%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 12:45:46 PM UTC 2026
% Result : Theorem 0.08s 0.47s
% Output : Proof 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 28 04:42:03 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.47 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 0.08/0.47
% 0.08/0.47 % SZS status Theorem
% 0.08/0.47
% 0.08/0.48 % SZS output start Proof
% 0.08/0.48 Axiom 1 (t51_tops_1_1): top_str(a) = true.
% 0.08/0.48 Axiom 2 (t51_tops_1): topological_space(a) = true.
% 0.08/0.48 Axiom 3 (t51_tops_1_2): element(b, powerset(the_carrier(a))) = true.
% 0.08/0.48 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.08/0.48 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.08/0.48 Axiom 6 (dt_k3_subset_1): ifeq(element(X, powerset(Y)), true, element(subset_complement(Y, X), powerset(Y)), true) = true.
% 0.08/0.48 Axiom 7 (dt_k6_pre_topc): ifeq(element(X, powerset(the_carrier(Y))), true, ifeq(top_str(Y), true, element(topstr_closure(Y, X), powerset(the_carrier(Y))), true), true) = true.
% 0.08/0.48 Axiom 8 (fc2_tops_1): ifeq(element(X, powerset(the_carrier(Y))), true, ifeq(top_str(Y), true, ifeq(topological_space(Y), true, closed_subset(topstr_closure(Y, X), Y), true), true), true) = true.
% 0.08/0.48 Axiom 9 (d1_tops_1): ifeq2(element(X, powerset(the_carrier(Y))), true, ifeq2(top_str(Y), true, subset_complement(the_carrier(Y), topstr_closure(Y, subset_complement(the_carrier(Y), X))), interior(Y, X)), interior(Y, X)) = interior(Y, X).
% 0.08/0.48 Axiom 10 (fc3_tops_1): ifeq(element(X, powerset(the_carrier(Y))), true, ifeq(closed_subset(X, Y), true, ifeq(top_str(Y), true, ifeq(topological_space(Y), true, open_subset(subset_complement(the_carrier(Y), X), Y), true), true), true), true) = true.
% 0.08/0.48
% 0.08/0.48 Goal 1 (t51_tops_1_3): open_subset(interior(a, b), a) = true.
% 0.08/0.48 Proof:
% 0.08/0.48 open_subset(interior(a, b), a)
% 0.08/0.48 = { by axiom 9 (d1_tops_1) R->L }
% 0.08/0.48 open_subset(ifeq2(element(b, powerset(the_carrier(a))), true, ifeq2(top_str(a), true, subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), interior(a, b)), interior(a, b)), a)
% 0.08/0.48 = { by axiom 3 (t51_tops_1_2) }
% 0.08/0.48 open_subset(ifeq2(true, true, ifeq2(top_str(a), true, subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), interior(a, b)), interior(a, b)), a)
% 0.08/0.48 = { by axiom 5 (ifeq_axiom) }
% 0.08/0.48 open_subset(ifeq2(top_str(a), true, subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), interior(a, b)), a)
% 0.08/0.48 = { by axiom 1 (t51_tops_1_1) }
% 0.08/0.48 open_subset(ifeq2(true, true, subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), interior(a, b)), a)
% 0.08/0.48 = { by axiom 5 (ifeq_axiom) }
% 0.08/0.48 open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a)
% 0.08/0.48 = { by axiom 4 (ifeq_axiom) R->L }
% 0.08/0.48 ifeq(true, true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true)
% 0.08/0.48 = { by axiom 2 (t51_tops_1) R->L }
% 0.08/0.48 ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true)
% 0.08/0.48 = { by axiom 4 (ifeq_axiom) R->L }
% 0.08/0.48 ifeq(true, true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true)
% 0.08/0.48 = { by axiom 1 (t51_tops_1_1) R->L }
% 0.08/0.48 ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true)
% 0.08/0.48 = { by axiom 4 (ifeq_axiom) R->L }
% 0.08/0.48 ifeq(true, true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true)
% 0.08/0.48 = { by axiom 8 (fc2_tops_1) R->L }
% 0.08/0.48 ifeq(ifeq(element(subset_complement(the_carrier(a), b), powerset(the_carrier(a))), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true), true), true), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true)
% 0.08/0.48 = { by axiom 4 (ifeq_axiom) R->L }
% 0.08/0.48 ifeq(ifeq(ifeq(true, true, element(subset_complement(the_carrier(a), b), powerset(the_carrier(a))), true), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true), true), true), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true)
% 0.08/0.48 = { by axiom 3 (t51_tops_1_2) R->L }
