TSTP Solution File: MGT027-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT027-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %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 22:18:57 EDT 2022
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 23
% Syntax : Number of clauses : 116 ( 20 unt; 31 nHn; 114 RR)
% Number of literals : 327 ( 36 equ; 184 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(mp_contracts_from_24,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ in_environment(A,B)
| greater(cardinality_at_time(first_movers,sk1(B,A)),zero)
| contracts_from(B,first_movers) ) ).
cnf(mp_contracts_from_25,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ in_environment(A,B)
| greater_or_equal(sk1(B,A),B)
| contracts_from(B,first_movers) ) ).
cnf(mp_contracts_from_26,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ in_environment(A,B)
| ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
| contracts_from(B,first_movers) ) ).
cnf(mp_non_empty_fm_and_ep_27,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(cardinality_at_time(first_movers,B),zero)
| ~ greater(cardinality_at_time(efficient_producers,B),zero)
| subpopulations(first_movers,efficient_producers,A,B) ) ).
cnf(mp_long_stable_environments_28,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ in_environment(A,B)
| ~ greater(C,B)
| in_environment(A,C) ) ).
cnf(mp_EP_in_stable_environments_29,axiom,
( ~ environment(A)
| ~ stable(A)
| in_environment(A,appear(efficient_producers,A)) ) ).
cnf(mp_greater_transitivity_30,axiom,
( ~ greater(A,B)
| ~ greater(B,C)
| greater(A,C) ) ).
cnf(mp_greater_or_equal_31,axiom,
( ~ greater_or_equal(A,B)
| greater(A,B)
| A = B ) ).
cnf(mp_greater_or_equal_32,axiom,
( ~ greater(A,B)
| greater_or_equal(A,B) ) ).
cnf(mp_greater_or_equal_33,axiom,
( A != B
| greater_or_equal(A,B) ) ).
cnf(t6_34,hypothesis,
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater_or_equal(B,appear(efficient_producers,A))
| greater(cardinality_at_time(efficient_producers,B),zero) ) ).
cnf(l10_35,hypothesis,
( ~ environment(A)
| ~ stable(A)
| greater(sk2(A),appear(efficient_producers,A)) ) ).
cnf(l10_36,hypothesis,
( ~ environment(A)
| ~ stable(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ greater_or_equal(B,sk2(A))
| greater(zero,growth_rate(first_movers,B)) ) ).
cnf(prove_l9_37,negated_conjecture,
environment(sk3) ).
cnf(prove_l9_38,negated_conjecture,
stable(sk3) ).
cnf(prove_l9_39,negated_conjecture,
( ~ greater(A,appear(efficient_producers,sk3))
| ~ contracts_from(A,first_movers) ) ).
cnf(refute_0_0,plain,
( ~ environment(sk3)
| ~ greater_or_equal(sk2(sk3),sk2(sk3))
| ~ stable(sk3)
| ~ subpopulations(first_movers,efficient_producers,sk3,sk2(sk3))
| greater(zero,growth_rate(first_movers,sk2(sk3))) ),
inference(subst,[],[l10_36:[bind(A,$fot(sk3)),bind(B,$fot(sk2(sk3)))]]) ).
cnf(refute_0_1,plain,
( ~ environment(sk3)
| ~ stable(sk3)
| greater(sk2(sk3),appear(efficient_producers,sk3)) ),
inference(subst,[],[l10_35:[bind(A,$fot(sk3))]]) ).
cnf(refute_0_2,plain,
( ~ environment(sk3)
| greater(sk2(sk3),appear(efficient_producers,sk3)) ),
inference(resolve,[$cnf( stable(sk3) )],[prove_l9_38,refute_0_1]) ).
cnf(refute_0_3,plain,
greater(sk2(sk3),appear(efficient_producers,sk3)),
inference(resolve,[$cnf( environment(sk3) )],[prove_l9_37,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ environment(sk3)
| ~ stable(sk3)
| in_environment(sk3,appear(efficient_producers,sk3)) ),
inference(subst,[],[mp_EP_in_stable_environments_29:[bind(A,$fot(sk3))]]) ).
