TSTP Solution File: MGT036-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : MGT036-2 : 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 : n027.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 09:17:07 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
% 0.12/0.12 % Problem : MGT036-2 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 06:38:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.40 Command-line arguments: --ground-connectedness --complete-subsets
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% 0.19/0.40 % SZS status Unsatisfiable
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% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 Take the following subset of the input axioms:
% 0.19/0.41 fof(a13_11, hypothesis, ![B, C, D, A2]: (~environment(A2) | (~in_environment(A2, B) | (greater(zero, growth_rate(C, B)) | (~greater(resilience(D), resilience(C)) | ~greater(zero, growth_rate(D, B))))))).
% 0.19/0.41 fof(a2_10, hypothesis, greater(resilience(efficient_producers), resilience(first_movers))).
% 0.19/0.41 fof(d2_8, hypothesis, ![B2, A2_2, C2, D2]: (~environment(A2_2) | (~subpopulations(B2, C2, A2_2, D2) | (~outcompetes(C2, B2, D2) | greater_or_equal(growth_rate(C2, D2), zero))))).
% 0.19/0.41 fof(d2_9, hypothesis, ![B2, A2_2, C2, D2]: (~environment(A2_2) | (~subpopulations(B2, C2, A2_2, D2) | (~outcompetes(C2, B2, D2) | greater(zero, growth_rate(B2, D2)))))).
% 0.19/0.41 fof(mp_growth_rate_relationships_3, axiom, ![B2, A2_2, C2]: (environment(A2_2) | ~greater(zero, growth_rate(B2, C2)))).
% 0.19/0.41 fof(mp_growth_rate_relationships_4, axiom, ![B2, A2_2, C2, D2]: (subpopulations(A2_2, B2, C2, D2) | ~greater(zero, growth_rate(A2_2, D2)))).
% 0.19/0.41 fof(mp_growth_rate_relationships_5, axiom, ![A, B2]: (~greater_or_equal(growth_rate(A, B2), zero) | ~greater(zero, growth_rate(A, B2)))).
% 0.19/0.41 fof(mp_symmetry_of_subpopulations_1, axiom, ![B2, A2_2, C2, D2]: (~environment(A2_2) | (~subpopulations(B2, C2, A2_2, D2) | subpopulations(C2, B2, A2_2, D2)))).
% 0.19/0.41 fof(mp_time_point_occur_2, axiom, ![B2, A2_2]: (~environment(A2_2) | (~subpopulations(first_movers, efficient_producers, A2_2, B2) | in_environment(A2_2, B2)))).
% 0.19/0.41 fof(prove_t5_12, negated_conjecture, environment(sk1)).
% 0.19/0.41 fof(prove_t5_13, negated_conjecture, subpopulations(first_movers, efficient_producers, sk1, sk2)).
% 0.19/0.41 fof(prove_t5_14, negated_conjecture, outcompetes(first_movers, efficient_producers, sk2)).
% 0.19/0.41
% 0.19/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.41 fresh(y, y, x1...xn) = u
% 0.19/0.41 C => fresh(s, t, x1...xn) = v
% 0.19/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.41 variables of u and v.
% 0.19/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.41 input problem has no model of domain size 1).
% 0.19/0.41
% 0.19/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.41
% 0.19/0.41 Axiom 1 (prove_t5_12): environment(sk1) = true2.
% 0.19/0.41 Axiom 2 (mp_growth_rate_relationships_3): fresh6(X, X, Y) = true2.
% 0.19/0.41 Axiom 3 (prove_t5_14): outcompetes(first_movers, efficient_producers, sk2) = true2.
% 0.19/0.41 Axiom 4 (mp_time_point_occur_2): fresh(X, X, Y, Z) = true2.
% 0.19/0.41 Axiom 5 (d2_8): fresh16(X, X, Y, Z) = true2.
% 0.19/0.41 Axiom 6 (d2_9): fresh14(X, X, Y, Z) = true2.
% 0.19/0.41 Axiom 7 (a13_11): fresh12(X, X, Y, Z) = true2.
% 0.19/0.41 Axiom 8 (mp_time_point_occur_2): fresh2(X, X, Y, Z) = in_environment(Y, Z).
