TSTP Solution File: MGT026-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT026-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 22:18:56 EDT 2022
% Result : Unsatisfiable 0.19s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 22
% Syntax : Number of clauses : 111 ( 18 unt; 40 nHn; 109 RR)
% Number of literals : 334 ( 94 equ; 176 neg)
% Maximal clause size : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(mp1_high_growth_rates_28,axiom,
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| selection_favors(C,B,D) ) ).
cnf(mp2_favour_members_29,axiom,
( ~ environment(A)
| ~ subpopulation(B,A,C)
| ~ subpopulation(D,A,C)
| ~ greater(cardinality_at_time(B,C),zero)
| cardinality_at_time(D,C) != zero
| selection_favors(B,D,C) ) ).
cnf(mp_non_empty_fm_and_ep_30,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_first_movers_exist_31,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| greater_or_equal(cardinality_at_time(first_movers,B),zero) ) ).
cnf(mp_subpopulations_32,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| subpopulation(first_movers,A,B) ) ).
cnf(mp_subpopulations_33,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| subpopulation(efficient_producers,A,B) ) ).
cnf(mp_critical_point_after_EP_34,axiom,
( ~ environment(A)
| greater_or_equal(critical_point(A),appear(efficient_producers,A)) ) ).
cnf(mp_greater_transitivity_35,axiom,
( ~ greater(A,B)
| ~ greater(B,C)
| greater(A,C) ) ).
cnf(mp_greater_or_equal_36,axiom,
( ~ greater_or_equal(A,B)
| greater(A,B)
| A = B ) ).
cnf(mp_greater_or_equal_37,axiom,
( ~ greater(A,B)
| greater_or_equal(A,B) ) ).
cnf(d1_40,hypothesis,
( ~ environment(A)
| B != critical_point(A)
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(C,B)
| greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) ) ).
cnf(t6_41,hypothesis,
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater_or_equal(B,appear(efficient_producers,A))
| greater(cardinality_at_time(efficient_producers,B),zero) ) ).
cnf(prove_l8_42,negated_conjecture,
environment(sk1) ).
cnf(prove_l8_43,negated_conjecture,
in_environment(sk1,sk2) ).
cnf(prove_l8_44,negated_conjecture,
greater(sk2,critical_point(sk1)) ).
cnf(prove_l8_45,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,sk2) ).
cnf(refute_0_0,plain,
( ~ environment(sk1)
| ~ in_environment(sk1,sk2)
| subpopulation(first_movers,sk1,sk2) ),
inference(subst,[],[mp_subpopulations_32:[bind(A,$fot(sk1)),bind(B,$fot(sk2))]]) ).
cnf(refute_0_1,plain,
( ~ environment(sk1)
| subpopulation(first_movers,sk1,sk2) ),
inference(resolve,[$cnf( in_environment(sk1,sk2) )],[prove_l8_43,refute_0_0]) ).
cnf(refute_0_2,plain,
subpopulation(first_movers,sk1,sk2),
inference(resolve,[$cnf( environment(sk1) )],[prove_l8_42,refute_0_1]) ).
cnf(refute_0_3,plain,
( cardinality_at_time(D,sk2) != zero
| ~ environment(A)
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ subpopulation(D,A,sk2)
| ~ subpopulation(efficient_producers,A,sk2)
| selection_favors(efficient_producers,D,sk2) ),
inference(subst,[],[mp2_favour_members_29:[bind(B,$fot(efficient_producers)),bind(C,$fot(sk2))]]) ).
cnf(refute_0_4,plain,
( ~ greater(sk2,critical_point(sk1))
| greater_or_equal(sk2,critical_point(sk1)) ),
inference(subst,[],[mp_greater_or_equal_37:[bind(A,$fot(sk2)),bind(B,$fot(critical_point(sk1)))]]) ).
cnf(refute_0_5,plain,
greater_or_equal(sk2,critical_point(sk1)),
inference(resolve,[$cnf( greater(sk2,critical_point(sk1)) )],[prove_l8_44,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ environment(sk1)
| ~ greater_or_equal(B,appear(efficient_producers,sk1))
| ~ in_environment(sk1,B)
| greater(cardinality_at_time(efficient_producers,B),zero) ),
inference(subst,[],[t6_41:[bind(A,$fot(sk1))]]) ).