cnf(refute_0_5,plain,
( ~ environment(sk3)
| in_environment(sk3,appear(efficient_producers,sk3)) ),
inference(resolve,[$cnf( stable(sk3) )],[prove_l9_38,refute_0_4]) ).
cnf(refute_0_6,plain,
in_environment(sk3,appear(efficient_producers,sk3)),
inference(resolve,[$cnf( environment(sk3) )],[prove_l9_37,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ environment(sk3)
| ~ greater(X_28,appear(efficient_producers,sk3))
| ~ in_environment(sk3,appear(efficient_producers,sk3))
| ~ stable(sk3)
| in_environment(sk3,X_28) ),
inference(subst,[],[mp_long_stable_environments_28:[bind(A,$fot(sk3)),bind(B,$fot(appear(efficient_producers,sk3))),bind(C,$fot(X_28))]]) ).
cnf(refute_0_8,plain,
( ~ environment(sk3)
| ~ greater(X_28,appear(efficient_producers,sk3))
| ~ stable(sk3)
| in_environment(sk3,X_28) ),
inference(resolve,[$cnf( in_environment(sk3,appear(efficient_producers,sk3)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ greater(X_28,appear(efficient_producers,sk3))
| ~ stable(sk3)
| in_environment(sk3,X_28) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l9_37,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ greater(X_28,appear(efficient_producers,sk3))
| in_environment(sk3,X_28) ),
inference(resolve,[$cnf( stable(sk3) )],[prove_l9_38,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ greater(sk2(sk3),appear(efficient_producers,sk3))
| in_environment(sk3,sk2(sk3)) ),
inference(subst,[],[refute_0_10:[bind(X_28,$fot(sk2(sk3)))]]) ).
cnf(refute_0_12,plain,
in_environment(sk3,sk2(sk3)),
inference(resolve,[$cnf( greater(sk2(sk3),appear(efficient_producers,sk3)) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ environment(sk3)
| ~ in_environment(sk3,sk2(sk3))
| ~ stable(sk3)
| contracts_from(sk2(sk3),first_movers)
| greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero) ),
inference(subst,[],[mp_contracts_from_24:[bind(A,$fot(sk3)),bind(B,$fot(sk2(sk3)))]]) ).
cnf(refute_0_14,plain,
( ~ environment(sk3)
| ~ stable(sk3)
| contracts_from(sk2(sk3),first_movers)
| greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero) ),
inference(resolve,[$cnf( in_environment(sk3,sk2(sk3)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ stable(sk3)
| contracts_from(sk2(sk3),first_movers)
| greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l9_37,refute_0_14]) ).
cnf(refute_0_16,plain,
( contracts_from(sk2(sk3),first_movers)
| greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero) ),
inference(resolve,[$cnf( stable(sk3) )],[prove_l9_38,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ contracts_from(sk2(sk3),first_movers)
| ~ greater(sk2(sk3),appear(efficient_producers,sk3)) ),
inference(subst,[],[prove_l9_39:[bind(A,$fot(sk2(sk3)))]]) ).
cnf(refute_0_18,plain,
~ contracts_from(sk2(sk3),first_movers),
inference(resolve,[$cnf( greater(sk2(sk3),appear(efficient_producers,sk3)) )],[refute_0_3,refute_0_17]) ).
cnf(refute_0_19,plain,
greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero),
inference(resolve,[$cnf( contracts_from(sk2(sk3),first_movers) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ environment(X_44)
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| ~ greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero)
| ~ in_environment(X_44,sk1(sk2(sk3),sk3))
| subpopulations(first_movers,efficient_producers,X_44,sk1(sk2(sk3),sk3)) ),
inference(subst,[],[mp_non_empty_fm_and_ep_27:[bind(A,$fot(X_44)),bind(B,$fot(sk1(sk2(sk3),sk3)))]]) ).
cnf(refute_0_21,plain,
( ~ environment(X_44)
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| ~ in_environment(X_44,sk1(sk2(sk3),sk3))
| subpopulations(first_movers,efficient_producers,X_44,sk1(sk2(sk3),sk3)) ),
inference(resolve,[$cnf( greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ environment(sk3)
| ~ greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| ~ in_environment(sk3,sk2(sk3))
| ~ stable(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(subst,[],[mp_contracts_from_26:[bind(A,$fot(sk3)),bind(B,$fot(sk2(sk3)))]]) ).
