%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT022-2 : TPTP v9.3.0. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n009.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 8 06:23:59 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.43s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT022-2 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 7 12:06:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.43 % SZS status Unsatisfiable
% 0.10/0.43 % SZS output start Proof
% 0.10/0.43 tff(constant_type, type, (
% 0.10/0.43 constant: $i > $o)).
% 0.10/0.43 tff(resources_type, type, (
% 0.10/0.43 resources: ( $i * $i ) > $i)).
% 0.10/0.43 tff(sk2_type, type, (
% 0.10/0.43 sk2: $i)).
% 0.10/0.43 tff(sk1_type, type, (
% 0.10/0.43 sk1: $i)).
% 0.10/0.43 tff(increases_type, type, (
% 0.10/0.43 increases: $i > $o)).
% 0.10/0.43 tff(difference_type, type, (
% 0.10/0.43 difference: ( $i * $i ) > $i)).
% 0.10/0.43 tff(disbanding_rate_type, type, (
% 0.10/0.43 disbanding_rate: ( $i * $i ) > $i)).
% 0.10/0.43 tff(efficient_producers_type, type, (
% 0.10/0.43 efficient_producers: $i)).
% 0.10/0.43 tff(first_movers_type, type, (
% 0.10/0.43 first_movers: $i)).
% 0.10/0.43 tff(decreases_type, type, (
% 0.10/0.43 decreases: $i > $o)).
% 0.10/0.43 tff(subpopulations_type, type, (
% 0.10/0.43 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.10/0.43 tff(environment_type, type, (
% 0.10/0.43 environment: $i > $o)).
% 0.10/0.43 tff(greater_type, type, (
% 0.10/0.43 greater: ( $i * $i ) > $o)).
% 0.10/0.43 tff(resilience_type, type, (
% 0.10/0.43 resilience: $i > $i)).
% 0.10/0.43 tff(1,assumption,(~decreases(resources(sk1, sk2))), introduced(assumption)).
% 0.10/0.43 tff(2,plain,
% 0.10/0.43 ((decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))) <=> (decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2)))),
% 0.10/0.43 inference(rewrite,[status(thm)],[])).
% 0.10/0.43 tff(3,axiom,(decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l4_7')).
% 0.10/0.43 tff(4,plain,
% 0.10/0.43 (decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.10/0.43 tff(5,plain,
% 0.10/0.43 (decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[4, 2])).
% 0.10/0.43 tff(6,plain,
% 0.10/0.43 (decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.10/0.43 tff(7,plain,
% 0.10/0.43 (decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.10/0.43 tff(8,plain,
% 0.10/0.43 (decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.10/0.43 tff(9,plain,
% 0.10/0.43 (constant(resources(sk1, sk2))),
% 0.10/0.43 inference(unit_resolution,[status(thm)],[8, 1])).
% 0.10/0.43 tff(10,plain,
% 0.10/0.43 (subpopulations(first_movers, efficient_producers, sk1, sk2) <=> subpopulations(first_movers, efficient_producers, sk1, sk2)),
% 0.10/0.43 inference(rewrite,[status(thm)],[])).
% 0.10/0.43 tff(11,axiom,(subpopulations(first_movers, efficient_producers, sk1, sk2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l4_6')).
% 0.10/0.43 tff(12,plain,
% 0.10/0.43 (subpopulations(first_movers, efficient_producers, sk1, sk2)),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.10/0.43 tff(13,plain,
% 0.10/0.43 (environment(sk1) <=> environment(sk1)),
% 0.10/0.43 inference(rewrite,[status(thm)],[])).
% 0.10/0.43 tff(14,axiom,(environment(sk1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l4_5')).
% 0.10/0.43 tff(15,plain,
% 0.10/0.43 (environment(sk1)),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.10/0.43 tff(16,plain,
% 0.10/0.43 (greater(resilience(efficient_producers), resilience(first_movers)) <=> greater(resilience(efficient_producers), resilience(first_movers))),
% 0.10/0.43 inference(rewrite,[status(thm)],[])).