cnf(refute_0_7,plain,
( ~ greater(sk2,appear(efficient_producers,sk1))
| greater_or_equal(sk2,appear(efficient_producers,sk1)) ),
inference(subst,[],[mp_greater_or_equal_37:[bind(A,$fot(sk2)),bind(B,$fot(appear(efficient_producers,sk1)))]]) ).
cnf(refute_0_8,plain,
( ~ environment(sk1)
| greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1)) ),
inference(subst,[],[mp_critical_point_after_EP_34:[bind(A,$fot(sk1))]]) ).
cnf(refute_0_9,plain,
greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1)),
inference(resolve,[$cnf( environment(sk1) )],[prove_l8_42,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1))
| critical_point(sk1) = appear(efficient_producers,sk1)
| greater(critical_point(sk1),appear(efficient_producers,sk1)) ),
inference(subst,[],[mp_greater_or_equal_36:[bind(A,$fot(critical_point(sk1))),bind(B,$fot(appear(efficient_producers,sk1)))]]) ).
cnf(refute_0_11,plain,
( critical_point(sk1) = appear(efficient_producers,sk1)
| greater(critical_point(sk1),appear(efficient_producers,sk1)) ),
inference(resolve,[$cnf( greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ greater(X_13,critical_point(sk1))
| ~ greater(critical_point(sk1),appear(efficient_producers,sk1))
| greater(X_13,appear(efficient_producers,sk1)) ),
inference(subst,[],[mp_greater_transitivity_35:[bind(A,$fot(X_13)),bind(B,$fot(critical_point(sk1))),bind(C,$fot(appear(efficient_producers,sk1)))]]) ).
cnf(refute_0_13,plain,
( ~ greater(X_13,critical_point(sk1))
| critical_point(sk1) = appear(efficient_producers,sk1)
| greater(X_13,appear(efficient_producers,sk1)) ),
inference(resolve,[$cnf( greater(critical_point(sk1),appear(efficient_producers,sk1)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ greater(sk2,critical_point(sk1))
| critical_point(sk1) = appear(efficient_producers,sk1)
| greater(sk2,appear(efficient_producers,sk1)) ),
inference(subst,[],[refute_0_13:[bind(X_13,$fot(sk2))]]) ).
cnf(refute_0_15,plain,
( critical_point(sk1) = appear(efficient_producers,sk1)
| greater(sk2,appear(efficient_producers,sk1)) ),
inference(resolve,[$cnf( greater(sk2,critical_point(sk1)) )],[prove_l8_44,refute_0_14]) ).
cnf(refute_0_16,plain,
( critical_point(sk1) = appear(efficient_producers,sk1)
| greater_or_equal(sk2,appear(efficient_producers,sk1)) ),
inference(resolve,[$cnf( greater(sk2,appear(efficient_producers,sk1)) )],[refute_0_15,refute_0_7]) ).
cnf(refute_0_17,plain,
( ~ environment(sk1)
| ~ greater_or_equal(sk2,appear(efficient_producers,sk1))
| ~ in_environment(sk1,sk2)
| greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(subst,[],[t6_41:[bind(A,$fot(sk1)),bind(B,$fot(sk2))]]) ).
cnf(refute_0_18,plain,
( ~ environment(sk1)
| ~ in_environment(sk1,sk2)
| critical_point(sk1) = appear(efficient_producers,sk1)
| greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(resolve,[$cnf( greater_or_equal(sk2,appear(efficient_producers,sk1)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ in_environment(sk1,sk2)
| critical_point(sk1) = appear(efficient_producers,sk1)
| greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(resolve,[$cnf( environment(sk1) )],[prove_l8_42,refute_0_18]) ).
cnf(refute_0_20,plain,
( critical_point(sk1) = appear(efficient_producers,sk1)
| greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(resolve,[$cnf( in_environment(sk1,sk2) )],[prove_l8_43,refute_0_19]) ).