cnf(refute_0_23,plain,
( ~ environment(sk3)
| ~ greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3))
| ~ stable(sk3)
| ~ subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3))
| greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(subst,[],[l10_36:[bind(A,$fot(sk3)),bind(B,$fot(sk1(sk2(sk3),sk3)))]]) ).
cnf(refute_0_24,plain,
( ~ environment(sk3)
| ~ greater(C,sk2(sk3))
| ~ in_environment(sk3,sk2(sk3))
| ~ stable(sk3)
| in_environment(sk3,C) ),
inference(subst,[],[mp_long_stable_environments_28:[bind(A,$fot(sk3)),bind(B,$fot(sk2(sk3)))]]) ).
cnf(refute_0_25,plain,
( ~ environment(sk3)
| ~ greater(C,sk2(sk3))
| ~ stable(sk3)
| in_environment(sk3,C) ),
inference(resolve,[$cnf( in_environment(sk3,sk2(sk3)) )],[refute_0_12,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ greater(C,sk2(sk3))
| ~ stable(sk3)
| in_environment(sk3,C) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l9_37,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ greater(C,sk2(sk3))
| in_environment(sk3,C) ),
inference(resolve,[$cnf( stable(sk3) )],[prove_l9_38,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ greater(sk1(sk2(sk3),sk3),sk2(sk3))
| in_environment(sk3,sk1(sk2(sk3),sk3)) ),
inference(subst,[],[refute_0_27:[bind(C,$fot(sk1(sk2(sk3),sk3)))]]) ).
cnf(refute_0_29,plain,
( ~ greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3))
| sk1(sk2(sk3),sk3) = sk2(sk3)
| greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(subst,[],[mp_greater_or_equal_31:[bind(A,$fot(sk1(sk2(sk3),sk3))),bind(B,$fot(sk2(sk3)))]]) ).
cnf(refute_0_30,plain,
( ~ environment(sk3)
| ~ in_environment(sk3,sk2(sk3))
| ~ stable(sk3)
| contracts_from(sk2(sk3),first_movers)
| greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(subst,[],[mp_contracts_from_25:[bind(A,$fot(sk3)),bind(B,$fot(sk2(sk3)))]]) ).
cnf(refute_0_31,plain,
( ~ environment(sk3)
| ~ stable(sk3)
| contracts_from(sk2(sk3),first_movers)
| greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(resolve,[$cnf( in_environment(sk3,sk2(sk3)) )],[refute_0_12,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ stable(sk3)
| contracts_from(sk2(sk3),first_movers)
| greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l9_37,refute_0_31]) ).
cnf(refute_0_33,plain,
( contracts_from(sk2(sk3),first_movers)
| greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(resolve,[$cnf( stable(sk3) )],[prove_l9_38,refute_0_32]) ).
cnf(refute_0_34,plain,
greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3)),
inference(resolve,[$cnf( contracts_from(sk2(sk3),first_movers) )],[refute_0_33,refute_0_18]) ).
cnf(refute_0_35,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(resolve,[$cnf( greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3)) )],[refute_0_34,refute_0_29]) ).
cnf(refute_0_36,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| in_environment(sk3,sk1(sk2(sk3),sk3)) ),
inference(resolve,[$cnf( greater(sk1(sk2(sk3),sk3),sk2(sk3)) )],[refute_0_35,refute_0_28]) ).
cnf(refute_0_37,plain,
( ~ environment(sk3)
| ~ greater_or_equal(sk1(sk2(sk3),sk3),appear(efficient_producers,sk3))
| ~ in_environment(sk3,sk1(sk2(sk3),sk3))
| greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero) ),
inference(subst,[],[t6_34:[bind(A,$fot(sk3)),bind(B,$fot(sk1(sk2(sk3),sk3)))]]) ).