% 0.19/0.41 Axiom 9 (prove_t5_13): subpopulations(first_movers, efficient_producers, sk1, sk2) = true2.
% 0.19/0.41 Axiom 10 (a2_10): greater(resilience(efficient_producers), resilience(first_movers)) = true2.
% 0.19/0.41 Axiom 11 (a13_11): fresh11(X, X, Y, Z, W) = fresh12(environment(Y), true2, Z, W).
% 0.19/0.41 Axiom 12 (a13_11): fresh10(X, X, Y, Z, W) = greater(zero, growth_rate(W, Z)).
% 0.19/0.41 Axiom 13 (d2_8): fresh8(X, X, Y, Z, W) = greater_or_equal(growth_rate(Z, W), zero).
% 0.19/0.41 Axiom 14 (d2_9): fresh7(X, X, Y, Z, W) = greater(zero, growth_rate(Z, W)).
% 0.19/0.41 Axiom 15 (d2_8): fresh15(X, X, Y, Z, W, V) = fresh16(environment(Y), true2, W, V).
% 0.19/0.41 Axiom 16 (d2_9): fresh13(X, X, Y, Z, W, V) = fresh14(environment(Y), true2, Z, V).
% 0.19/0.41 Axiom 17 (mp_growth_rate_relationships_4): fresh5(X, X, Y, Z, W, V) = true2.
% 0.19/0.41 Axiom 18 (mp_symmetry_of_subpopulations_1): fresh4(X, X, Y, Z, W, V) = subpopulations(W, Z, Y, V).
% 0.19/0.41 Axiom 19 (mp_symmetry_of_subpopulations_1): fresh3(X, X, Y, Z, W, V) = true2.
% 0.19/0.41 Axiom 20 (a13_11): fresh9(X, X, Y, Z, W, V) = fresh10(in_environment(Y, Z), true2, Y, Z, W).
% 0.19/0.41 Axiom 21 (mp_growth_rate_relationships_3): fresh6(greater(zero, growth_rate(X, Y)), true2, Z) = environment(Z).
% 0.19/0.41 Axiom 22 (mp_time_point_occur_2): fresh2(subpopulations(first_movers, efficient_producers, X, Y), true2, X, Y) = fresh(environment(X), true2, X, Y).
% 0.19/0.41 Axiom 23 (d2_8): fresh15(outcompetes(X, Y, Z), true2, W, Y, X, Z) = fresh8(subpopulations(Y, X, W, Z), true2, W, X, Z).
% 0.19/0.41 Axiom 24 (d2_9): fresh13(outcompetes(X, Y, Z), true2, W, Y, X, Z) = fresh7(subpopulations(Y, X, W, Z), true2, W, Y, Z).
% 0.19/0.41 Axiom 25 (a13_11): fresh9(greater(resilience(X), resilience(Y)), true2, Z, W, Y, X) = fresh11(greater(zero, growth_rate(X, W)), true2, Z, W, Y).
% 0.19/0.41 Axiom 26 (mp_growth_rate_relationships_4): fresh5(greater(zero, growth_rate(X, Y)), true2, X, Z, W, Y) = subpopulations(X, Z, W, Y).
% 0.19/0.41 Axiom 27 (mp_symmetry_of_subpopulations_1): fresh4(subpopulations(X, Y, Z, W), true2, Z, X, Y, W) = fresh3(environment(Z), true2, Z, X, Y, W).
% 0.19/0.41
% 0.19/0.41 Lemma 28: subpopulations(efficient_producers, first_movers, sk1, sk2) = true2.
% 0.19/0.41 Proof:
% 0.19/0.41 subpopulations(efficient_producers, first_movers, sk1, sk2)
% 0.19/0.41 = { by axiom 18 (mp_symmetry_of_subpopulations_1) R->L }
% 0.19/0.41 fresh4(true2, true2, sk1, first_movers, efficient_producers, sk2)
% 0.19/0.41 = { by axiom 9 (prove_t5_13) R->L }
% 0.19/0.41 fresh4(subpopulations(first_movers, efficient_producers, sk1, sk2), true2, sk1, first_movers, efficient_producers, sk2)
% 0.19/0.41 = { by axiom 27 (mp_symmetry_of_subpopulations_1) }
% 0.19/0.41 fresh3(environment(sk1), true2, sk1, first_movers, efficient_producers, sk2)
% 0.19/0.41 = { by axiom 1 (prove_t5_12) }
% 0.19/0.41 fresh3(true2, true2, sk1, first_movers, efficient_producers, sk2)
% 0.19/0.41 = { by axiom 19 (mp_symmetry_of_subpopulations_1) }
% 0.19/0.41 true2
% 0.19/0.41
% 0.19/0.41 Lemma 29: greater(zero, growth_rate(efficient_producers, sk2)) = true2.