% 0.10/0.43 tff(17,axiom,(greater(resilience(efficient_producers), resilience(first_movers))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a2_4')).
% 0.10/0.43 tff(18,plain,
% 0.10/0.43 (greater(resilience(efficient_producers), resilience(first_movers))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.10/0.43 tff(19,plain,
% 0.10/0.43 (^[B: $i, D: $i, A: $i, C: $i] : refl(((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D)))) <=> ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D)))))),
% 0.10/0.43 inference(bind,[status(th)],[])).
% 0.10/0.43 tff(20,plain,
% 0.10/0.43 (![B: $i, D: $i, A: $i, C: $i] : ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D)))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D))))),
% 0.10/0.43 inference(quant_intro,[status(thm)],[19])).
% 0.10/0.43 tff(21,plain,
% 0.10/0.43 (![B: $i, D: $i, A: $i, C: $i] : ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D)))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D))))),
% 0.10/0.43 inference(rewrite,[status(thm)],[])).
% 0.10/0.43 tff(22,plain,
% 0.10/0.43 (^[B: $i, D: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(resilience(C), resilience(B)))) <=> ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)))), (((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(resilience(C), resilience(B)))) | (~constant(resources(A, D)))) <=> (((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A))) | (~constant(resources(A, D)))))), rewrite((((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A))) | (~constant(resources(A, D)))) <=> ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | (~constant(resources(A, D))))), (((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(resilience(C), resilience(B)))) | (~constant(resources(A, D)))) <=> ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | (~constant(resources(A, D)))))), ((((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(resilience(C), resilience(B)))) | (~constant(resources(A, D)))) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D)))) <=> (((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | (~constant(resources(A, D)))) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D)))))), rewrite((((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | (~constant(resources(A, D)))) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D)))) <=> ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D))))), ((((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(resilience(C), resilience(B)))) | (~constant(resources(A, D)))) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D)))) <=> ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D))))))),
% 0.10/0.43 inference(bind,[status(th)],[])).
% 0.10/0.43 tff(23,plain,
% 0.10/0.43 (![B: $i, D: $i, A: $i, C: $i] : (((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(resilience(C), resilience(B)))) | (~constant(resources(A, D)))) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D)))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D))))),
% 0.10/0.43 inference(quant_intro,[status(thm)],[22])).
% 0.10/0.43 tff(24,axiom,(![B: $i, D: $i, A: $i, C: $i] : (((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(resilience(C), resilience(B)))) | (~constant(resources(A, D)))) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a6_3')).
% 0.10/0.43 tff(25,plain,
% 0.10/0.43 (![B: $i, D: $i, A: $i, C: $i] : ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D))))),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.10/0.44 tff(26,plain,
% 0.10/0.44 (![B: $i, D: $i, A: $i, C: $i] : ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D))))),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.10/0.44 tff(27,plain,(
% 0.10/0.44 ![B: $i, D: $i, A: $i, C: $i] : ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D))))),
% 0.10/0.44 inference(skolemize,[status(sab)],[26])).
% 0.10/0.44 tff(28,plain,
% 0.10/0.44 (![B: $i, D: $i, A: $i, C: $i] : ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D))))),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.10/0.44 tff(29,plain,
% 0.10/0.44 (((~![B: $i, D: $i, A: $i, C: $i] : ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D))))) | ((~greater(resilience(efficient_producers), resilience(first_movers))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | constant(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~constant(resources(sk1, sk2))))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D))))) | (~greater(resilience(efficient_producers), resilience(first_movers))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | constant(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~constant(resources(sk1, sk2))))),
% 0.10/0.44 inference(rewrite,[status(thm)],[])).
% 0.10/0.44 tff(30,plain,
% 0.10/0.44 ((~![B: $i, D: $i, A: $i, C: $i] : ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D))))) | ((~greater(resilience(efficient_producers), resilience(first_movers))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | constant(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~constant(resources(sk1, sk2))))),
% 0.10/0.44 inference(quant_inst,[status(thm)],[])).