cnf(refute_0_38,plain,
( ~ greater(sk1(sk2(sk3),sk3),appear(efficient_producers,sk3))
| greater_or_equal(sk1(sk2(sk3),sk3),appear(efficient_producers,sk3)) ),
inference(subst,[],[mp_greater_or_equal_32:[bind(A,$fot(sk1(sk2(sk3),sk3))),bind(B,$fot(appear(efficient_producers,sk3)))]]) ).
cnf(refute_0_39,plain,
( ~ greater(X_8,sk2(sk3))
| ~ greater(sk2(sk3),appear(efficient_producers,sk3))
| greater(X_8,appear(efficient_producers,sk3)) ),
inference(subst,[],[mp_greater_transitivity_30:[bind(A,$fot(X_8)),bind(B,$fot(sk2(sk3))),bind(C,$fot(appear(efficient_producers,sk3)))]]) ).
cnf(refute_0_40,plain,
( ~ greater(X_8,sk2(sk3))
| greater(X_8,appear(efficient_producers,sk3)) ),
inference(resolve,[$cnf( greater(sk2(sk3),appear(efficient_producers,sk3)) )],[refute_0_3,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ greater(sk1(sk2(sk3),sk3),sk2(sk3))
| greater(sk1(sk2(sk3),sk3),appear(efficient_producers,sk3)) ),
inference(subst,[],[refute_0_40:[bind(X_8,$fot(sk1(sk2(sk3),sk3)))]]) ).
cnf(refute_0_42,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| greater(sk1(sk2(sk3),sk3),appear(efficient_producers,sk3)) ),
inference(resolve,[$cnf( greater(sk1(sk2(sk3),sk3),sk2(sk3)) )],[refute_0_35,refute_0_41]) ).
cnf(refute_0_43,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| greater_or_equal(sk1(sk2(sk3),sk3),appear(efficient_producers,sk3)) ),
inference(resolve,[$cnf( greater(sk1(sk2(sk3),sk3),appear(efficient_producers,sk3)) )],[refute_0_42,refute_0_38]) ).
cnf(refute_0_44,plain,
( ~ environment(sk3)
| ~ in_environment(sk3,sk1(sk2(sk3),sk3))
| sk1(sk2(sk3),sk3) = sk2(sk3)
| greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero) ),
inference(resolve,[$cnf( greater_or_equal(sk1(sk2(sk3),sk3),appear(efficient_producers,sk3)) )],[refute_0_43,refute_0_37]) ).
cnf(refute_0_45,plain,
( ~ in_environment(sk3,sk1(sk2(sk3),sk3))
| sk1(sk2(sk3),sk3) = sk2(sk3)
| greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l9_37,refute_0_44]) ).
cnf(refute_0_46,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero) ),
inference(resolve,[$cnf( in_environment(sk3,sk1(sk2(sk3),sk3)) )],[refute_0_36,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ environment(X_46)
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| ~ in_environment(X_46,sk1(sk2(sk3),sk3))
| subpopulations(first_movers,efficient_producers,X_46,sk1(sk2(sk3),sk3)) ),
inference(subst,[],[refute_0_21:[bind(X_44,$fot(X_46))]]) ).
cnf(refute_0_48,plain,
( ~ environment(X_46)
| ~ in_environment(X_46,sk1(sk2(sk3),sk3))
| sk1(sk2(sk3),sk3) = sk2(sk3)
| subpopulations(first_movers,efficient_producers,X_46,sk1(sk2(sk3),sk3)) ),
inference(resolve,[$cnf( greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ environment(sk3)
| ~ in_environment(sk3,sk1(sk2(sk3),sk3))
| sk1(sk2(sk3),sk3) = sk2(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(subst,[],[refute_0_48:[bind(X_46,$fot(sk3))]]) ).
cnf(refute_0_50,plain,
( ~ environment(sk3)
| sk1(sk2(sk3),sk3) = sk2(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(resolve,[$cnf( in_environment(sk3,sk1(sk2(sk3),sk3)) )],[refute_0_36,refute_0_49]) ).
cnf(refute_0_51,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l9_37,refute_0_50]) ).
