TSTP Solution File: MGT027-1 by SPASS---3.9
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% File : SPASS---3.9
% Problem : MGT027-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 22:26:15 EDT 2022
% Result : Unsatisfiable 0.46s 0.70s
% Output : Refutation 0.54s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : MGT027-1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n028.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 09:29:17 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.46/0.70
% 0.46/0.70 SPASS V 3.9
% 0.46/0.70 SPASS beiseite: Proof found.
% 0.46/0.70 % SZS status Theorem
% 0.46/0.70 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.70 SPASS derived 641 clauses, backtracked 0 clauses, performed 4 splits and kept 477 clauses.
% 0.46/0.70 SPASS allocated 76712 KBytes.
% 0.46/0.70 SPASS spent 0:00:00.35 on the problem.
% 0.46/0.70 0:00:00.03 for the input.
% 0.46/0.70 0:00:00.00 for the FLOTTER CNF translation.
% 0.46/0.70 0:00:00.04 for inferences.
% 0.46/0.70 0:00:00.00 for the backtracking.
% 0.46/0.70 0:00:00.26 for the reduction.
% 0.46/0.70
% 0.46/0.70
% 0.46/0.70 Here is a proof with depth 4, length 59 :
% 0.46/0.70 % SZS output start Refutation
% 0.46/0.70 1[0:Inp] stable(u) environment(u) || in_environment(u,v) -> contracts_from(v,first_movers) greater(cardinality_at_time(first_movers,sk1(v,u)),zero)*l.
% 0.46/0.70 2[0:Inp] stable(u) environment(u) || in_environment(u,v) -> contracts_from(v,first_movers) greater_or_equal(sk1(v,u),v)*.
% 0.46/0.70 3[0:Inp] stable(u) environment(u) || in_environment(u,v) greater(zero,growth_rate(first_movers,sk1(v,u)))*r -> contracts_from(v,first_movers).
% 0.46/0.70 4[0:Inp] environment(u) || in_environment(u,v) greater(cardinality_at_time(efficient_producers,v),zero) greater(cardinality_at_time(first_movers,v),zero) -> subpopulations(first_movers,efficient_producers,u,v)*.
% 0.46/0.70 5[0:Inp] stable(u) environment(u) || greater(v,w)*+ in_environment(u,w)* -> in_environment(u,v)*.
% 0.46/0.70 6[0:Inp] stable(u) environment(u) || -> in_environment(u,appear(efficient_producers,u))*.
% 0.46/0.70 7[0:Inp] || greater(u,v)* greater(v,w)* -> greater(u,w)*.
% 0.46/0.70 8[0:Inp] || greater_or_equal(u,v)* -> equal(u,v) greater(u,v).
% 0.46/0.70 9[0:Inp] || greater(u,v) -> greater_or_equal(u,v)*.
% 0.46/0.70 11[0:Inp] environment(u) || in_environment(u,v) greater_or_equal(v,appear(efficient_producers,u))* -> greater(cardinality_at_time(efficient_producers,v),zero).
% 0.46/0.70 12[0:Inp] stable(u) environment(u) || -> greater(sk2(u),appear(efficient_producers,u))*r.
% 0.46/0.70 13[0:Inp] stable(u) environment(u) || greater_or_equal(v,sk2(u)) subpopulations(first_movers,efficient_producers,u,v)* -> greater(zero,growth_rate(first_movers,v)).
% 0.46/0.70 14[0:Inp] || -> environment(sk3)*.
% 0.46/0.70 15[0:Inp] || -> stable(sk3)*.
% 0.46/0.70 16[0:Inp] || contracts_from(u,first_movers)* greater(u,appear(efficient_producers,sk3))*+ -> .
% 0.46/0.70 20[0:Res:15.0,5.1] environment(sk3) || in_environment(sk3,u)* greater(v,u)* -> in_environment(sk3,v)*.
% 0.46/0.70 21[0:Res:15.0,2.1] environment(sk3) || in_environment(sk3,u) -> greater_or_equal(sk1(u,sk3),u)* contracts_from(u,first_movers).
% 0.46/0.70 22[0:Res:15.0,12.1] environment(sk3) || -> greater(sk2(sk3),appear(efficient_producers,sk3))*r.
% 0.46/0.70 23[0:Res:15.0,6.1] environment(sk3) || -> in_environment(sk3,appear(efficient_producers,sk3))*.
% 0.46/0.70 26[0:Res:14.0,3.0] stable(sk3) || in_environment(sk3,u) greater(zero,growth_rate(first_movers,sk1(u,sk3)))*r -> contracts_from(u,first_movers).
% 0.46/0.70 27[0:Res:14.0,1.0] stable(sk3) || in_environment(sk3,u) -> greater(cardinality_at_time(first_movers,sk1(u,sk3)),zero)*l contracts_from(u,first_movers).