cnf(refute_0_21,plain,
( cardinality_at_time(X_48,sk2) != zero
| ~ environment(X_45)
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ subpopulation(X_48,X_45,sk2)
| ~ subpopulation(efficient_producers,X_45,sk2)
| selection_favors(efficient_producers,X_48,sk2) ),
inference(subst,[],[mp2_favour_members_29:[bind(A,$fot(X_45)),bind(B,$fot(efficient_producers)),bind(C,$fot(sk2)),bind(D,$fot(X_48))]]) ).
cnf(refute_0_22,plain,
( cardinality_at_time(X_48,sk2) != zero
| ~ environment(X_45)
| ~ subpopulation(X_48,X_45,sk2)
| ~ subpopulation(efficient_producers,X_45,sk2)
| critical_point(sk1) = appear(efficient_producers,sk1)
| selection_favors(efficient_producers,X_48,sk2) ),
inference(resolve,[$cnf( greater(cardinality_at_time(efficient_producers,sk2),zero) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( cardinality_at_time(first_movers,sk2) != zero
| ~ environment(sk1)
| ~ subpopulation(efficient_producers,sk1,sk2)
| ~ subpopulation(first_movers,sk1,sk2)
| critical_point(sk1) = appear(efficient_producers,sk1)
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(subst,[],[refute_0_22:[bind(X_45,$fot(sk1)),bind(X_48,$fot(first_movers))]]) ).
cnf(refute_0_24,plain,
( cardinality_at_time(first_movers,sk2) != zero
| ~ environment(sk1)
| ~ subpopulation(efficient_producers,sk1,sk2)
| critical_point(sk1) = appear(efficient_producers,sk1)
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(resolve,[$cnf( subpopulation(first_movers,sk1,sk2) )],[refute_0_2,refute_0_23]) ).
cnf(refute_0_25,plain,
( cardinality_at_time(first_movers,sk2) != zero
| ~ subpopulation(efficient_producers,sk1,sk2)
| critical_point(sk1) = appear(efficient_producers,sk1)
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(resolve,[$cnf( environment(sk1) )],[prove_l8_42,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ environment(sk1)
| ~ in_environment(sk1,sk2)
| subpopulation(efficient_producers,sk1,sk2) ),
inference(subst,[],[mp_subpopulations_33:[bind(A,$fot(sk1)),bind(B,$fot(sk2))]]) ).
cnf(refute_0_27,plain,
( ~ environment(sk1)
| subpopulation(efficient_producers,sk1,sk2) ),
inference(resolve,[$cnf( in_environment(sk1,sk2) )],[prove_l8_43,refute_0_26]) ).
cnf(refute_0_28,plain,
subpopulation(efficient_producers,sk1,sk2),
inference(resolve,[$cnf( environment(sk1) )],[prove_l8_42,refute_0_27]) ).
cnf(refute_0_29,plain,
( cardinality_at_time(first_movers,sk2) != zero
| critical_point(sk1) = appear(efficient_producers,sk1)
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(resolve,[$cnf( subpopulation(efficient_producers,sk1,sk2) )],[refute_0_28,refute_0_25]) ).
cnf(refute_0_30,plain,
( cardinality_at_time(first_movers,sk2) != zero
| critical_point(sk1) = appear(efficient_producers,sk1) ),
inference(resolve,[$cnf( selection_favors(efficient_producers,first_movers,sk2) )],[refute_0_29,prove_l8_45]) ).
cnf(refute_0_31,plain,
( ~ greater_or_equal(cardinality_at_time(first_movers,sk2),zero)
| cardinality_at_time(first_movers,sk2) = zero
| greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(subst,[],[mp_greater_or_equal_36:[bind(A,$fot(cardinality_at_time(first_movers,sk2))),bind(B,$fot(zero))]]) ).
cnf(refute_0_32,plain,
( ~ environment(sk1)
| ~ in_environment(sk1,sk2)
| greater_or_equal(cardinality_at_time(first_movers,sk2),zero) ),
inference(subst,[],[mp_first_movers_exist_31:[bind(A,$fot(sk1)),bind(B,$fot(sk2))]]) ).
