset(b(w), v), true), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.30 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.30 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, ifeq(ifeq(ifeq(ifeq(true, true, a_vector_space(w), true), true, basis_of(b(w), w), true), true, lin_ind_subset(b(w), w), true), true, lin_ind_subset(b(w), v), true), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.30 = { by axiom 2 (bg_2_4_3_1) R->L }
% 0.20/0.30 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, ifeq(ifeq(ifeq(ifeq(a_vector_subspace_of(w, v), true, a_vector_space(w), true), true, basis_of(b(w), w), true), true, lin_ind_subset(b(w), w), true), true, lin_ind_subset(b(w), v), true), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.30 = { by axiom 4 (bg_2_4_a) }
% 0.20/0.30 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, ifeq(ifeq(ifeq(true, true, basis_of(b(w), w), true), true, lin_ind_subset(b(w), w), true), true, lin_ind_subset(b(w), v), true), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.30 = { by axiom 3 (ifeq_axiom) }
% 0.20/0.30 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, ifeq(ifeq(basis_of(b(w), w), true, lin_ind_subset(b(w), w), true), true, lin_ind_subset(b(w), v), true), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.31 = { by axiom 6 (basis_of) }
% 0.20/0.31 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, ifeq(true, true, lin_ind_subset(b(w), v), true), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.31 = { by axiom 3 (ifeq_axiom) }
% 0.20/0.31 tuple(basis_of(b(w), w), ifeq(ifeq(a_vector_subspace_of(w, v), true, lin_ind_subset(b(w), v), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.31 = { by axiom 2 (bg_2_4_3_1) }
% 0.20/0.31 tuple(basis_of(b(w), w), ifeq(ifeq(true, true, lin_ind_subset(b(w), v), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.31 = { by axiom 3 (ifeq_axiom) }
% 0.20/0.31 tuple(basis_of(b(w), w), ifeq(lin_ind_subset(b(w), v), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true))
% 0.20/0.31 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.31 tuple(basis_of(b(w), w), ifeq(lin_ind_subset(b(w), v), true, ifeq(true, true, basis_of(union(b(w), u(b(w), b(v), v)), v), true), true))
% 0.20/0.31 = { by axiom 5 (bg_remark_63_a) R->L }
% 0.20/0.31 tuple(basis_of(b(w), w), ifeq(lin_ind_subset(b(w), v), true, ifeq(ifeq(a_vector_space(v), true, basis_of(b(v), v), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true), true))
% 0.20/0.31 = { by axiom 1 (bg_2_4_3) }
% 0.20/0.31 tuple(basis_of(b(w), w), ifeq(lin_ind_subset(b(w), v), true, ifeq(ifeq(true, true, basis_of(b(v), v), true), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true), true))
% 0.20/0.31 = { by axiom 3 (ifeq_axiom) }
% 0.20/0.31 tuple(basis_of(b(w), w), ifeq(lin_ind_subset(b(w), v), true, ifeq(basis_of(b(v), v), true, basis_of(union(b(w), u(b(w), b(v), v)), v), true), true))
% 0.20/0.31 = { by axiom 8 (bg_2_2_5) }
% 0.20/0.31 tuple(basis_of(b(w), w), true)
% 0.20/0.31 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.31 tuple(ifeq(true, true, basis_of(b(w), w), true), true)
% 0.20/0.31 = { by axiom 4 (bg_2_4_a) R->L }
% 0.20/0.31 tuple(ifeq(ifeq(a_vector_subspace_of(w, v), true, a_vector_space(w), true), true, basis_of(b(w), w), true), true)
% 0.20/0.31 = { by axiom 2 (bg_2_4_3_1) }
% 0.20/0.31 tuple(ifeq(ifeq(true, true, a_vector_space(w), true), true, basis_of(b(w), w), true), true)
% 0.20/0.31 = { by axiom 3 (ifeq_axiom) }
% 0.20/0.31 tuple(ifeq(a_vector_space(w), true, basis_of(b(w), w), true), true)
% 0.20/0.31 = { by axiom 5 (bg_remark_63_a) }
% 0.20/0.31 tuple(true, true)
% 0.20/0.31 % SZS output end Proof
% 0.20/0.31
% 0.20/0.31 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------