% 0.46/0.70 33[0:MRR:23.0,14.0] || -> in_environment(sk3,appear(efficient_producers,sk3))*.
% 0.46/0.70 34[0:MRR:22.0,14.0] || -> greater(sk2(sk3),appear(efficient_producers,sk3))*r.
% 0.46/0.70 35[0:MRR:21.0,14.0] || in_environment(sk3,u) -> contracts_from(u,first_movers) greater_or_equal(sk1(u,sk3),u)*.
% 0.46/0.70 36[0:MRR:20.0,14.0] || greater(u,v)*+ in_environment(sk3,v)* -> in_environment(sk3,u)*.
% 0.46/0.70 37[0:MRR:27.0,15.0] || in_environment(sk3,u) -> contracts_from(u,first_movers) greater(cardinality_at_time(first_movers,sk1(u,sk3)),zero)*l.
% 0.46/0.70 38[0:MRR:26.0,15.0] || in_environment(sk3,u) greater(zero,growth_rate(first_movers,sk1(u,sk3)))*r -> contracts_from(u,first_movers).
% 0.46/0.70 40[0:Res:34.0,16.1] || contracts_from(sk2(sk3),first_movers)* -> .
% 0.46/0.70 45[0:Res:35.2,8.0] || in_environment(sk3,u) -> contracts_from(u,first_movers) equal(sk1(u,sk3),u) greater(sk1(u,sk3),u)*l.
% 0.46/0.70 46[0:Res:34.0,36.0] || in_environment(sk3,appear(efficient_producers,sk3))* -> in_environment(sk3,sk2(sk3)).
% 0.46/0.70 48[0:NCh:7.2,7.1,36.0,34.0] || equal(u,sk2(sk3)) in_environment(sk3,appear(efficient_producers,sk3))* -> in_environment(sk3,u)*.
% 0.46/0.70 49[0:MRR:46.0,33.0] || -> in_environment(sk3,sk2(sk3))*.
% 0.46/0.70 50[0:MRR:48.1,33.0] || equal(u,sk2(sk3)) -> in_environment(sk3,u)*.
% 0.46/0.70 63[0:Res:2.4,8.0] stable(u) environment(u) || in_environment(u,v) -> contracts_from(v,first_movers) equal(sk1(v,u),v) greater(sk1(v,u),v)*l.
% 0.46/0.70 82[0:NCh:7.2,7.1,5.2,12.2] stable(u) environment(u) stable(v) environment(v) || equal(w,sk2(v))* in_environment(u,appear(efficient_producers,v))*+ -> in_environment(u,w)*.
% 0.46/0.70 98[0:Res:9.1,11.2] environment(u) || greater(v,appear(efficient_producers,u))*+ in_environment(u,v)* -> greater(cardinality_at_time(efficient_producers,v),zero)*l.
% 0.46/0.70 144[0:Res:4.4,13.3] environment(u) stable(u) environment(u) || in_environment(u,v) greater(cardinality_at_time(efficient_producers,v),zero) greater(cardinality_at_time(first_movers,v),zero) greater_or_equal(v,sk2(u))* -> greater(zero,growth_rate(first_movers,v)).
% 0.46/0.70 146[0:Obv:144.0] stable(u) environment(u) || in_environment(u,v) greater(cardinality_at_time(efficient_producers,v),zero) greater(cardinality_at_time(first_movers,v),zero) greater_or_equal(v,sk2(u))* -> greater(zero,growth_rate(first_movers,v)).
% 0.46/0.70 199[0:Res:6.2,82.5] stable(u) environment(u) stable(u) environment(u) stable(u) environment(u) || equal(v,sk2(u)) -> in_environment(u,v)*.
% 0.46/0.70 203[0:Obv:199.3] stable(u) environment(u) || equal(v,sk2(u)) -> in_environment(u,v)*.
% 0.46/0.70 249[0:NCh:7.2,7.1,98.1,12.2] environment(u) stable(u) environment(u) || greater(v,sk2(u)) in_environment(u,v)* -> greater(cardinality_at_time(efficient_producers,v),zero)*l.
% 0.46/0.70 250[0:NCh:7.2,7.1,98.1,12.2] environment(u) stable(u) environment(u) || equal(v,sk2(u)) in_environment(u,v)* -> greater(cardinality_at_time(efficient_producers,v),zero)*l.
% 0.46/0.70 259[0:Obv:250.0] stable(u) environment(u) || equal(v,sk2(u)) in_environment(u,v)* -> greater(cardinality_at_time(efficient_producers,v),zero)*l.
% 0.46/0.70 260[0:MRR:259.3,203.3] stable(u) environment(u) || equal(v,sk2(u))*+ -> greater(cardinality_at_time(efficient_producers,v),zero)*l.