cnf(refute_0_33,plain,
( ~ environment(sk1)
| greater_or_equal(cardinality_at_time(first_movers,sk2),zero) ),
inference(resolve,[$cnf( in_environment(sk1,sk2) )],[prove_l8_43,refute_0_32]) ).
cnf(refute_0_34,plain,
greater_or_equal(cardinality_at_time(first_movers,sk2),zero),
inference(resolve,[$cnf( environment(sk1) )],[prove_l8_42,refute_0_33]) ).
cnf(refute_0_35,plain,
( cardinality_at_time(first_movers,sk2) = zero
| greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(resolve,[$cnf( greater_or_equal(cardinality_at_time(first_movers,sk2),zero) )],[refute_0_34,refute_0_31]) ).
cnf(refute_0_36,plain,
( ~ environment(X_29)
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ greater(cardinality_at_time(first_movers,sk2),zero)
| ~ in_environment(X_29,sk2)
| subpopulations(first_movers,efficient_producers,X_29,sk2) ),
inference(subst,[],[mp_non_empty_fm_and_ep_30:[bind(A,$fot(X_29)),bind(B,$fot(sk2))]]) ).
cnf(refute_0_37,plain,
( ~ environment(X_29)
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ in_environment(X_29,sk2)
| cardinality_at_time(first_movers,sk2) = zero
| subpopulations(first_movers,efficient_producers,X_29,sk2) ),
inference(resolve,[$cnf( greater(cardinality_at_time(first_movers,sk2),zero) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ environment(X_31)
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ in_environment(X_31,sk2)
| cardinality_at_time(first_movers,sk2) = zero
| subpopulations(first_movers,efficient_producers,X_31,sk2) ),
inference(subst,[],[refute_0_37:[bind(X_29,$fot(X_31))]]) ).
cnf(refute_0_39,plain,
( ~ environment(X_31)
| ~ in_environment(X_31,sk2)
| cardinality_at_time(first_movers,sk2) = zero
| critical_point(sk1) = appear(efficient_producers,sk1)
| subpopulations(first_movers,efficient_producers,X_31,sk2) ),
inference(resolve,[$cnf( greater(cardinality_at_time(efficient_producers,sk2),zero) )],[refute_0_20,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ environment(sk1)
| ~ in_environment(sk1,sk2)
| cardinality_at_time(first_movers,sk2) = zero
| critical_point(sk1) = appear(efficient_producers,sk1)
| subpopulations(first_movers,efficient_producers,sk1,sk2) ),
inference(subst,[],[refute_0_39:[bind(X_31,$fot(sk1))]]) ).
cnf(refute_0_41,plain,
( ~ environment(sk1)
| cardinality_at_time(first_movers,sk2) = zero
| critical_point(sk1) = appear(efficient_producers,sk1)
| subpopulations(first_movers,efficient_producers,sk1,sk2) ),
inference(resolve,[$cnf( in_environment(sk1,sk2) )],[prove_l8_43,refute_0_40]) ).
cnf(refute_0_42,plain,
( cardinality_at_time(first_movers,sk2) = zero
| critical_point(sk1) = appear(efficient_producers,sk1)
| subpopulations(first_movers,efficient_producers,sk1,sk2) ),
inference(resolve,[$cnf( environment(sk1) )],[prove_l8_42,refute_0_41]) ).
cnf(refute_0_43,plain,
( critical_point(A) != critical_point(A)
| ~ environment(A)
| ~ greater(C,critical_point(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) ),
inference(subst,[],[d1_40:[bind(B,$fot(critical_point(A)))]]) ).
cnf(refute_0_44,plain,
critical_point(A) = critical_point(A),
introduced(tautology,[refl,[$fot(critical_point(A))]]) ).
cnf(refute_0_45,plain,
( ~ environment(A)
| ~ greater(C,critical_point(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) ),
inference(resolve,[$cnf( $equal(critical_point(A),critical_point(A)) )],[refute_0_44,refute_0_43]) ).
cnf(refute_0_46,plain,
( ~ environment(sk1)
| ~ greater(sk2,critical_point(sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
inference(subst,[],[refute_0_45:[bind(A,$fot(sk1)),bind(C,$fot(sk2))]]) ).
