TSTP Solution File: MGT032-2 by Moca---0.1
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% File : Moca---0.1
% Problem : MGT032-2 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n025.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 : 600s
% DateTime : Sun Jul 17 22:20:25 EDT 2022
% Result : Unsatisfiable 8.00s 8.03s
% Output : Proof 8.00s
% 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 v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jun 9 09:24:20 EDT 2022
% 0.14/0.35 % CPUTime :
% 8.00/8.03 % SZS status Unsatisfiable
% 8.00/8.03 % SZS output start Proof
% 8.00/8.03 The input problem is unsatisfiable because
% 8.00/8.03
% 8.00/8.03 [1] the following set of Horn clauses is unsatisfiable:
% 8.00/8.03
% 8.00/8.03 environment(A) & subpopulations(B, C, A, D) & greater(growth_rate(C, D), growth_rate(B, D)) ==> selection_favors(C, B, D)
% 8.00/8.03 environment(A) & stable(A) ==> in_environment(A, sk1(A))
% 8.00/8.03 environment(A) & stable(A) & subpopulations(first_movers, efficient_producers, A, B) & greater_or_equal(B, sk1(A)) ==> greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))
% 8.00/8.03 environment(sk2)
% 8.00/8.03 stable(sk2)
% 8.00/8.03 in_environment(sk2, A) ==> subpopulations(first_movers, efficient_producers, sk2, sk3(A))
% 8.00/8.03 in_environment(sk2, A) ==> greater_or_equal(sk3(A), A)
% 8.00/8.03 in_environment(sk2, A) & selection_favors(efficient_producers, first_movers, sk3(A)) ==> \bottom
% 8.00/8.03
% 8.00/8.03 This holds because
% 8.00/8.03
% 8.00/8.03 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 8.00/8.03
% 8.00/8.03 E:
% 8.00/8.03 environment(sk2) = true__
% 8.00/8.03 f1(true__, C, B, D) = selection_favors(C, B, D)
% 8.00/8.03 f10(in_environment(sk2, A), A) = true__
% 8.00/8.03 f10(true__, A) = subpopulations(first_movers, efficient_producers, sk2, sk3(A))
% 8.00/8.03 f11(in_environment(sk2, A), A) = true__
% 8.00/8.03 f11(true__, A) = greater_or_equal(sk3(A), A)
% 8.00/8.03 f12(true__) = false__
% 8.00/8.03 f13(selection_favors(efficient_producers, first_movers, sk3(A)), A) = true__
% 8.00/8.03 f13(true__, A) = f12(in_environment(sk2, A))
% 8.00/8.03 f2(true__, A, C, B, D) = f1(environment(A), C, B, D)
% 8.00/8.03 f3(greater(growth_rate(C, D), growth_rate(B, D)), B, C, A, D) = true__
% 8.00/8.03 f3(true__, B, C, A, D) = f2(subpopulations(B, C, A, D), A, C, B, D)
% 8.00/8.03 f4(true__, A) = in_environment(A, sk1(A))
% 8.00/8.03 f5(stable(A), A) = true__
% 8.00/8.03 f5(true__, A) = f4(environment(A), A)
% 8.00/8.03 f6(true__, B) = greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))
% 8.00/8.03 f7(true__, A, B) = f6(environment(A), B)
% 8.00/8.03 f8(true__, A, B) = f7(stable(A), A, B)
% 8.00/8.03 f9(greater_or_equal(B, sk1(A)), A, B) = true__
% 8.00/8.03 f9(true__, A, B) = f8(subpopulations(first_movers, efficient_producers, A, B), A, B)
% 8.00/8.03 stable(sk2) = true__
% 8.00/8.03 G:
% 8.00/8.03 true__ = false__
% 8.00/8.03
% 8.00/8.03 This holds because
% 8.00/8.03
% 8.00/8.03 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 8.00/8.03
% 8.00/8.03
% 8.00/8.03 environment(sk2) -> true__
% 8.00/8.03 f1(true__, C, B, D) -> selection_favors(C, B, D)
% 8.00/8.03 f10(in_environment(sk2, A), A) -> true__
% 8.00/8.03 f10(true__, A) -> subpopulations(first_movers, efficient_producers, sk2, sk3(A))
% 8.00/8.03 f11(in_environment(sk2, A), A) -> true__
% 8.00/8.03 f11(true__, A) -> greater_or_equal(sk3(A), A)
% 8.00/8.03 f12(true__) -> false__
% 8.00/8.03 f13(selection_favors(efficient_producers, first_movers, sk3(A)), A) -> true__
% 8.00/8.03 f13(true__, A) -> f12(in_environment(sk2, A))
% 8.00/8.03 f2(subpopulations(first_movers, efficient_producers, Y3, sk3(sk1(sk2))), Y3, efficient_producers, first_movers, sk3(sk1(sk2))) -> true__
% 8.00/8.03 f2(true__, A, C, B, D) -> f1(environment(A), C, B, D)
% 8.00/8.03 f3(greater(growth_rate(C, D), growth_rate(B, D)), B, C, A, D) -> true__
% 8.00/8.03 f3(true__, B, C, A, D) -> f2(subpopulations(B, C, A, D), A, C, B, D)
% 8.00/8.03 f4(true__, A) -> in_environment(A, sk1(A))
% 8.00/8.03 f5(stable(A), A) -> true__
% 8.00/8.03 f5(true__, A) -> f4(environment(A), A)
% 8.00/8.03 f6(true__, B) -> greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))
% 8.00/8.03 f7(true__, A, B) -> f6(environment(A), B)
% 8.00/8.03 f8(true__, A, B) -> f7(stable(A), A, B)
% 8.00/8.03 f9(greater_or_equal(B, sk1(A)), A, B) -> true__
% 8.00/8.03 f9(true__, A, B) -> f8(subpopulations(first_movers, efficient_producers, A, B), A, B)
% 8.00/8.03 false__ -> true__
% 8.00/8.03 greater(growth_rate(efficient_producers, sk3(sk1(sk2))), growth_rate(first_movers, sk3(sk1(sk2)))) -> true__
% 8.00/8.03 greater_or_equal(sk3(sk1(sk2)), sk1(sk2)) -> true__
% 8.00/8.03 in_environment(sk2, sk1(sk2)) -> true__
% 8.00/8.03 selection_favors(efficient_producers, first_movers, sk3(sk1(sk2))) -> true__
% 8.00/8.03 stable(sk2) -> true__
% 8.00/8.03 subpopulations(first_movers, efficient_producers, sk2, sk3(sk1(sk2))) -> true__
% 8.00/8.03 with the LPO induced by
% 8.00/8.03 f10 > f3 > f2 > f9 > subpopulations > f8 > f7 > f5 > f4 > f13 > sk2 > f6 > growth_rate > greater > f1 > first_movers > efficient_producers > selection_favors > f11 > sk3 > greater_or_equal > in_environment > sk1 > f12 > stable > environment > false__ > true__
% 8.00/8.03
% 8.00/8.03 % SZS output end Proof
% 8.00/8.03
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