% 0.08/0.48 ifeq(ifeq(ifeq(element(b, powerset(the_carrier(a))), true, element(subset_complement(the_carrier(a), b), powerset(the_carrier(a))), true), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true), true), true), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true)
% 0.08/0.48 = { by axiom 6 (dt_k3_subset_1) }
% 0.08/0.48 ifeq(ifeq(true, true, ifeq(top_str(a), true, ifeq(topological_space(a), true, closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true), true), true), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true)
% 0.08/0.48 = { by axiom 4 (ifeq_axiom) }
% 0.08/0.48 ifeq(ifeq(top_str(a), true, ifeq(topological_space(a), true, closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true), true), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true)
% 0.08/0.48 = { by axiom 1 (t51_tops_1_1) }
% 0.08/0.48 ifeq(ifeq(true, true, ifeq(topological_space(a), true, closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true), true), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true)
% 0.08/0.48 = { by axiom 4 (ifeq_axiom) }
% 0.08/0.48 ifeq(ifeq(topological_space(a), true, closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true)
% 0.08/0.48 = { by axiom 2 (t51_tops_1) }
% 0.08/0.48 ifeq(ifeq(true, true, closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true)
% 0.08/0.48 = { by axiom 4 (ifeq_axiom) }
% 0.08/0.48 ifeq(closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true)
% 0.08/0.48 = { by axiom 4 (ifeq_axiom) R->L }
% 0.08/0.48 ifeq(true, true, ifeq(closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true), true)
% 0.08/0.48 = { by axiom 7 (dt_k6_pre_topc) R->L }
% 0.08/0.48 ifeq(ifeq(element(subset_complement(the_carrier(a), b), powerset(the_carrier(a))), true, ifeq(top_str(a), true, element(topstr_closure(a, subset_complement(the_carrier(a), b)), powerset(the_carrier(a))), true), true), true, ifeq(closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true), true)
% 0.08/0.48 = { by axiom 4 (ifeq_axiom) R->L }
% 0.08/0.48 ifeq(ifeq(ifeq(true, true, element(subset_complement(the_carrier(a), b), powerset(the_carrier(a))), true), true, ifeq(top_str(a), true, element(topstr_closure(a, subset_complement(the_carrier(a), b)), powerset(the_carrier(a))), true), true), true, ifeq(closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true), true)
% 0.08/0.48 = { by axiom 3 (t51_tops_1_2) R->L }
% 0.08/0.48 ifeq(ifeq(ifeq(element(b, powerset(the_carrier(a))), true, element(subset_complement(the_carrier(a), b), powerset(the_carrier(a))), true), true, ifeq(top_str(a), true, element(topstr_closure(a, subset_complement(the_carrier(a), b)), powerset(the_carrier(a))), true), true), true, ifeq(closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true), true)
% 0.08/0.48 = { by axiom 6 (dt_k3_subset_1) }
% 0.08/0.48 ifeq(ifeq(true, true, ifeq(top_str(a), true, element(topstr_closure(a, subset_complement(the_carrier(a), b)), powerset(the_carrier(a))), true), true), true, ifeq(closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true), true)
% 0.08/0.48 = { by axiom 4 (ifeq_axiom) }
% 0.08/0.48 ifeq(ifeq(top_str(a), true, element(topstr_closure(a, subset_complement(the_carrier(a), b)), powerset(the_carrier(a))), true), true, ifeq(closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true), true)
% 0.08/0.48 = { by axiom 1 (t51_tops_1_1) }
% 0.08/0.48 ifeq(ifeq(true, true, element(topstr_closure(a, subset_complement(the_carrier(a), b)), powerset(the_carrier(a))), true), true, ifeq(closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true), true)
% 0.08/0.48 = { by axiom 4 (ifeq_axiom) }
% 0.08/0.48 ifeq(element(topstr_closure(a, subset_complement(the_carrier(a), b)), powerset(the_carrier(a))), true, ifeq(closed_subset(topstr_closure(a, subset_complement(the_carrier(a), b)), a), true, ifeq(top_str(a), true, ifeq(topological_space(a), true, open_subset(subset_complement(the_carrier(a), topstr_closure(a, subset_complement(the_carrier(a), b))), a), true), true), true), true)
% 0.08/0.48 = { by axiom 10 (fc3_tops_1) }
% 0.08/0.48 true
% 0.08/0.48 % SZS output end Proof
% 0.08/0.48
% 0.08/0.48 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------