TSTP Solution File: MGT032-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : MGT032-2 : 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 : n017.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 09:17:05 EDT 2023
% Result : Unsatisfiable 0.19s 0.39s
% 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
% 0.07/0.12 % Problem : MGT032-2 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 05:46:42 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.39 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
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% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39
% 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(l1_2, hypothesis, ![A2]: (~environment(A2) | (~stable(A2) | in_environment(A2, sk1(A2))))).
% 0.19/0.40 fof(l1_3, hypothesis, ![B, A2_2]: (~environment(A2_2) | (~stable(A2_2) | (~subpopulations(first_movers, efficient_producers, A2_2, B) | (~greater_or_equal(B, sk1(A2_2)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))))))).
% 0.19/0.40 fof(mp1_high_growth_rates_1, axiom, ![C, D, A2_2, B2]: (~environment(A2_2) | (~subpopulations(B2, C, A2_2, D) | (~greater(growth_rate(C, D), growth_rate(B2, D)) | selection_favors(C, B2, D))))).
% 0.19/0.40 fof(prove_t1_4, negated_conjecture, environment(sk2)).
% 0.19/0.40 fof(prove_t1_5, negated_conjecture, stable(sk2)).
% 0.19/0.40 fof(prove_t1_6, negated_conjecture, ![A2_2]: (~in_environment(sk2, A2_2) | subpopulations(first_movers, efficient_producers, sk2, sk3(A2_2)))).
% 0.19/0.40 fof(prove_t1_7, negated_conjecture, ![A2_2]: (~in_environment(sk2, A2_2) | greater_or_equal(sk3(A2_2), A2_2))).
% 0.19/0.40 fof(prove_t1_8, negated_conjecture, ![A]: (~in_environment(sk2, A) | ~selection_favors(efficient_producers, first_movers, sk3(A)))).
% 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 (prove_t1_4): environment(sk2) = true2.
% 0.19/0.40 Axiom 2 (prove_t1_5): stable(sk2) = true2.
% 0.19/0.40 Axiom 3 (prove_t1_7): fresh(X, X, Y) = true2.
% 0.19/0.40 Axiom 4 (l1_3): fresh9(X, X, Y) = true2.
% 0.19/0.40 Axiom 5 (l1_2): fresh5(X, X, Y) = true2.
% 0.19/0.40 Axiom 6 (l1_2): fresh4(X, X, Y) = in_environment(Y, sk1(Y)).
% 0.19/0.40 Axiom 7 (prove_t1_6): fresh2(X, X, Y) = true2.
% 0.19/0.40 Axiom 8 (l1_3): fresh8(X, X, Y, Z) = fresh9(environment(Y), true2, Z).
% 0.19/0.40 Axiom 9 (l1_2): fresh4(stable(X), true2, X) = fresh5(environment(X), true2, X).
% 0.19/0.40 Axiom 10 (prove_t1_7): fresh(in_environment(sk2, X), true2, X) = greater_or_equal(sk3(X), X).
% 0.19/0.40 Axiom 11 (mp1_high_growth_rates_1): fresh11(X, X, Y, Z, W) = true2.
% 0.19/0.40 Axiom 12 (l1_3): fresh6(X, X, Y, Z) = fresh7(stable(Y), true2, Y, Z).
% 0.19/0.40 Axiom 13 (prove_t1_6): fresh2(in_environment(sk2, X), true2, X) = subpopulations(first_movers, efficient_producers, sk2, sk3(X)).
% 0.19/0.40 Axiom 14 (l1_3): fresh7(X, X, Y, Z) = greater(growth_rate(efficient_producers, Z), growth_rate(first_movers, Z)).
% 0.19/0.40 Axiom 15 (mp1_high_growth_rates_1): fresh10(X, X, Y, Z, W, V) = fresh11(environment(Y), true2, Z, W, V).
% 0.19/0.40 Axiom 16 (mp1_high_growth_rates_1): fresh3(X, X, Y, Z, W, V) = selection_favors(W, Z, V).
% 0.19/0.40 Axiom 17 (l1_3): fresh6(greater_or_equal(X, sk1(Y)), true2, Y, X) = fresh8(subpopulations(first_movers, efficient_producers, Y, X), true2, Y, X).
% 0.19/0.40 Axiom 18 (mp1_high_growth_rates_1): fresh10(greater(growth_rate(X, Y), growth_rate(Z, Y)), true2, W, Z, X, Y) = fresh3(subpopulations(Z, X, W, Y), true2, W, Z, X, Y).
% 0.19/0.40
% 0.19/0.40 Lemma 19: in_environment(sk2, sk1(sk2)) = true2.
% 0.19/0.40 Proof:
% 0.19/0.40 in_environment(sk2, sk1(sk2))
% 0.19/0.40 = { by axiom 6 (l1_2) R->L }
% 0.19/0.40 fresh4(true2, true2, sk2)
% 0.19/0.40 = { by axiom 2 (prove_t1_5) R->L }
% 0.19/0.40 fresh4(stable(sk2), true2, sk2)
% 0.19/0.40 = { by axiom 9 (l1_2) }
% 0.19/0.40 fresh5(environment(sk2), true2, sk2)
% 0.19/0.40 = { by axiom 1 (prove_t1_4) }
% 0.19/0.40 fresh5(true2, true2, sk2)
% 0.19/0.40 = { by axiom 5 (l1_2) }
% 0.19/0.40 true2
% 0.19/0.40
% 0.19/0.40 Lemma 20: subpopulations(first_movers, efficient_producers, sk2, sk3(sk1(sk2))) = true2.