% 0.10/0.44 tff(31,plain,
% 0.10/0.44 ((~![B: $i, D: $i, A: $i, C: $i] : ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)) | constant(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~constant(resources(A, D))))) | (~greater(resilience(efficient_producers), resilience(first_movers))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | constant(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~constant(resources(sk1, sk2)))),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.10/0.44 tff(32,plain,
% 0.10/0.44 (constant(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~constant(resources(sk1, sk2)))),
% 0.10/0.44 inference(unit_resolution,[status(thm)],[31, 28, 18, 15, 12])).
% 0.10/0.44 tff(33,plain,
% 0.10/0.44 (constant(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))),
% 0.10/0.44 inference(unit_resolution,[status(thm)],[32, 9])).
% 0.10/0.44 tff(34,plain,
% 0.10/0.44 ((decreases(resources(sk1, sk2)) | decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) <=> (decreases(resources(sk1, sk2)) | decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))))),
% 0.10/0.44 inference(rewrite,[status(thm)],[])).
% 0.10/0.44 tff(35,axiom,(decreases(resources(sk1, sk2)) | decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l4_8')).
% 0.10/0.44 tff(36,plain,
% 0.10/0.44 (decreases(resources(sk1, sk2)) | decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.10/0.44 tff(37,plain,
% 0.10/0.44 (decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))),
% 0.10/0.44 inference(unit_resolution,[status(thm)],[36, 1])).
% 0.10/0.44 tff(38,plain,
% 0.10/0.44 (^[A: $i] : refl(((~constant(A)) | (~decreases(A))) <=> ((~constant(A)) | (~decreases(A))))),
% 0.10/0.44 inference(bind,[status(th)],[])).
% 0.10/0.44 tff(39,plain,
% 0.10/0.44 (![A: $i] : ((~constant(A)) | (~decreases(A))) <=> ![A: $i] : ((~constant(A)) | (~decreases(A)))),
% 0.10/0.44 inference(quant_intro,[status(thm)],[38])).
% 0.10/0.44 tff(40,plain,
% 0.10/0.44 (![A: $i] : ((~constant(A)) | (~decreases(A))) <=> ![A: $i] : ((~constant(A)) | (~decreases(A)))),
% 0.10/0.44 inference(rewrite,[status(thm)],[])).
% 0.10/0.44 tff(41,axiom,(![A: $i] : ((~constant(A)) | (~decreases(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_constant_not_decrease_1')).
% 0.10/0.44 tff(42,plain,
% 0.10/0.44 (![A: $i] : ((~constant(A)) | (~decreases(A)))),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.10/0.44 tff(43,plain,(
% 0.10/0.44 ![A: $i] : ((~constant(A)) | (~decreases(A)))),
% 0.10/0.44 inference(skolemize,[status(sab)],[42])).
% 0.10/0.44 tff(44,plain,
% 0.10/0.44 (![A: $i] : ((~constant(A)) | (~decreases(A)))),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.10/0.44 tff(45,plain,
% 0.10/0.44 (((~![A: $i] : ((~constant(A)) | (~decreases(A)))) | ((~constant(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))))) <=> ((~![A: $i] : ((~constant(A)) | (~decreases(A)))) | (~constant(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))))),
% 0.10/0.44 inference(rewrite,[status(thm)],[])).
% 0.10/0.44 tff(46,plain,
% 0.10/0.44 ((~![A: $i] : ((~constant(A)) | (~decreases(A)))) | ((~constant(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))))),
% 0.10/0.44 inference(quant_inst,[status(thm)],[])).
% 0.10/0.44 tff(47,plain,
% 0.10/0.44 ((~![A: $i] : ((~constant(A)) | (~decreases(A)))) | (~constant(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))))),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.10/0.44 tff(48,plain,
% 0.10/0.44 ($false),
% 0.10/0.44 inference(unit_resolution,[status(thm)],[47, 44, 37, 33])).