cnf(refute_0_52,plain,
( ~ environment(sk3)
| ~ greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3))
| ~ stable(sk3)
| sk1(sk2(sk3),sk3) = sk2(sk3)
| greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) )],[refute_0_51,refute_0_23]) ).
cnf(refute_0_53,plain,
( ~ greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3))
| ~ stable(sk3)
| sk1(sk2(sk3),sk3) = sk2(sk3)
| greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l9_37,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ stable(sk3)
| sk1(sk2(sk3),sk3) = sk2(sk3)
| greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(resolve,[$cnf( greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3)) )],[refute_0_34,refute_0_53]) ).
cnf(refute_0_55,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(resolve,[$cnf( stable(sk3) )],[prove_l9_38,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ environment(sk3)
| ~ in_environment(sk3,sk2(sk3))
| ~ stable(sk3)
| sk1(sk2(sk3),sk3) = sk2(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolve,[$cnf( greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3))) )],[refute_0_55,refute_0_22]) ).
cnf(refute_0_57,plain,
( ~ in_environment(sk3,sk2(sk3))
| ~ stable(sk3)
| sk1(sk2(sk3),sk3) = sk2(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l9_37,refute_0_56]) ).
cnf(refute_0_58,plain,
( ~ stable(sk3)
| sk1(sk2(sk3),sk3) = sk2(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolve,[$cnf( in_environment(sk3,sk2(sk3)) )],[refute_0_12,refute_0_57]) ).
cnf(refute_0_59,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolve,[$cnf( stable(sk3) )],[prove_l9_38,refute_0_58]) ).
cnf(refute_0_60,plain,
sk1(sk2(sk3),sk3) = sk2(sk3),
inference(resolve,[$cnf( contracts_from(sk2(sk3),first_movers) )],[refute_0_59,refute_0_18]) ).
cnf(refute_0_61,plain,
cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)) = cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),
introduced(tautology,[refl,[$fot(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)))]]) ).
cnf(refute_0_62,plain,
( cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)) != cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3))
| sk1(sk2(sk3),sk3) != sk2(sk3)
| cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)) = cardinality_at_time(efficient_producers,sk2(sk3)) ),
introduced(tautology,[equality,[$cnf( $equal(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3))) ),[1,1],$fot(sk2(sk3))]]) ).
cnf(refute_0_63,plain,
( sk1(sk2(sk3),sk3) != sk2(sk3)
| cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)) = cardinality_at_time(efficient_producers,sk2(sk3)) ),
inference(resolve,[$cnf( $equal(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)) = cardinality_at_time(efficient_producers,sk2(sk3)),
inference(resolve,[$cnf( $equal(sk1(sk2(sk3),sk3),sk2(sk3)) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
( cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)) != cardinality_at_time(efficient_producers,sk2(sk3))
| ~ greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero)
| greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero) ),
introduced(tautology,[equality,[$cnf( ~ greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero) ),[0],$fot(cardinality_at_time(efficient_producers,sk2(sk3)))]]) ).
cnf(refute_0_66,plain,
( ~ greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero)
| greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero) ),
inference(resolve,[$cnf( $equal(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),cardinality_at_time(efficient_producers,sk2(sk3))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( ~ environment(X_44)
| ~ greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero)
| ~ in_environment(X_44,sk1(sk2(sk3),sk3))
| subpopulations(first_movers,efficient_producers,X_44,sk1(sk2(sk3),sk3)) ),
inference(resolve,[$cnf( greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero) )],[refute_0_66,refute_0_21]) ).
cnf(refute_0_68,plain,
( sk1(sk2(sk3),sk3) != sk2(sk3)
| ~ in_environment(X_44,sk2(sk3))
| in_environment(X_44,sk1(sk2(sk3),sk3)) ),
introduced(tautology,[equality,[$cnf( ~ in_environment(X_44,sk1(sk2(sk3),sk3)) ),[1],$fot(sk2(sk3))]]) ).