cnf(refute_0_47,plain,
( ~ environment(sk1)
| ~ greater(sk2,critical_point(sk1))
| cardinality_at_time(first_movers,sk2) = zero
| critical_point(sk1) = appear(efficient_producers,sk1)
| greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,sk1,sk2) )],[refute_0_42,refute_0_46]) ).
cnf(refute_0_48,plain,
( ~ greater(sk2,critical_point(sk1))
| cardinality_at_time(first_movers,sk2) = zero
| critical_point(sk1) = appear(efficient_producers,sk1)
| greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
inference(resolve,[$cnf( environment(sk1) )],[prove_l8_42,refute_0_47]) ).
cnf(refute_0_49,plain,
( cardinality_at_time(first_movers,sk2) = zero
| critical_point(sk1) = appear(efficient_producers,sk1)
| greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
inference(resolve,[$cnf( greater(sk2,critical_point(sk1)) )],[prove_l8_44,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ environment(X_35)
| ~ greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2))
| ~ subpopulations(first_movers,efficient_producers,X_35,sk2)
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(subst,[],[mp1_high_growth_rates_28:[bind(A,$fot(X_35)),bind(B,$fot(first_movers)),bind(C,$fot(efficient_producers)),bind(D,$fot(sk2))]]) ).
cnf(refute_0_51,plain,
( ~ environment(X_35)
| ~ subpopulations(first_movers,efficient_producers,X_35,sk2)
| cardinality_at_time(first_movers,sk2) = zero
| critical_point(sk1) = appear(efficient_producers,sk1)
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(resolve,[$cnf( greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( ~ environment(X_35)
| ~ subpopulations(first_movers,efficient_producers,X_35,sk2)
| cardinality_at_time(first_movers,sk2) = zero
| critical_point(sk1) = appear(efficient_producers,sk1) ),
inference(resolve,[$cnf( selection_favors(efficient_producers,first_movers,sk2) )],[refute_0_51,prove_l8_45]) ).
cnf(refute_0_53,plain,
( ~ environment(sk1)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| cardinality_at_time(first_movers,sk2) = zero
| critical_point(sk1) = appear(efficient_producers,sk1) ),
inference(subst,[],[refute_0_52:[bind(X_35,$fot(sk1))]]) ).
cnf(refute_0_54,plain,
( ~ environment(sk1)
| cardinality_at_time(first_movers,sk2) = zero
| critical_point(sk1) = appear(efficient_producers,sk1) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,sk1,sk2) )],[refute_0_42,refute_0_53]) ).
cnf(refute_0_55,plain,
( cardinality_at_time(first_movers,sk2) = zero
| critical_point(sk1) = appear(efficient_producers,sk1) ),
inference(resolve,[$cnf( environment(sk1) )],[prove_l8_42,refute_0_54]) ).
cnf(refute_0_56,plain,
( cardinality_at_time(first_movers,sk2) != zero
| zero != zero
| cardinality_at_time(first_movers,sk2) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(cardinality_at_time(first_movers,sk2),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_57,plain,
( zero != zero
| cardinality_at_time(first_movers,sk2) = zero
| critical_point(sk1) = appear(efficient_producers,sk1) ),
inference(resolve,[$cnf( $equal(cardinality_at_time(first_movers,sk2),zero) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( zero != zero
| critical_point(sk1) = appear(efficient_producers,sk1) ),
inference(resolve,[$cnf( $equal(cardinality_at_time(first_movers,sk2),zero) )],[refute_0_57,refute_0_30]) ).
cnf(refute_0_59,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_60,plain,
critical_point(sk1) = appear(efficient_producers,sk1),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_59,refute_0_58]) ).
cnf(refute_0_61,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_62,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_63,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( critical_point(sk1) != appear(efficient_producers,sk1)
| appear(efficient_producers,sk1) = critical_point(sk1) ),
inference(subst,[],[refute_0_63:[bind(X,$fot(critical_point(sk1))),bind(Y,$fot(appear(efficient_producers,sk1)))]]) ).
