%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : MGT036+3 : TPTP v9.3.1. Released v2.0.0.
% 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 12:01:47 PM UTC 2026
% Result : Theorem 0.15s 0.45s
% Output : Proof 0.15s
% 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 : MGT036+3 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 17:23:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.45 Command-line arguments: --flatten-regeneralise
% 0.15/0.45
% 0.15/0.45 % SZS status Theorem
% 0.15/0.45
% 0.15/0.46 % SZS output start Proof
% 0.15/0.46 Axiom 1 (a13_star): environment(e) = true.
% 0.15/0.46 Axiom 2 (a13_star_2): greater_or_equal(growth_rate(first_movers, t), zero) = true.
% 0.15/0.46 Axiom 3 (a13_star_3): greater(zero, growth_rate(efficient_producers, t)) = true.
% 0.15/0.46 Axiom 4 (a13_star_1): subpopulations(first_movers, efficient_producers, e, t) = true.
% 0.15/0.46 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.15/0.46 Axiom 6 (mp_symmetry_of_subpopulations): ifeq(subpopulations(X, Y, Z, W), true, ifeq(environment(Z), true, subpopulations(Y, X, Z, W), true), true) = true.
% 0.15/0.46 Axiom 7 (d2): ifeq(greater(zero, growth_rate(X, Y)), true, ifeq(greater_or_equal(growth_rate(Z, Y), zero), true, ifeq(subpopulations(X, Z, W, Y), true, ifeq(environment(W), true, outcompetes(Z, X, Y), true), true), true), true) = true.
% 0.15/0.46
% 0.15/0.46 Goal 1 (prove_t5_star): tuple(environment(X), subpopulations(first_movers, efficient_producers, X, Y), outcompetes(first_movers, efficient_producers, Y)) = tuple(true, true, true).
% 0.15/0.46 The goal is true when:
% 0.15/0.46 X = e
% 0.15/0.46 Y = t
% 0.15/0.46
% 0.15/0.46 Proof:
% 0.15/0.46 tuple(environment(e), subpopulations(first_movers, efficient_producers, e, t), outcompetes(first_movers, efficient_producers, t))
% 0.15/0.46 = { by axiom 4 (a13_star_1) }
% 0.15/0.46 tuple(environment(e), true, outcompetes(first_movers, efficient_producers, t))
% 0.15/0.46 = { by axiom 1 (a13_star) }
% 0.15/0.46 tuple(true, true, outcompetes(first_movers, efficient_producers, t))
% 0.15/0.46 = { by axiom 5 (ifeq_axiom) R->L }
% 0.15/0.46 tuple(true, true, ifeq(true, true, outcompetes(first_movers, efficient_producers, t), true))
% 0.15/0.46 = { by axiom 1 (a13_star) R->L }
% 0.15/0.46 tuple(true, true, ifeq(environment(e), true, outcompetes(first_movers, efficient_producers, t), true))
% 0.15/0.46 = { by axiom 5 (ifeq_axiom) R->L }
% 0.15/0.46 tuple(true, true, ifeq(true, true, ifeq(environment(e), true, outcompetes(first_movers, efficient_producers, t), true), true))
% 0.15/0.46 = { by axiom 5 (ifeq_axiom) R->L }
% 0.15/0.46 tuple(true, true, ifeq(true, true, ifeq(true, true, ifeq(environment(e), true, outcompetes(first_movers, efficient_producers, t), true), true), true))
% 0.15/0.46 = { by axiom 2 (a13_star_2) R->L }
% 0.15/0.46 tuple(true, true, ifeq(greater_or_equal(growth_rate(first_movers, t), zero), true, ifeq(true, true, ifeq(environment(e), true, outcompetes(first_movers, efficient_producers, t), true), true), true))
% 0.15/0.46 = { by axiom 5 (ifeq_axiom) R->L }
% 0.15/0.46 tuple(true, true, ifeq(true, true, ifeq(greater_or_equal(growth_rate(first_movers, t), zero), true, ifeq(true, true, ifeq(environment(e), true, outcompetes(first_movers, efficient_producers, t), true), true), true), true))
% 0.15/0.46 = { by axiom 3 (a13_star_3) R->L }
% 0.15/0.46 tuple(true, true, ifeq(greater(zero, growth_rate(efficient_producers, t)), true, ifeq(greater_or_equal(growth_rate(first_movers, t), zero), true, ifeq(true, true, ifeq(environment(e), true, outcompetes(first_movers, efficient_producers, t), true), true), true), true))
% 0.15/0.46 = { by axiom 6 (mp_symmetry_of_subpopulations) R->L }
% 0.15/0.46 tuple(true, true, ifeq(greater(zero, growth_rate(efficient_producers, t)), true, ifeq(greater_or_equal(growth_rate(first_movers, t), zero), true, ifeq(ifeq(subpopulations(first_movers, efficient_producers, e, t), true, ifeq(environment(e), true, subpopulations(efficient_producers, first_movers, e, t), true), true), true, ifeq(environment(e), true, outcompetes(first_movers, efficient_producers, t), true), true), true), true))
% 0.15/0.46 = { by axiom 4 (a13_star_1) }
% 0.15/0.46 tuple(true, true, ifeq(greater(zero, growth_rate(efficient_producers, t)), true, ifeq(greater_or_equal(growth_rate(first_movers, t), zero), true, ifeq(ifeq(true, true, ifeq(environment(e), true, subpopulations(efficient_producers, first_movers, e, t), true), true), true, ifeq(environment(e), true, outcompetes(first_movers, efficient_producers, t), true), true), true), true))
% 0.15/0.46 = { by axiom 5 (ifeq_axiom) }
% 0.15/0.46 tuple(true, true, ifeq(greater(zero, growth_rate(efficient_producers, t)), true, ifeq(greater_or_equal(growth_rate(first_movers, t), zero), true, ifeq(ifeq(environment(e), true, subpopulations(efficient_producers, first_movers, e, t), true), true, ifeq(environment(e), true, outcompetes(first_movers, efficient_producers, t), true), true), true), true))
% 0.15/0.46 = { by axiom 1 (a13_star) }
% 0.15/0.46 tuple(true, true, ifeq(greater(zero, growth_rate(efficient_producers, t)), true, ifeq(greater_or_equal(growth_rate(first_movers, t), zero), true, ifeq(ifeq(true, true, subpopulations(efficient_producers, first_movers, e, t), true), true, ifeq(environment(e), true, outcompetes(first_movers, efficient_producers, t), true), true), true), true))
% 0.15/0.46 = { by axiom 5 (ifeq_axiom) }
% 0.15/0.46 tuple(true, true, ifeq(greater(zero, growth_rate(efficient_producers, t)), true, ifeq(greater_or_equal(growth_rate(first_movers, t), zero), true, ifeq(subpopulations(efficient_producers, first_movers, e, t), true, ifeq(environment(e), true, outcompetes(first_movers, efficient_producers, t), true), true), true), true))
% 0.15/0.46 = { by axiom 7 (d2) }
% 0.15/0.46 tuple(true, true, true)
% 0.15/0.46 % SZS output end Proof
% 0.15/0.46
% 0.15/0.46 RESULT: Theorem (the conjecture is true).
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