TSTP Solution File: MGT036-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : MGT036-3 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 09:17:08 EDT 2023
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT036-3 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.34 % Computer : n013.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon Aug 28 06:19:32 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.40 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
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% 0.19/0.40 % SZS status Unsatisfiable
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% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 Take the following subset of the input axioms:
% 0.19/0.40 fof(a13_star_5, hypothesis, environment(sk1)).
% 0.19/0.40 fof(a13_star_6, hypothesis, subpopulations(first_movers, efficient_producers, sk1, sk2)).
% 0.19/0.40 fof(a13_star_7, hypothesis, greater_or_equal(growth_rate(first_movers, sk2), zero)).
% 0.19/0.40 fof(a13_star_8, hypothesis, greater(zero, growth_rate(efficient_producers, sk2))).
% 0.19/0.40 fof(d2_2, hypothesis, ![B, C, D, A2]: (~environment(A2) | (~subpopulations(B, C, A2, D) | (~greater_or_equal(growth_rate(C, D), zero) | (~greater(zero, growth_rate(B, D)) | outcompetes(C, B, D)))))).
% 0.19/0.40 fof(mp_symmetry_of_subpopulations_1, axiom, ![B2, C2, D2, A2_2]: (~environment(A2_2) | (~subpopulations(B2, C2, A2_2, D2) | subpopulations(C2, B2, A2_2, D2)))).
% 0.19/0.40 fof(prove_t5_star_9, negated_conjecture, ![A, B2]: (~environment(A) | (~subpopulations(first_movers, efficient_producers, A, B2) | ~outcompetes(first_movers, efficient_producers, B2)))).
% 0.19/0.40
% 0.19/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.40 fresh(y, y, x1...xn) = u
% 0.19/0.40 C => fresh(s, t, x1...xn) = v
% 0.19/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.40 variables of u and v.
% 0.19/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.40 input problem has no model of domain size 1).
% 0.19/0.40
% 0.19/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.40
% 0.19/0.40 Axiom 1 (a13_star_5): environment(sk1) = true2.
% 0.19/0.40 Axiom 2 (a13_star_6): subpopulations(first_movers, efficient_producers, sk1, sk2) = true2.
% 0.19/0.40 Axiom 3 (a13_star_7): greater_or_equal(growth_rate(first_movers, sk2), zero) = true2.
% 0.19/0.40 Axiom 4 (a13_star_8): greater(zero, growth_rate(efficient_producers, sk2)) = true2.
% 0.19/0.40 Axiom 5 (d2_2): fresh12(X, X, Y, Z, W) = true2.
% 0.19/0.40 Axiom 6 (mp_symmetry_of_subpopulations_1): fresh(X, X, Y, Z, W, V) = true2.
% 0.19/0.40 Axiom 7 (d2_2): fresh11(X, X, Y, Z, W, V) = fresh12(environment(Y), true2, Z, W, V).
% 0.19/0.40 Axiom 8 (d2_2): fresh10(X, X, Y, Z, W, V) = outcompetes(W, Z, V).
% 0.19/0.40 Axiom 9 (mp_symmetry_of_subpopulations_1): fresh2(X, X, Y, Z, W, V) = subpopulations(W, Z, Y, V).
% 0.19/0.40 Axiom 10 (d2_2): fresh9(X, X, Y, Z, W, V) = fresh10(subpopulations(Z, W, Y, V), true2, Y, Z, W, V).
% 0.19/0.40 Axiom 11 (d2_2): fresh9(greater(zero, growth_rate(X, Y)), true2, Z, X, W, Y) = fresh11(greater_or_equal(growth_rate(W, Y), zero), true2, Z, X, W, Y).
% 0.19/0.40 Axiom 12 (mp_symmetry_of_subpopulations_1): fresh2(subpopulations(X, Y, Z, W), true2, Z, X, Y, W) = fresh(environment(Z), true2, Z, X, Y, W).
% 0.19/0.40
% 0.19/0.40 Goal 1 (prove_t5_star_9): tuple(environment(X), subpopulations(first_movers, efficient_producers, X, Y), outcompetes(first_movers, efficient_producers, Y)) = tuple(true2, true2, true2).