% 0.10/0.44 tff(49,plain,(decreases(resources(sk1, sk2))), inference(lemma,lemma(discharge,[]))).
% 0.10/0.44 tff(50,plain,
% 0.10/0.44 (^[B: $i, D: $i, A: $i, C: $i] : refl((increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A))) <=> (increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A))))),
% 0.10/0.44 inference(bind,[status(th)],[])).
% 0.10/0.44 tff(51,plain,
% 0.10/0.44 (![B: $i, D: $i, A: $i, C: $i] : (increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A))) <=> ![B: $i, D: $i, A: $i, C: $i] : (increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.10/0.44 inference(quant_intro,[status(thm)],[50])).
% 0.10/0.44 tff(52,plain,
% 0.10/0.44 (![B: $i, D: $i, A: $i, C: $i] : (increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A))) <=> ![B: $i, D: $i, A: $i, C: $i] : (increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.10/0.44 inference(rewrite,[status(thm)],[])).
% 0.10/0.44 tff(53,plain,
% 0.10/0.44 (^[B: $i, D: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(resilience(C), resilience(B)))) <=> ((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)))), (((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(resilience(C), resilience(B)))) | (~decreases(resources(A, D)))) <=> (((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A))) | (~decreases(resources(A, D)))))), rewrite((((~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A))) | (~decreases(resources(A, D)))) <=> ((~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)))), (((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(resilience(C), resilience(B)))) | (~decreases(resources(A, D)))) <=> ((~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A))))), ((((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(resilience(C), resilience(B)))) | (~decreases(resources(A, D)))) | increases(difference(disbanding_rate(B, D), disbanding_rate(C, D)))) <=> (((~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A))) | increases(difference(disbanding_rate(B, D), disbanding_rate(C, D)))))), rewrite((((~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A))) | increases(difference(disbanding_rate(B, D), disbanding_rate(C, D)))) <=> (increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)))), ((((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(resilience(C), resilience(B)))) | (~decreases(resources(A, D)))) | increases(difference(disbanding_rate(B, D), disbanding_rate(C, D)))) <=> (increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)))))),
% 0.10/0.44 inference(bind,[status(th)],[])).
% 0.10/0.44 tff(54,plain,
% 0.10/0.44 (![B: $i, D: $i, A: $i, C: $i] : (((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(resilience(C), resilience(B)))) | (~decreases(resources(A, D)))) | increases(difference(disbanding_rate(B, D), disbanding_rate(C, D)))) <=> ![B: $i, D: $i, A: $i, C: $i] : (increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.10/0.44 inference(quant_intro,[status(thm)],[53])).
% 0.10/0.44 tff(55,axiom,(![B: $i, D: $i, A: $i, C: $i] : (((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(resilience(C), resilience(B)))) | (~decreases(resources(A, D)))) | increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a6_2')).
% 0.10/0.44 tff(56,plain,
% 0.10/0.44 (![B: $i, D: $i, A: $i, C: $i] : (increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.10/0.44 tff(57,plain,
% 0.10/0.44 (![B: $i, D: $i, A: $i, C: $i] : (increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.10/0.44 tff(58,plain,(
% 0.10/0.44 ![B: $i, D: $i, A: $i, C: $i] : (increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.10/0.44 inference(skolemize,[status(sab)],[57])).
% 0.10/0.44 tff(59,plain,
% 0.10/0.44 (![B: $i, D: $i, A: $i, C: $i] : (increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.10/0.44 tff(60,plain,
% 0.10/0.44 (((~![B: $i, D: $i, A: $i, C: $i] : (increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~decreases(resources(sk1, sk2))) | (~greater(resilience(efficient_producers), resilience(first_movers))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~decreases(resources(sk1, sk2))) | (~greater(resilience(efficient_producers), resilience(first_movers))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)))),
% 0.10/0.44 inference(rewrite,[status(thm)],[])).