cnf(refute_0_69,plain,
( ~ in_environment(X_44,sk2(sk3))
| in_environment(X_44,sk1(sk2(sk3),sk3)) ),
inference(resolve,[$cnf( $equal(sk1(sk2(sk3),sk3),sk2(sk3)) )],[refute_0_60,refute_0_68]) ).
cnf(refute_0_70,plain,
( ~ environment(X_44)
| ~ greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero)
| ~ in_environment(X_44,sk2(sk3))
| subpopulations(first_movers,efficient_producers,X_44,sk1(sk2(sk3),sk3)) ),
inference(resolve,[$cnf( in_environment(X_44,sk1(sk2(sk3),sk3)) )],[refute_0_69,refute_0_67]) ).
cnf(refute_0_71,plain,
( sk1(sk2(sk3),sk3) != sk2(sk3)
| ~ subpopulations(first_movers,efficient_producers,X_44,sk1(sk2(sk3),sk3))
| subpopulations(first_movers,efficient_producers,X_44,sk2(sk3)) ),
introduced(tautology,[equality,[$cnf( subpopulations(first_movers,efficient_producers,X_44,sk1(sk2(sk3),sk3)) ),[3],$fot(sk2(sk3))]]) ).
cnf(refute_0_72,plain,
( ~ subpopulations(first_movers,efficient_producers,X_44,sk1(sk2(sk3),sk3))
| subpopulations(first_movers,efficient_producers,X_44,sk2(sk3)) ),
inference(resolve,[$cnf( $equal(sk1(sk2(sk3),sk3),sk2(sk3)) )],[refute_0_60,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ environment(X_44)
| ~ greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero)
| ~ in_environment(X_44,sk2(sk3))
| subpopulations(first_movers,efficient_producers,X_44,sk2(sk3)) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,X_44,sk1(sk2(sk3),sk3)) )],[refute_0_70,refute_0_72]) ).
cnf(refute_0_74,plain,
( ~ greater(sk2(sk3),appear(efficient_producers,sk3))
| greater_or_equal(sk2(sk3),appear(efficient_producers,sk3)) ),
inference(subst,[],[mp_greater_or_equal_32:[bind(A,$fot(sk2(sk3))),bind(B,$fot(appear(efficient_producers,sk3)))]]) ).
cnf(refute_0_75,plain,
greater_or_equal(sk2(sk3),appear(efficient_producers,sk3)),
inference(resolve,[$cnf( greater(sk2(sk3),appear(efficient_producers,sk3)) )],[refute_0_3,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ environment(sk3)
| ~ greater_or_equal(sk2(sk3),appear(efficient_producers,sk3))
| ~ in_environment(sk3,sk2(sk3))
| greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero) ),
inference(subst,[],[t6_34:[bind(A,$fot(sk3)),bind(B,$fot(sk2(sk3)))]]) ).
cnf(refute_0_77,plain,
( ~ environment(sk3)
| ~ in_environment(sk3,sk2(sk3))
| greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero) ),
inference(resolve,[$cnf( greater_or_equal(sk2(sk3),appear(efficient_producers,sk3)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
( ~ in_environment(sk3,sk2(sk3))
| greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l9_37,refute_0_77]) ).
cnf(refute_0_79,plain,
greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero),
inference(resolve,[$cnf( in_environment(sk3,sk2(sk3)) )],[refute_0_12,refute_0_78]) ).
cnf(refute_0_80,plain,
( ~ environment(X_44)
| ~ in_environment(X_44,sk2(sk3))
| subpopulations(first_movers,efficient_producers,X_44,sk2(sk3)) ),
inference(resolve,[$cnf( greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero) )],[refute_0_79,refute_0_73]) ).
cnf(refute_0_81,plain,
( ~ environment(sk3)
| ~ in_environment(sk3,sk2(sk3))
| subpopulations(first_movers,efficient_producers,sk3,sk2(sk3)) ),
inference(subst,[],[refute_0_80:[bind(X_44,$fot(sk3))]]) ).
cnf(refute_0_82,plain,
( ~ environment(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk2(sk3)) ),
inference(resolve,[$cnf( in_environment(sk3,sk2(sk3)) )],[refute_0_12,refute_0_81]) ).
