%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : MGT032+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 12:01:46 PM UTC 2026
% Result : Theorem 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT032+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.39 % Computer : n010.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 17:21:31 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 Command-line arguments: --flatten --complete-subsets
% 0.19/0.47
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 Axiom 1 (prove_t1): environment(e) = true.
% 0.19/0.48 Axiom 2 (prove_t1_1): stable(e) = true.
% 0.19/0.48 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.19/0.48 Axiom 4 (prove_t1_4): ifeq(in_environment(e, X), true, greater_or_equal(t(X), X), true) = true.
% 0.19/0.48 Axiom 5 (prove_t1_3): ifeq(in_environment(e, X), true, subpopulations(first_movers, efficient_producers, e, t(X)), true) = true.
% 0.19/0.48 Axiom 6 (l1_1): ifeq(stable(X), true, ifeq(environment(X), true, in_environment(X, to(X)), true), true) = true.
% 0.19/0.48 Axiom 7 (mp1_high_growth_rates): ifeq(greater(growth_rate(X, Y), growth_rate(Z, Y)), true, ifeq(subpopulations(Z, X, W, Y), true, ifeq(environment(W), true, selection_favors(X, Z, Y), true), true), true) = true.
% 0.19/0.48 Axiom 8 (l1): ifeq(greater_or_equal(X, to(Y)), true, ifeq(stable(Y), true, ifeq(subpopulations(first_movers, efficient_producers, Y, X), true, ifeq(environment(Y), true, greater(growth_rate(efficient_producers, X), growth_rate(first_movers, X)), true), true), true), true) = true.
% 0.19/0.48
% 0.19/0.48 Lemma 9: stable(e) = environment(e).
% 0.19/0.48 Proof:
% 0.19/0.48 stable(e)
% 0.19/0.48 = { by axiom 2 (prove_t1_1) }
% 0.19/0.48 true
% 0.19/0.48 = { by axiom 1 (prove_t1) R->L }
% 0.19/0.48 environment(e)
% 0.19/0.48
% 0.19/0.48 Lemma 10: in_environment(e, to(e)) = environment(e).
% 0.19/0.48 Proof:
% 0.19/0.48 in_environment(e, to(e))
% 0.19/0.48 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.48 ifeq(environment(e), environment(e), in_environment(e, to(e)), environment(e))
% 0.19/0.48 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.48 ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), in_environment(e, to(e)), environment(e)), environment(e))
% 0.19/0.48 = { by lemma 9 R->L }
% 0.19/0.48 ifeq(stable(e), environment(e), ifeq(environment(e), environment(e), in_environment(e, to(e)), environment(e)), environment(e))
% 0.19/0.48 = { by axiom 1 (prove_t1) }
% 0.19/0.48 ifeq(stable(e), true, ifeq(environment(e), environment(e), in_environment(e, to(e)), environment(e)), environment(e))
% 0.19/0.48 = { by axiom 1 (prove_t1) }
% 0.19/0.48 ifeq(stable(e), true, ifeq(environment(e), true, in_environment(e, to(e)), environment(e)), environment(e))
% 0.19/0.48 = { by axiom 1 (prove_t1) }
% 0.19/0.48 ifeq(stable(e), true, ifeq(environment(e), true, in_environment(e, to(e)), true), environment(e))
% 0.19/0.48 = { by axiom 1 (prove_t1) }
% 0.19/0.48 ifeq(stable(e), true, ifeq(environment(e), true, in_environment(e, to(e)), true), true)
% 0.19/0.48 = { by axiom 6 (l1_1) }
% 0.19/0.48 true
% 0.19/0.48 = { by axiom 1 (prove_t1) R->L }
% 0.19/0.48 environment(e)
% 0.19/0.48
% 0.19/0.48 Lemma 11: subpopulations(first_movers, efficient_producers, e, t(to(e))) = environment(e).
% 0.19/0.48 Proof:
% 0.19/0.48 subpopulations(first_movers, efficient_producers, e, t(to(e)))
% 0.19/0.48 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.48 ifeq(environment(e), environment(e), subpopulations(first_movers, efficient_producers, e, t(to(e))), environment(e))
% 0.19/0.48 = { by lemma 10 R->L }
% 0.19/0.48 ifeq(in_environment(e, to(e)), environment(e), subpopulations(first_movers, efficient_producers, e, t(to(e))), environment(e))
% 0.19/0.48 = { by axiom 1 (prove_t1) }
% 0.19/0.48 ifeq(in_environment(e, to(e)), true, subpopulations(first_movers, efficient_producers, e, t(to(e))), environment(e))
% 0.19/0.48 = { by axiom 1 (prove_t1) }
% 0.19/0.48 ifeq(in_environment(e, to(e)), true, subpopulations(first_movers, efficient_producers, e, t(to(e))), true)
% 0.19/0.48 = { by axiom 5 (prove_t1_3) }
% 0.19/0.48 true
% 0.19/0.48 = { by axiom 1 (prove_t1) R->L }
% 0.19/0.48 environment(e)
% 0.19/0.48
% 0.19/0.48 Goal 1 (prove_t1_2): tuple(selection_favors(efficient_producers, first_movers, t(X)), in_environment(e, X)) = tuple(true, true).
