%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 02:33:40 PM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Proof 0.07s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n011.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 18:48:45 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.26 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.07/0.26
% 0.07/0.26 % SZS status Theorem
% 0.07/0.26
% 0.07/0.26 % SZS output start Proof
% 0.07/0.26 Axiom 1 (kelley_5_19a): a_locally_compact_top_space(the_product_top_space_over(x1, a1)) = true.
% 0.07/0.26 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.07/0.26 Axiom 3 (kelley_p90a): a_continuous_function_from_onto(the_projection_function(X, Y, Z), the_product_top_space_over(Y, Z), apply(Y, X)) = true.
% 0.07/0.26 Axiom 4 (kelley_3_2): an_open_function_from_onto(the_projection_function(X, Y, Z), the_product_top_space_over(W, Z), apply(W, X)) = true.
% 0.07/0.26 Axiom 5 (kelley_p_147e): ifeq(a_locally_compact_top_space(X), true, ifeq(an_open_function_from_onto(Y, X, Z), true, ifeq(a_continuous_function_from_onto(Y, X, Z), true, a_locally_compact_top_space(Z), true), true), true) = true.
% 0.07/0.26
% 0.07/0.26 Goal 1 (kelley_5_19a_1): a_locally_compact_top_space(apply(x1, a)) = true.
% 0.07/0.26 Proof:
% 0.07/0.26 a_locally_compact_top_space(apply(x1, a))
% 0.07/0.26 = { by axiom 2 (ifeq_axiom) R->L }
% 0.07/0.26 ifeq(true, true, a_locally_compact_top_space(apply(x1, a)), true)
% 0.07/0.26 = { by axiom 1 (kelley_5_19a) R->L }
% 0.07/0.26 ifeq(a_locally_compact_top_space(the_product_top_space_over(x1, a1)), true, a_locally_compact_top_space(apply(x1, a)), true)
% 0.07/0.26 = { by axiom 2 (ifeq_axiom) R->L }
% 0.07/0.26 ifeq(a_locally_compact_top_space(the_product_top_space_over(x1, a1)), true, ifeq(true, true, a_locally_compact_top_space(apply(x1, a)), true), true)
% 0.07/0.26 = { by axiom 2 (ifeq_axiom) R->L }
% 0.07/0.26 ifeq(a_locally_compact_top_space(the_product_top_space_over(x1, a1)), true, ifeq(true, true, ifeq(true, true, a_locally_compact_top_space(apply(x1, a)), true), true), true)
% 0.07/0.26 = { by axiom 4 (kelley_3_2) R->L }
% 0.07/0.26 ifeq(a_locally_compact_top_space(the_product_top_space_over(x1, a1)), true, ifeq(an_open_function_from_onto(the_projection_function(a, x1, a1), the_product_top_space_over(x1, a1), apply(x1, a)), true, ifeq(true, true, a_locally_compact_top_space(apply(x1, a)), true), true), true)
% 0.07/0.26 = { by axiom 3 (kelley_p90a) R->L }
% 0.07/0.27 ifeq(a_locally_compact_top_space(the_product_top_space_over(x1, a1)), true, ifeq(an_open_function_from_onto(the_projection_function(a, x1, a1), the_product_top_space_over(x1, a1), apply(x1, a)), true, ifeq(a_continuous_function_from_onto(the_projection_function(a, x1, a1), the_product_top_space_over(x1, a1), apply(x1, a)), true, a_locally_compact_top_space(apply(x1, a)), true), true), true)
% 0.07/0.27 = { by axiom 5 (kelley_p_147e) }
% 0.07/0.27 true
% 0.07/0.27 % SZS output end Proof
% 0.07/0.27
% 0.07/0.27 RESULT: Theorem (the conjecture is true).
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