% 0.10/0.44 tff(61,plain,
% 0.10/0.44 ((~![B: $i, D: $i, A: $i, C: $i] : (increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~decreases(resources(sk1, sk2))) | (~greater(resilience(efficient_producers), resilience(first_movers))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)))),
% 0.10/0.44 inference(quant_inst,[status(thm)],[])).
% 0.10/0.44 tff(62,plain,
% 0.10/0.44 ((~![B: $i, D: $i, A: $i, C: $i] : (increases(difference(disbanding_rate(B, D), disbanding_rate(C, D))) | (~decreases(resources(A, D))) | (~greater(resilience(C), resilience(B))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~decreases(resources(sk1, sk2))) | (~greater(resilience(efficient_producers), resilience(first_movers))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1))),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.10/0.44 tff(63,plain,
% 0.10/0.44 (increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~decreases(resources(sk1, sk2)))),
% 0.10/0.44 inference(unit_resolution,[status(thm)],[62, 59, 18, 15, 12])).
% 0.10/0.44 tff(64,plain,
% 0.10/0.44 (increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))),
% 0.10/0.44 inference(unit_resolution,[status(thm)],[63, 49])).
% 0.10/0.44 tff(65,plain,
% 0.10/0.44 ((constant(resources(sk1, sk2)) | (~increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))))) <=> (constant(resources(sk1, sk2)) | (~increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))))),
% 0.10/0.44 inference(rewrite,[status(thm)],[])).
% 0.10/0.44 tff(66,plain,
% 0.10/0.44 (((~increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) | constant(resources(sk1, sk2))) <=> (constant(resources(sk1, sk2)) | (~increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))))),
% 0.10/0.45 inference(rewrite,[status(thm)],[])).
% 0.10/0.45 tff(67,axiom,((~increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) | constant(resources(sk1, sk2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l4_9')).
% 0.10/0.45 tff(68,plain,
% 0.10/0.45 (constant(resources(sk1, sk2)) | (~increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))))),
% 0.10/0.45 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.10/0.45 tff(69,plain,
% 0.10/0.45 (constant(resources(sk1, sk2)) | (~increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))))),
% 0.10/0.45 inference(modus_ponens,[status(thm)],[68, 65])).
% 0.10/0.45 tff(70,plain,
% 0.10/0.45 (constant(resources(sk1, sk2))),
% 0.10/0.45 inference(unit_resolution,[status(thm)],[69, 64])).
% 0.10/0.45 tff(71,plain,
% 0.10/0.45 (((~![A: $i] : ((~constant(A)) | (~decreases(A)))) | ((~constant(resources(sk1, sk2))) | (~decreases(resources(sk1, sk2))))) <=> ((~![A: $i] : ((~constant(A)) | (~decreases(A)))) | (~constant(resources(sk1, sk2))) | (~decreases(resources(sk1, sk2))))),
% 0.10/0.45 inference(rewrite,[status(thm)],[])).
% 0.10/0.45 tff(72,plain,
% 0.10/0.45 ((~![A: $i] : ((~constant(A)) | (~decreases(A)))) | ((~constant(resources(sk1, sk2))) | (~decreases(resources(sk1, sk2))))),
% 0.10/0.45 inference(quant_inst,[status(thm)],[])).
% 0.10/0.45 tff(73,plain,
% 0.10/0.45 ((~![A: $i] : ((~constant(A)) | (~decreases(A)))) | (~constant(resources(sk1, sk2))) | (~decreases(resources(sk1, sk2)))),
% 0.10/0.45 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.10/0.45 tff(74,plain,
% 0.10/0.45 ($false),
% 0.10/0.45 inference(unit_resolution,[status(thm)],[73, 44, 49, 70])).
% 0.10/0.45 % SZS output end Proof
% 0.10/0.45 % E exiting
%------------------------------------------------------------------------------