% 0.19/0.48 The goal is true when:
% 0.19/0.48 X = to(e)
% 0.19/0.48
% 0.19/0.48 Proof:
% 0.19/0.48 tuple(selection_favors(efficient_producers, first_movers, t(to(e))), in_environment(e, to(e)))
% 0.19/0.48 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.48 tuple(ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), in_environment(e, to(e)))
% 0.19/0.48 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.48 tuple(ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.48 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.48 tuple(ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.48 = { by axiom 1 (prove_t1) }
% 0.19/0.48 tuple(ifeq(true, environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.48 = { by axiom 8 (l1) R->L }
% 0.19/0.48 tuple(ifeq(ifeq(greater_or_equal(t(to(e)), to(e)), true, ifeq(stable(e), true, ifeq(subpopulations(first_movers, efficient_producers, e, t(to(e))), true, ifeq(environment(e), true, greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), true), true), true), true), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.48 = { by axiom 1 (prove_t1) R->L }
% 0.19/0.49 tuple(ifeq(ifeq(greater_or_equal(t(to(e)), to(e)), true, ifeq(stable(e), true, ifeq(subpopulations(first_movers, efficient_producers, e, t(to(e))), true, ifeq(environment(e), true, greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), true), true), true), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.49 = { by axiom 1 (prove_t1) R->L }
% 0.19/0.49 tuple(ifeq(ifeq(greater_or_equal(t(to(e)), to(e)), true, ifeq(stable(e), true, ifeq(subpopulations(first_movers, efficient_producers, e, t(to(e))), true, ifeq(environment(e), true, greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), true), true), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.49 = { by axiom 1 (prove_t1) R->L }
% 0.19/0.49 tuple(ifeq(ifeq(greater_or_equal(t(to(e)), to(e)), true, ifeq(stable(e), true, ifeq(subpopulations(first_movers, efficient_producers, e, t(to(e))), true, ifeq(environment(e), true, greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), true), environment(e)), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.49 = { by axiom 1 (prove_t1) R->L }
% 0.19/0.49 tuple(ifeq(ifeq(greater_or_equal(t(to(e)), to(e)), true, ifeq(stable(e), true, ifeq(subpopulations(first_movers, efficient_producers, e, t(to(e))), true, ifeq(environment(e), true, greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e)), environment(e)), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.49 = { by axiom 1 (prove_t1) R->L }
% 0.19/0.49 tuple(ifeq(ifeq(greater_or_equal(t(to(e)), to(e)), true, ifeq(stable(e), true, ifeq(subpopulations(first_movers, efficient_producers, e, t(to(e))), true, ifeq(environment(e), environment(e), greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e)), environment(e)), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.49 = { by axiom 1 (prove_t1) R->L }
% 0.19/0.49 tuple(ifeq(ifeq(greater_or_equal(t(to(e)), to(e)), true, ifeq(stable(e), true, ifeq(subpopulations(first_movers, efficient_producers, e, t(to(e))), environment(e), ifeq(environment(e), environment(e), greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e)), environment(e)), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.49 = { by axiom 1 (prove_t1) R->L }
% 0.19/0.49 tuple(ifeq(ifeq(greater_or_equal(t(to(e)), to(e)), true, ifeq(stable(e), environment(e), ifeq(subpopulations(first_movers, efficient_producers, e, t(to(e))), environment(e), ifeq(environment(e), environment(e), greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e)), environment(e)), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.49 = { by axiom 1 (prove_t1) R->L }
% 0.19/0.49 tuple(ifeq(ifeq(greater_or_equal(t(to(e)), to(e)), environment(e), ifeq(stable(e), environment(e), ifeq(subpopulations(first_movers, efficient_producers, e, t(to(e))), environment(e), ifeq(environment(e), environment(e), greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e)), environment(e)), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.49 = { by lemma 11 }
% 0.19/0.49 tuple(ifeq(ifeq(greater_or_equal(t(to(e)), to(e)), environment(e), ifeq(stable(e), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e)), environment(e)), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 tuple(ifeq(ifeq(ifeq(environment(e), environment(e), greater_or_equal(t(to(e)), to(e)), environment(e)), environment(e), ifeq(stable(e), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e)), environment(e)), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.49 = { by lemma 10 R->L }
% 0.19/0.49 tuple(ifeq(ifeq(ifeq(in_environment(e, to(e)), environment(e), greater_or_equal(t(to(e)), to(e)), environment(e)), environment(e), ifeq(stable(e), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e)), environment(e)), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.49 = { by axiom 1 (prove_t1) }