% 0.19/0.41 Proof:
% 0.19/0.41 greater(zero, growth_rate(efficient_producers, sk2))
% 0.19/0.41 = { by axiom 14 (d2_9) R->L }
% 0.19/0.41 fresh7(true2, true2, sk1, efficient_producers, sk2)
% 0.19/0.41 = { by lemma 28 R->L }
% 0.19/0.41 fresh7(subpopulations(efficient_producers, first_movers, sk1, sk2), true2, sk1, efficient_producers, sk2)
% 0.19/0.41 = { by axiom 24 (d2_9) R->L }
% 0.19/0.41 fresh13(outcompetes(first_movers, efficient_producers, sk2), true2, sk1, efficient_producers, first_movers, sk2)
% 0.19/0.41 = { by axiom 3 (prove_t5_14) }
% 0.19/0.41 fresh13(true2, true2, sk1, efficient_producers, first_movers, sk2)
% 0.19/0.41 = { by axiom 16 (d2_9) }
% 0.19/0.41 fresh14(environment(sk1), true2, efficient_producers, sk2)
% 0.19/0.41 = { by axiom 1 (prove_t5_12) }
% 0.19/0.41 fresh14(true2, true2, efficient_producers, sk2)
% 0.19/0.41 = { by axiom 6 (d2_9) }
% 0.19/0.41 true2
% 0.19/0.41
% 0.19/0.41 Lemma 30: environment(X) = true2.
% 0.19/0.41 Proof:
% 0.19/0.41 environment(X)
% 0.19/0.41 = { by axiom 21 (mp_growth_rate_relationships_3) R->L }
% 0.19/0.41 fresh6(greater(zero, growth_rate(efficient_producers, sk2)), true2, X)
% 0.19/0.41 = { by lemma 29 }
% 0.19/0.41 fresh6(true2, true2, X)
% 0.19/0.41 = { by axiom 2 (mp_growth_rate_relationships_3) }
% 0.19/0.41 true2
% 0.19/0.41
% 0.19/0.41 Goal 1 (mp_growth_rate_relationships_5): tuple(greater(zero, growth_rate(X, Y)), greater_or_equal(growth_rate(X, Y), zero)) = tuple(true2, true2).
% 0.19/0.41 The goal is true when:
% 0.19/0.41 X = first_movers
% 0.19/0.41 Y = sk2
% 0.19/0.41
% 0.19/0.41 Proof:
% 0.19/0.41 tuple(greater(zero, growth_rate(first_movers, sk2)), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.41 = { by axiom 12 (a13_11) R->L }
% 0.19/0.41 tuple(fresh10(true2, true2, X, sk2, first_movers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.41 = { by axiom 4 (mp_time_point_occur_2) R->L }
% 0.19/0.41 tuple(fresh10(fresh(true2, true2, X, sk2), true2, X, sk2, first_movers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.41 = { by lemma 30 R->L }
% 0.19/0.41 tuple(fresh10(fresh(environment(X), true2, X, sk2), true2, X, sk2, first_movers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.41 = { by axiom 22 (mp_time_point_occur_2) R->L }
% 0.19/0.41 tuple(fresh10(fresh2(subpopulations(first_movers, efficient_producers, X, sk2), true2, X, sk2), true2, X, sk2, first_movers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.41 = { by axiom 18 (mp_symmetry_of_subpopulations_1) R->L }
% 0.19/0.41 tuple(fresh10(fresh2(fresh4(true2, true2, X, efficient_producers, first_movers, sk2), true2, X, sk2), true2, X, sk2, first_movers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.41 = { by axiom 17 (mp_growth_rate_relationships_4) R->L }
% 0.19/0.41 tuple(fresh10(fresh2(fresh4(fresh5(true2, true2, efficient_producers, first_movers, X, sk2), true2, X, efficient_producers, first_movers, sk2), true2, X, sk2), true2, X, sk2, first_movers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.42 = { by lemma 29 R->L }
% 0.19/0.42 tuple(fresh10(fresh2(fresh4(fresh5(greater(zero, growth_rate(efficient_producers, sk2)), true2, efficient_producers, first_movers, X, sk2), true2, X, efficient_producers, first_movers, sk2), true2, X, sk2), true2, X, sk2, first_movers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.42 = { by axiom 26 (mp_growth_rate_relationships_4) }