% 0.46/0.70 261[0:Obv:249.0] stable(u) environment(u) || greater(v,sk2(u))+ in_environment(u,v)* -> greater(cardinality_at_time(efficient_producers,v),zero)*l.
% 0.46/0.70 275[0:Res:63.5,36.0] stable(u) environment(u) || in_environment(u,v) in_environment(sk3,v) -> contracts_from(v,first_movers) equal(sk1(v,u),v) in_environment(sk3,sk1(v,u))*.
% 0.46/0.70 495[0:Res:35.2,146.5] stable(u) environment(u) || in_environment(sk3,sk2(u)) in_environment(u,sk1(sk2(u),sk3))* greater(cardinality_at_time(efficient_producers,sk1(sk2(u),sk3)),zero) greater(cardinality_at_time(first_movers,sk1(sk2(u),sk3)),zero) -> contracts_from(sk2(u),first_movers) greater(zero,growth_rate(first_movers,sk1(sk2(u),sk3)))*r.
% 0.46/0.70 499[0:MRR:495.5,495.7,37.2,38.1] stable(u) environment(u) || in_environment(sk3,sk2(u)) in_environment(u,sk1(sk2(u),sk3))* greater(cardinality_at_time(efficient_producers,sk1(sk2(u),sk3)),zero)*l -> contracts_from(sk2(u),first_movers).
% 0.46/0.70 810[0:Res:45.3,261.2] stable(u) environment(u) || in_environment(sk3,sk2(u)) in_environment(u,sk1(sk2(u),sk3))* -> contracts_from(sk2(u),first_movers) equal(sk1(sk2(u),sk3),sk2(u)) greater(cardinality_at_time(efficient_producers,sk1(sk2(u),sk3)),zero)*l.
% 0.46/0.70 834[0:MRR:810.5,260.2] stable(u) environment(u) || in_environment(sk3,sk2(u)) in_environment(u,sk1(sk2(u),sk3))* -> contracts_from(sk2(u),first_movers) greater(cardinality_at_time(efficient_producers,sk1(sk2(u),sk3)),zero)*l.
% 0.46/0.70 835[0:MRR:834.5,499.4] stable(u) environment(u) || in_environment(sk3,sk2(u)) in_environment(u,sk1(sk2(u),sk3))* -> contracts_from(sk2(u),first_movers).
% 0.46/0.70 839[0:Res:50.1,835.3] stable(sk3) environment(sk3) || equal(sk1(sk2(sk3),sk3),sk2(sk3))** in_environment(sk3,sk2(sk3)) -> contracts_from(sk2(sk3),first_movers).
% 0.46/0.70 841[0:Res:275.6,835.3] stable(sk3) environment(sk3) stable(sk3) environment(sk3) || in_environment(sk3,sk2(sk3)) in_environment(sk3,sk2(sk3)) in_environment(sk3,sk2(sk3)) -> contracts_from(sk2(sk3),first_movers) equal(sk1(sk2(sk3),sk3),sk2(sk3))** contracts_from(sk2(sk3),first_movers).
% 0.46/0.70 844[0:SSi:839.1,839.0,15.0,14.0,15.0,14.0] || equal(sk1(sk2(sk3),sk3),sk2(sk3))** in_environment(sk3,sk2(sk3)) -> contracts_from(sk2(sk3),first_movers).
% 0.46/0.70 845[0:MRR:844.1,844.2,49.0,40.0] || equal(sk1(sk2(sk3),sk3),sk2(sk3))** -> .
% 0.46/0.70 856[0:Obv:841.7] stable(sk3) environment(sk3) || in_environment(sk3,sk2(sk3)) -> equal(sk1(sk2(sk3),sk3),sk2(sk3))** contracts_from(sk2(sk3),first_movers).
% 0.54/0.71 857[0:SSi:856.1,856.0,15.0,14.0,15.0,14.0] || in_environment(sk3,sk2(sk3)) -> equal(sk1(sk2(sk3),sk3),sk2(sk3))** contracts_from(sk2(sk3),first_movers).
% 0.54/0.71 858[0:MRR:857.0,857.2,49.0,40.0] || -> equal(sk1(sk2(sk3),sk3),sk2(sk3))**.
% 0.54/0.71 859[0:MRR:858.0,845.0] || -> .
% 0.54/0.71 % SZS output end Refutation
% 0.54/0.71 Formulae used in the proof : mp_contracts_from_24 mp_contracts_from_25 mp_contracts_from_26 mp_non_empty_fm_and_ep_27 mp_long_stable_environments_28 mp_EP_in_stable_environments_29 mp_greater_transitivity_30 mp_greater_or_equal_31 mp_greater_or_equal_32 t6_34 l10_35 l10_36 prove_l9_37 prove_l9_38 prove_l9_39
% 0.54/0.71
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