cnf(refute_0_83,plain,
subpopulations(first_movers,efficient_producers,sk3,sk2(sk3)),
inference(resolve,[$cnf( environment(sk3) )],[prove_l9_37,refute_0_82]) ).
cnf(refute_0_84,plain,
( ~ environment(sk3)
| ~ greater_or_equal(sk2(sk3),sk2(sk3))
| ~ stable(sk3)
| greater(zero,growth_rate(first_movers,sk2(sk3))) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,sk3,sk2(sk3)) )],[refute_0_83,refute_0_0]) ).
cnf(refute_0_85,plain,
( ~ greater_or_equal(sk2(sk3),sk2(sk3))
| ~ stable(sk3)
| greater(zero,growth_rate(first_movers,sk2(sk3))) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l9_37,refute_0_84]) ).
cnf(refute_0_86,plain,
( B != B
| greater_or_equal(B,B) ),
inference(subst,[],[mp_greater_or_equal_33:[bind(A,$fot(B))]]) ).
cnf(refute_0_87,plain,
B = B,
introduced(tautology,[refl,[$fot(B)]]) ).
cnf(refute_0_88,plain,
greater_or_equal(B,B),
inference(resolve,[$cnf( $equal(B,B) )],[refute_0_87,refute_0_86]) ).
cnf(refute_0_89,plain,
greater_or_equal(sk2(sk3),sk2(sk3)),
inference(subst,[],[refute_0_88:[bind(B,$fot(sk2(sk3)))]]) ).
cnf(refute_0_90,plain,
( ~ stable(sk3)
| greater(zero,growth_rate(first_movers,sk2(sk3))) ),
inference(resolve,[$cnf( greater_or_equal(sk2(sk3),sk2(sk3)) )],[refute_0_89,refute_0_85]) ).
cnf(refute_0_91,plain,
greater(zero,growth_rate(first_movers,sk2(sk3))),
inference(resolve,[$cnf( stable(sk3) )],[prove_l9_38,refute_0_90]) ).
cnf(refute_0_92,plain,
( sk1(sk2(sk3),sk3) != sk2(sk3)
| ~ greater(zero,growth_rate(first_movers,sk2(sk3)))
| greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
introduced(tautology,[equality,[$cnf( ~ greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),[1,1],$fot(sk2(sk3))]]) ).
cnf(refute_0_93,plain,
( ~ greater(zero,growth_rate(first_movers,sk2(sk3)))
| greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(resolve,[$cnf( $equal(sk1(sk2(sk3),sk3),sk2(sk3)) )],[refute_0_60,refute_0_92]) ).
cnf(refute_0_94,plain,
( ~ environment(sk3)
| ~ greater(zero,growth_rate(first_movers,sk2(sk3)))
| ~ in_environment(sk3,sk2(sk3))
| ~ stable(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolve,[$cnf( greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3))) )],[refute_0_93,refute_0_22]) ).
cnf(refute_0_95,plain,
( ~ greater(zero,growth_rate(first_movers,sk2(sk3)))
| ~ in_environment(sk3,sk2(sk3))
| ~ stable(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l9_37,refute_0_94]) ).
cnf(refute_0_96,plain,
( ~ greater(zero,growth_rate(first_movers,sk2(sk3)))
| ~ stable(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolve,[$cnf( in_environment(sk3,sk2(sk3)) )],[refute_0_12,refute_0_95]) ).
cnf(refute_0_97,plain,
( ~ greater(zero,growth_rate(first_movers,sk2(sk3)))
| contracts_from(sk2(sk3),first_movers) ),
inference(resolve,[$cnf( stable(sk3) )],[prove_l9_38,refute_0_96]) ).
cnf(refute_0_98,plain,
~ greater(zero,growth_rate(first_movers,sk2(sk3))),
inference(resolve,[$cnf( contracts_from(sk2(sk3),first_movers) )],[refute_0_97,refute_0_18]) ).
cnf(refute_0_99,plain,
$false,
inference(resolve,[$cnf( greater(zero,growth_rate(first_movers,sk2(sk3))) )],[refute_0_91,refute_0_98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MGT027-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 9 09:29:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------