% 0.19/0.42 tuple(fresh10(fresh2(fresh4(subpopulations(efficient_producers, first_movers, X, sk2), true2, X, efficient_producers, first_movers, sk2), true2, X, sk2), true2, X, sk2, first_movers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.42 = { by axiom 27 (mp_symmetry_of_subpopulations_1) }
% 0.19/0.42 tuple(fresh10(fresh2(fresh3(environment(X), true2, X, efficient_producers, first_movers, sk2), true2, X, sk2), true2, X, sk2, first_movers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.42 = { by lemma 30 }
% 0.19/0.42 tuple(fresh10(fresh2(fresh3(true2, true2, X, efficient_producers, first_movers, sk2), true2, X, sk2), true2, X, sk2, first_movers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.42 = { by axiom 19 (mp_symmetry_of_subpopulations_1) }
% 0.19/0.42 tuple(fresh10(fresh2(true2, true2, X, sk2), true2, X, sk2, first_movers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.42 = { by axiom 8 (mp_time_point_occur_2) }
% 0.19/0.42 tuple(fresh10(in_environment(X, sk2), true2, X, sk2, first_movers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.42 = { by axiom 20 (a13_11) R->L }
% 0.19/0.42 tuple(fresh9(true2, true2, X, sk2, first_movers, efficient_producers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.42 = { by axiom 10 (a2_10) R->L }
% 0.19/0.42 tuple(fresh9(greater(resilience(efficient_producers), resilience(first_movers)), true2, X, sk2, first_movers, efficient_producers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.42 = { by axiom 25 (a13_11) }
% 0.19/0.42 tuple(fresh11(greater(zero, growth_rate(efficient_producers, sk2)), true2, X, sk2, first_movers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.42 = { by lemma 29 }
% 0.19/0.42 tuple(fresh11(true2, true2, X, sk2, first_movers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.42 = { by axiom 11 (a13_11) }
% 0.19/0.42 tuple(fresh12(environment(X), true2, sk2, first_movers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.42 = { by lemma 30 }
% 0.19/0.42 tuple(fresh12(true2, true2, sk2, first_movers), greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.42 = { by axiom 7 (a13_11) }
% 0.19/0.42 tuple(true2, greater_or_equal(growth_rate(first_movers, sk2), zero))
% 0.19/0.42 = { by axiom 13 (d2_8) R->L }
% 0.19/0.42 tuple(true2, fresh8(true2, true2, sk1, first_movers, sk2))
% 0.19/0.42 = { by lemma 28 R->L }
% 0.19/0.42 tuple(true2, fresh8(subpopulations(efficient_producers, first_movers, sk1, sk2), true2, sk1, first_movers, sk2))
% 0.19/0.42 = { by axiom 23 (d2_8) R->L }
% 0.19/0.42 tuple(true2, fresh15(outcompetes(first_movers, efficient_producers, sk2), true2, sk1, efficient_producers, first_movers, sk2))
% 0.19/0.42 = { by axiom 3 (prove_t5_14) }
% 0.19/0.42 tuple(true2, fresh15(true2, true2, sk1, efficient_producers, first_movers, sk2))
% 0.19/0.42 = { by axiom 15 (d2_8) }
% 0.19/0.42 tuple(true2, fresh16(environment(sk1), true2, first_movers, sk2))
% 0.19/0.42 = { by axiom 1 (prove_t5_12) }
% 0.19/0.42 tuple(true2, fresh16(true2, true2, first_movers, sk2))
% 0.19/0.42 = { by axiom 5 (d2_8) }
% 0.19/0.42 tuple(true2, true2)
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42
% 0.19/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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