cnf(refute_0_65,plain,
appear(efficient_producers,sk1) = critical_point(sk1),
inference(resolve,[$cnf( $equal(critical_point(sk1),appear(efficient_producers,sk1)) )],[refute_0_60,refute_0_64]) ).
cnf(refute_0_66,plain,
( appear(efficient_producers,sk1) != critical_point(sk1)
| ~ greater_or_equal(B,critical_point(sk1))
| greater_or_equal(B,appear(efficient_producers,sk1)) ),
introduced(tautology,[equality,[$cnf( ~ greater_or_equal(B,appear(efficient_producers,sk1)) ),[1],$fot(critical_point(sk1))]]) ).
cnf(refute_0_67,plain,
( ~ greater_or_equal(B,critical_point(sk1))
| greater_or_equal(B,appear(efficient_producers,sk1)) ),
inference(resolve,[$cnf( $equal(appear(efficient_producers,sk1),critical_point(sk1)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ environment(sk1)
| ~ greater_or_equal(B,critical_point(sk1))
| ~ in_environment(sk1,B)
| greater(cardinality_at_time(efficient_producers,B),zero) ),
inference(resolve,[$cnf( greater_or_equal(B,appear(efficient_producers,sk1)) )],[refute_0_67,refute_0_6]) ).
cnf(refute_0_69,plain,
( ~ greater_or_equal(B,critical_point(sk1))
| ~ in_environment(sk1,B)
| greater(cardinality_at_time(efficient_producers,B),zero) ),
inference(resolve,[$cnf( environment(sk1) )],[prove_l8_42,refute_0_68]) ).
cnf(refute_0_70,plain,
( ~ greater_or_equal(sk2,critical_point(sk1))
| ~ in_environment(sk1,sk2)
| greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(subst,[],[refute_0_69:[bind(B,$fot(sk2))]]) ).
cnf(refute_0_71,plain,
( ~ in_environment(sk1,sk2)
| greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(resolve,[$cnf( greater_or_equal(sk2,critical_point(sk1)) )],[refute_0_5,refute_0_70]) ).
cnf(refute_0_72,plain,
greater(cardinality_at_time(efficient_producers,sk2),zero),
inference(resolve,[$cnf( in_environment(sk1,sk2) )],[prove_l8_43,refute_0_71]) ).
cnf(refute_0_73,plain,
( cardinality_at_time(D,sk2) != zero
| ~ environment(A)
| ~ subpopulation(D,A,sk2)
| ~ subpopulation(efficient_producers,A,sk2)
| selection_favors(efficient_producers,D,sk2) ),
inference(resolve,[$cnf( greater(cardinality_at_time(efficient_producers,sk2),zero) )],[refute_0_72,refute_0_3]) ).
cnf(refute_0_74,plain,
( cardinality_at_time(first_movers,sk2) != zero
| ~ environment(sk1)
| ~ subpopulation(efficient_producers,sk1,sk2)
| ~ subpopulation(first_movers,sk1,sk2)
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(subst,[],[refute_0_73:[bind(A,$fot(sk1)),bind(D,$fot(first_movers))]]) ).
cnf(refute_0_75,plain,
( cardinality_at_time(first_movers,sk2) != zero
| ~ environment(sk1)
| ~ subpopulation(efficient_producers,sk1,sk2)
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(resolve,[$cnf( subpopulation(first_movers,sk1,sk2) )],[refute_0_2,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ environment(X_29)
| ~ in_environment(X_29,sk2)
| cardinality_at_time(first_movers,sk2) = zero
| subpopulations(first_movers,efficient_producers,X_29,sk2) ),
inference(resolve,[$cnf( greater(cardinality_at_time(efficient_producers,sk2),zero) )],[refute_0_72,refute_0_37]) ).
cnf(refute_0_77,plain,
( ~ environment(sk1)
| ~ in_environment(sk1,sk2)
| cardinality_at_time(first_movers,sk2) = zero
| subpopulations(first_movers,efficient_producers,sk1,sk2) ),
inference(subst,[],[refute_0_76:[bind(X_29,$fot(sk1))]]) ).