% 0.19/0.49 tuple(ifeq(ifeq(ifeq(in_environment(e, to(e)), true, greater_or_equal(t(to(e)), to(e)), environment(e)), environment(e), ifeq(stable(e), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e)), environment(e)), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.49 = { by axiom 1 (prove_t1) }
% 0.19/0.50 tuple(ifeq(ifeq(ifeq(in_environment(e, to(e)), true, greater_or_equal(t(to(e)), to(e)), true), environment(e), ifeq(stable(e), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e)), environment(e)), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.50 = { by axiom 4 (prove_t1_4) }
% 0.19/0.50 tuple(ifeq(ifeq(true, environment(e), ifeq(stable(e), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e)), environment(e)), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.50 = { by axiom 1 (prove_t1) R->L }
% 0.19/0.50 tuple(ifeq(ifeq(environment(e), environment(e), ifeq(stable(e), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e)), environment(e)), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.50 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.50 tuple(ifeq(ifeq(stable(e), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e)), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.50 = { by lemma 9 }
% 0.19/0.50 tuple(ifeq(ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e)), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.50 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.50 tuple(ifeq(ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e)), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.50 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.50 tuple(ifeq(ifeq(environment(e), environment(e), greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e)), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.50 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.50 tuple(ifeq(greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e), ifeq(environment(e), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.50 = { by lemma 11 R->L }
% 0.19/0.50 tuple(ifeq(greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), environment(e), ifeq(subpopulations(first_movers, efficient_producers, e, t(to(e))), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.50 = { by axiom 1 (prove_t1) }
% 0.19/0.50 tuple(ifeq(greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), true, ifeq(subpopulations(first_movers, efficient_producers, e, t(to(e))), environment(e), ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.50 = { by axiom 1 (prove_t1) }
% 0.19/0.50 tuple(ifeq(greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), true, ifeq(subpopulations(first_movers, efficient_producers, e, t(to(e))), true, ifeq(environment(e), environment(e), selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.50 = { by axiom 1 (prove_t1) }
% 0.19/0.50 tuple(ifeq(greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), true, ifeq(subpopulations(first_movers, efficient_producers, e, t(to(e))), true, ifeq(environment(e), true, selection_favors(efficient_producers, first_movers, t(to(e))), environment(e)), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.50 = { by axiom 1 (prove_t1) }
% 0.19/0.50 tuple(ifeq(greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), true, ifeq(subpopulations(first_movers, efficient_producers, e, t(to(e))), true, ifeq(environment(e), true, selection_favors(efficient_producers, first_movers, t(to(e))), true), environment(e)), environment(e)), in_environment(e, to(e)))
% 0.19/0.50 = { by axiom 1 (prove_t1) }
% 0.19/0.50 tuple(ifeq(greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), true, ifeq(subpopulations(first_movers, efficient_producers, e, t(to(e))), true, ifeq(environment(e), true, selection_favors(efficient_producers, first_movers, t(to(e))), true), true), environment(e)), in_environment(e, to(e)))
% 0.19/0.50 = { by axiom 1 (prove_t1) }
% 0.19/0.50 tuple(ifeq(greater(growth_rate(efficient_producers, t(to(e))), growth_rate(first_movers, t(to(e)))), true, ifeq(subpopulations(first_movers, efficient_producers, e, t(to(e))), true, ifeq(environment(e), true, selection_favors(efficient_producers, first_movers, t(to(e))), true), true), true), in_environment(e, to(e)))
% 0.19/0.50 = { by axiom 7 (mp1_high_growth_rates) }
% 0.19/0.50 tuple(true, in_environment(e, to(e)))
% 0.19/0.50 = { by axiom 1 (prove_t1) R->L }
% 0.19/0.50 tuple(environment(e), in_environment(e, to(e)))
% 0.19/0.50 = { by lemma 10 }
% 0.19/0.50 tuple(environment(e), environment(e))
% 0.19/0.50 = { by axiom 1 (prove_t1) }
% 0.19/0.50 tuple(true, environment(e))
% 0.19/0.50 = { by axiom 1 (prove_t1) }
% 0.19/0.50 tuple(true, true)
% 0.19/0.50 % SZS output end Proof
% 0.19/0.50
% 0.19/0.50 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------