% 0.19/0.40 Proof:
% 0.19/0.40 subpopulations(first_movers, efficient_producers, sk2, sk3(sk1(sk2)))
% 0.19/0.40 = { by axiom 13 (prove_t1_6) R->L }
% 0.19/0.40 fresh2(in_environment(sk2, sk1(sk2)), true2, sk1(sk2))
% 0.19/0.40 = { by lemma 19 }
% 0.19/0.40 fresh2(true2, true2, sk1(sk2))
% 0.19/0.40 = { by axiom 7 (prove_t1_6) }
% 0.19/0.40 true2
% 0.19/0.40
% 0.19/0.40 Goal 1 (prove_t1_8): tuple(selection_favors(efficient_producers, first_movers, sk3(X)), in_environment(sk2, X)) = tuple(true2, true2).
% 0.19/0.40 The goal is true when:
% 0.19/0.40 X = sk1(sk2)
% 0.19/0.40
% 0.19/0.40 Proof:
% 0.19/0.40 tuple(selection_favors(efficient_producers, first_movers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by axiom 16 (mp1_high_growth_rates_1) R->L }
% 0.19/0.40 tuple(fresh3(true2, true2, sk2, first_movers, efficient_producers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by lemma 20 R->L }
% 0.19/0.40 tuple(fresh3(subpopulations(first_movers, efficient_producers, sk2, sk3(sk1(sk2))), true2, sk2, first_movers, efficient_producers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by axiom 18 (mp1_high_growth_rates_1) R->L }
% 0.19/0.40 tuple(fresh10(greater(growth_rate(efficient_producers, sk3(sk1(sk2))), growth_rate(first_movers, sk3(sk1(sk2)))), true2, sk2, first_movers, efficient_producers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by axiom 14 (l1_3) R->L }
% 0.19/0.40 tuple(fresh10(fresh7(true2, true2, sk2, sk3(sk1(sk2))), true2, sk2, first_movers, efficient_producers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by axiom 2 (prove_t1_5) R->L }
% 0.19/0.40 tuple(fresh10(fresh7(stable(sk2), true2, sk2, sk3(sk1(sk2))), true2, sk2, first_movers, efficient_producers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by axiom 12 (l1_3) R->L }
% 0.19/0.40 tuple(fresh10(fresh6(true2, true2, sk2, sk3(sk1(sk2))), true2, sk2, first_movers, efficient_producers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by axiom 3 (prove_t1_7) R->L }
% 0.19/0.40 tuple(fresh10(fresh6(fresh(true2, true2, sk1(sk2)), true2, sk2, sk3(sk1(sk2))), true2, sk2, first_movers, efficient_producers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by lemma 19 R->L }
% 0.19/0.40 tuple(fresh10(fresh6(fresh(in_environment(sk2, sk1(sk2)), true2, sk1(sk2)), true2, sk2, sk3(sk1(sk2))), true2, sk2, first_movers, efficient_producers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by axiom 10 (prove_t1_7) }
% 0.19/0.40 tuple(fresh10(fresh6(greater_or_equal(sk3(sk1(sk2)), sk1(sk2)), true2, sk2, sk3(sk1(sk2))), true2, sk2, first_movers, efficient_producers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by axiom 17 (l1_3) }
% 0.19/0.40 tuple(fresh10(fresh8(subpopulations(first_movers, efficient_producers, sk2, sk3(sk1(sk2))), true2, sk2, sk3(sk1(sk2))), true2, sk2, first_movers, efficient_producers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by lemma 20 }
% 0.19/0.40 tuple(fresh10(fresh8(true2, true2, sk2, sk3(sk1(sk2))), true2, sk2, first_movers, efficient_producers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by axiom 8 (l1_3) }
% 0.19/0.40 tuple(fresh10(fresh9(environment(sk2), true2, sk3(sk1(sk2))), true2, sk2, first_movers, efficient_producers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by axiom 1 (prove_t1_4) }
% 0.19/0.40 tuple(fresh10(fresh9(true2, true2, sk3(sk1(sk2))), true2, sk2, first_movers, efficient_producers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by axiom 4 (l1_3) }
% 0.19/0.40 tuple(fresh10(true2, true2, sk2, first_movers, efficient_producers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by axiom 15 (mp1_high_growth_rates_1) }
% 0.19/0.40 tuple(fresh11(environment(sk2), true2, first_movers, efficient_producers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by axiom 1 (prove_t1_4) }
% 0.19/0.40 tuple(fresh11(true2, true2, first_movers, efficient_producers, sk3(sk1(sk2))), in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by axiom 11 (mp1_high_growth_rates_1) }
% 0.19/0.40 tuple(true2, in_environment(sk2, sk1(sk2)))
% 0.19/0.40 = { by lemma 19 }
% 0.19/0.40 tuple(true2, true2)
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40
% 0.19/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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