TSTP Solution File: MGT022-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT022-2 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 : Sun Sep 18 05:21:54 EDT 2022
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT022-2 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n010.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 02:33:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(constant_type, type, (
% 0.21/0.39 constant: $i > $o)).
% 0.21/0.39 tff(resources_type, type, (
% 0.21/0.39 resources: ( $i * $i ) > $i)).
% 0.21/0.39 tff(sk2_type, type, (
% 0.21/0.39 sk2: $i)).
% 0.21/0.39 tff(sk1_type, type, (
% 0.21/0.39 sk1: $i)).
% 0.21/0.39 tff(increases_type, type, (
% 0.21/0.39 increases: $i > $o)).
% 0.21/0.39 tff(difference_type, type, (
% 0.21/0.39 difference: ( $i * $i ) > $i)).
% 0.21/0.39 tff(disbanding_rate_type, type, (
% 0.21/0.39 disbanding_rate: ( $i * $i ) > $i)).
% 0.21/0.39 tff(efficient_producers_type, type, (
% 0.21/0.39 efficient_producers: $i)).
% 0.21/0.39 tff(first_movers_type, type, (
% 0.21/0.39 first_movers: $i)).
% 0.21/0.39 tff(decreases_type, type, (
% 0.21/0.39 decreases: $i > $o)).
% 0.21/0.39 tff(subpopulations_type, type, (
% 0.21/0.39 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.21/0.39 tff(environment_type, type, (
% 0.21/0.39 environment: $i > $o)).
% 0.21/0.39 tff(greater_type, type, (
% 0.21/0.39 greater: ( $i * $i ) > $o)).
% 0.21/0.39 tff(resilience_type, type, (
% 0.21/0.39 resilience: $i > $i)).
% 0.21/0.39 tff(1,assumption,(~decreases(resources(sk1, sk2))), introduced(assumption)).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 ((decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))) <=> (decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(3,axiom,(decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l4_7')).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[4, 2])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (decreases(resources(sk1, sk2)) | constant(resources(sk1, sk2))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (constant(resources(sk1, sk2))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[11, 1])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (subpopulations(first_movers, efficient_producers, sk1, sk2) <=> subpopulations(first_movers, efficient_producers, sk1, sk2)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(14,axiom,(subpopulations(first_movers, efficient_producers, sk1, sk2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l4_6')).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (subpopulations(first_movers, efficient_producers, sk1, sk2)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (environment(sk1) <=> environment(sk1)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(17,axiom,(environment(sk1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l4_5')).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (environment(sk1)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (greater(resilience(efficient_producers), resilience(first_movers)) <=> greater(resilience(efficient_producers), resilience(first_movers))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(20,axiom,(greater(resilience(efficient_producers), resilience(first_movers))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a2_4')).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (greater(resilience(efficient_producers), resilience(first_movers))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (^[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)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (![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))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (![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))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (^[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))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (![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))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.39 tff(27,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/sandbox2/benchmark/theBenchmark.p','a6_3')).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 (![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))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (![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))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.21/0.39 tff(30,plain,(
% 0.21/0.39 ![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))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[29])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 (![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))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (((~![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))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 ((~![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))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 ((~![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)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 (constant(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~constant(resources(sk1, sk2)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[34, 31, 21, 18, 15])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (constant(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[35, 12])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 ((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))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(38,axiom,(decreases(resources(sk1, sk2)) | decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l4_8')).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (decreases(resources(sk1, sk2)) | decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[39, 1])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (^[A: $i] : refl(((~constant(A)) | (~decreases(A))) <=> ((~constant(A)) | (~decreases(A))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (![A: $i] : ((~constant(A)) | (~decreases(A))) <=> ![A: $i] : ((~constant(A)) | (~decreases(A)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (![A: $i] : ((~constant(A)) | (~decreases(A))) <=> ![A: $i] : ((~constant(A)) | (~decreases(A)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(44,axiom,(![A: $i] : ((~constant(A)) | (~decreases(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_constant_not_decrease_1')).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 (![A: $i] : ((~constant(A)) | (~decreases(A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.39 tff(46,plain,(
% 0.21/0.39 ![A: $i] : ((~constant(A)) | (~decreases(A)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[45])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 (![A: $i] : ((~constant(A)) | (~decreases(A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 (((~![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)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 ((~![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)))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 ((~![A: $i] : ((~constant(A)) | (~decreases(A)))) | (~constant(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.39 tff(51,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[50, 47, 40, 36])).
% 0.21/0.39 tff(52,plain,(decreases(resources(sk1, sk2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(53,plain,
% 0.21/0.39 (^[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))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(54,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.39 tff(55,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(56,plain,
% 0.21/0.39 (^[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)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(57,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.39 tff(58,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/sandbox2/benchmark/theBenchmark.p','a6_2')).
% 0.21/0.39 tff(59,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.39 tff(60,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.21/0.39 tff(61,plain,(
% 0.21/0.39 ![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)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[60])).
% 0.21/0.39 tff(62,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.21/0.39 tff(63,plain,
% 0.21/0.39 (((~![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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 ((~![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)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 ((~![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))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 (increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~decreases(resources(sk1, sk2)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[65, 62, 21, 18, 15])).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[66, 52])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 ((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)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 (((~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)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(70,axiom,((~increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) | constant(resources(sk1, sk2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l4_9')).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 (constant(resources(sk1, sk2)) | (~increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 (constant(resources(sk1, sk2)) | (~increases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[71, 68])).
% 0.21/0.40 tff(73,plain,
% 0.21/0.40 (constant(resources(sk1, sk2))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[72, 67])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 (((~![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))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 ((~![A: $i] : ((~constant(A)) | (~decreases(A)))) | ((~constant(resources(sk1, sk2))) | (~decreases(resources(sk1, sk2))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 ((~![A: $i] : ((~constant(A)) | (~decreases(A)))) | (~constant(resources(sk1, sk2))) | (~decreases(resources(sk1, sk2)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[76, 47, 52, 73])).
% 0.21/0.40 % SZS output end Proof
%------------------------------------------------------------------------------