% 0.19/0.40 The goal is true when:
% 0.19/0.40 X = sk1
% 0.19/0.40 Y = sk2
% 0.19/0.40
% 0.19/0.40 Proof:
% 0.19/0.40 tuple(environment(sk1), subpopulations(first_movers, efficient_producers, sk1, sk2), outcompetes(first_movers, efficient_producers, sk2))
% 0.19/0.40 = { by axiom 2 (a13_star_6) }
% 0.19/0.40 tuple(environment(sk1), true2, outcompetes(first_movers, efficient_producers, sk2))
% 0.19/0.40 = { by axiom 1 (a13_star_5) }
% 0.19/0.40 tuple(true2, true2, outcompetes(first_movers, efficient_producers, sk2))
% 0.19/0.40 = { by axiom 8 (d2_2) R->L }
% 0.19/0.40 tuple(true2, true2, fresh10(true2, true2, sk1, efficient_producers, first_movers, sk2))
% 0.19/0.40 = { by axiom 6 (mp_symmetry_of_subpopulations_1) R->L }
% 0.19/0.40 tuple(true2, true2, fresh10(fresh(true2, true2, sk1, first_movers, efficient_producers, sk2), true2, sk1, efficient_producers, first_movers, sk2))
% 0.19/0.41 = { by axiom 1 (a13_star_5) R->L }
% 0.19/0.41 tuple(true2, true2, fresh10(fresh(environment(sk1), true2, sk1, first_movers, efficient_producers, sk2), true2, sk1, efficient_producers, first_movers, sk2))
% 0.19/0.41 = { by axiom 12 (mp_symmetry_of_subpopulations_1) R->L }
% 0.19/0.41 tuple(true2, true2, fresh10(fresh2(subpopulations(first_movers, efficient_producers, sk1, sk2), true2, sk1, first_movers, efficient_producers, sk2), true2, sk1, efficient_producers, first_movers, sk2))
% 0.19/0.41 = { by axiom 2 (a13_star_6) }
% 0.19/0.41 tuple(true2, true2, fresh10(fresh2(true2, true2, sk1, first_movers, efficient_producers, sk2), true2, sk1, efficient_producers, first_movers, sk2))
% 0.19/0.41 = { by axiom 9 (mp_symmetry_of_subpopulations_1) }
% 0.19/0.41 tuple(true2, true2, fresh10(subpopulations(efficient_producers, first_movers, sk1, sk2), true2, sk1, efficient_producers, first_movers, sk2))
% 0.19/0.41 = { by axiom 10 (d2_2) R->L }
% 0.19/0.41 tuple(true2, true2, fresh9(true2, true2, sk1, efficient_producers, first_movers, sk2))
% 0.19/0.41 = { by axiom 4 (a13_star_8) R->L }
% 0.19/0.41 tuple(true2, true2, fresh9(greater(zero, growth_rate(efficient_producers, sk2)), true2, sk1, efficient_producers, first_movers, sk2))
% 0.19/0.41 = { by axiom 11 (d2_2) }
% 0.19/0.41 tuple(true2, true2, fresh11(greater_or_equal(growth_rate(first_movers, sk2), zero), true2, sk1, efficient_producers, first_movers, sk2))
% 0.19/0.41 = { by axiom 3 (a13_star_7) }
% 0.19/0.41 tuple(true2, true2, fresh11(true2, true2, sk1, efficient_producers, first_movers, sk2))
% 0.19/0.41 = { by axiom 7 (d2_2) }
% 0.19/0.41 tuple(true2, true2, fresh12(environment(sk1), true2, efficient_producers, first_movers, sk2))
% 0.19/0.41 = { by axiom 1 (a13_star_5) }
% 0.19/0.41 tuple(true2, true2, fresh12(true2, true2, efficient_producers, first_movers, sk2))
% 0.19/0.41 = { by axiom 5 (d2_2) }
% 0.19/0.41 tuple(true2, true2, true2)
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41
% 0.19/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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