cnf(refute_0_78,plain,
( ~ environment(sk1)
| cardinality_at_time(first_movers,sk2) = zero
| subpopulations(first_movers,efficient_producers,sk1,sk2) ),
inference(resolve,[$cnf( in_environment(sk1,sk2) )],[prove_l8_43,refute_0_77]) ).
cnf(refute_0_79,plain,
( cardinality_at_time(first_movers,sk2) = zero
| subpopulations(first_movers,efficient_producers,sk1,sk2) ),
inference(resolve,[$cnf( environment(sk1) )],[prove_l8_42,refute_0_78]) ).
cnf(refute_0_80,plain,
( ~ environment(A)
| ~ greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2))
| ~ subpopulations(first_movers,efficient_producers,A,sk2)
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(subst,[],[mp1_high_growth_rates_28:[bind(B,$fot(first_movers)),bind(C,$fot(efficient_producers)),bind(D,$fot(sk2))]]) ).
cnf(refute_0_81,plain,
( ~ environment(sk1)
| ~ greater(sk2,critical_point(sk1))
| cardinality_at_time(first_movers,sk2) = zero
| greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,sk1,sk2) )],[refute_0_79,refute_0_46]) ).
cnf(refute_0_82,plain,
( ~ greater(sk2,critical_point(sk1))
| cardinality_at_time(first_movers,sk2) = zero
| greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
inference(resolve,[$cnf( environment(sk1) )],[prove_l8_42,refute_0_81]) ).
cnf(refute_0_83,plain,
( cardinality_at_time(first_movers,sk2) = zero
| greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
inference(resolve,[$cnf( greater(sk2,critical_point(sk1)) )],[prove_l8_44,refute_0_82]) ).
cnf(refute_0_84,plain,
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,sk2)
| cardinality_at_time(first_movers,sk2) = zero
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(resolve,[$cnf( greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) )],[refute_0_83,refute_0_80]) ).
cnf(refute_0_85,plain,
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,sk2)
| cardinality_at_time(first_movers,sk2) = zero ),
inference(resolve,[$cnf( selection_favors(efficient_producers,first_movers,sk2) )],[refute_0_84,prove_l8_45]) ).
cnf(refute_0_86,plain,
( ~ environment(sk1)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| cardinality_at_time(first_movers,sk2) = zero ),
inference(subst,[],[refute_0_85:[bind(A,$fot(sk1))]]) ).
cnf(refute_0_87,plain,
( ~ environment(sk1)
| cardinality_at_time(first_movers,sk2) = zero ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,sk1,sk2) )],[refute_0_79,refute_0_86]) ).
cnf(refute_0_88,plain,
cardinality_at_time(first_movers,sk2) = zero,
inference(resolve,[$cnf( environment(sk1) )],[prove_l8_42,refute_0_87]) ).
cnf(refute_0_89,plain,
( zero != zero
| cardinality_at_time(first_movers,sk2) = zero ),
inference(resolve,[$cnf( $equal(cardinality_at_time(first_movers,sk2),zero) )],[refute_0_88,refute_0_56]) ).
cnf(refute_0_90,plain,
( zero != zero
| ~ environment(sk1)
| ~ subpopulation(efficient_producers,sk1,sk2)
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(resolve,[$cnf( $equal(cardinality_at_time(first_movers,sk2),zero) )],[refute_0_89,refute_0_75]) ).
cnf(refute_0_91,plain,
( ~ environment(sk1)
| ~ subpopulation(efficient_producers,sk1,sk2)
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_59,refute_0_90]) ).
cnf(refute_0_92,plain,
( ~ subpopulation(efficient_producers,sk1,sk2)
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(resolve,[$cnf( environment(sk1) )],[prove_l8_42,refute_0_91]) ).
cnf(refute_0_93,plain,
selection_favors(efficient_producers,first_movers,sk2),
inference(resolve,[$cnf( subpopulation(efficient_producers,sk1,sk2) )],[refute_0_28,refute_0_92]) ).
cnf(refute_0_94,plain,
$false,
inference(resolve,[$cnf( selection_favors(efficient_producers,first_movers,sk2) )],[refute_0_93,prove_l8_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT026-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n027.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 08:48:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.36
% 0.19/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.37
%------------------------------------------------------------------------------