TSTP Solution File: MGT026+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 : Theorem 0.19s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 17
% Syntax : Number of formulae : 158 ( 22 unt; 0 def)
% Number of atoms : 515 ( 109 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 622 ( 265 ~; 301 |; 40 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 166 ( 0 sgn 99 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp1_high_growth_rates,axiom,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T)
& greater(growth_rate(S2,T),growth_rate(S1,T)) )
=> selection_favors(S2,S1,T) ) ).
fof(mp2_favour_members,axiom,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulation(S1,E,T)
& subpopulation(S2,E,T)
& greater(cardinality_at_time(S1,T),zero)
& cardinality_at_time(S2,T) = zero )
=> selection_favors(S1,S2,T) ) ).
fof(mp_non_empty_fm_and_ep,axiom,
! [E,T] :
( ( environment(E)
& in_environment(E,T)
& greater(cardinality_at_time(first_movers,T),zero)
& greater(cardinality_at_time(efficient_producers,T),zero) )
=> subpopulations(first_movers,efficient_producers,E,T) ) ).
fof(mp_first_movers_exist,axiom,
! [E,T] :
( ( environment(E)
& in_environment(E,T) )
=> greater_or_equal(cardinality_at_time(first_movers,T),zero) ) ).
fof(mp_subpopulations,axiom,
! [E,T] :
( ( environment(E)
& in_environment(E,T) )
=> ( subpopulation(first_movers,E,T)
& subpopulation(efficient_producers,E,T) ) ) ).
fof(mp_critical_point_after_EP,axiom,
! [E] :
( environment(E)
=> greater_or_equal(critical_point(E),appear(efficient_producers,E)) ) ).
fof(mp_greater_transitivity,axiom,
! [X,Y,Z] :
( ( greater(X,Y)
& greater(Y,Z) )
=> greater(X,Z) ) ).
fof(mp_greater_or_equal,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( greater(X,Y)
| X = Y ) ) ).
fof(d1,hypothesis,
! [E,Tc] :
( ( environment(E)
& Tc = critical_point(E) )
=> ( ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc))
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater(T,Tc) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ) ).
fof(t6,hypothesis,
! [E,T] :
( ( environment(E)
& in_environment(E,T)
& greater_or_equal(T,appear(efficient_producers,E)) )
=> greater(cardinality_at_time(efficient_producers,T),zero) ) ).
fof(prove_l8,conjecture,
! [E,T] :
( ( environment(E)
& in_environment(E,T)
& greater(T,critical_point(E)) )
=> selection_favors(efficient_producers,first_movers,T) ) ).
fof(subgoal_0,plain,
! [E,T] :
( ( environment(E)
& in_environment(E,T)
& greater(T,critical_point(E)) )
=> selection_favors(efficient_producers,first_movers,T) ),
inference(strip,[],[prove_l8]) ).
fof(negate_0_0,plain,
~ ! [E,T] :
( ( environment(E)
& in_environment(E,T)
& greater(T,critical_point(E)) )
=> selection_favors(efficient_producers,first_movers,T) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [E,T] :
( ~ selection_favors(efficient_producers,first_movers,T)
& environment(E)
& greater(T,critical_point(E))
& in_environment(E,T) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T)
& environment(skolemFOFtoCNF_E)
& greater(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E))
& in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [E,T] :
( ~ environment(E)
| ~ in_environment(E,T)
| ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) ) ),
inference(canonicalize,[],[mp_subpopulations]) ).
fof(normalize_0_4,plain,
! [E,T] :
( ~ environment(E)
| ~ in_environment(E,T)
| ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [E,T] :
( ( ~ environment(E)
| ~ in_environment(E,T)
| subpopulation(efficient_producers,E,T) )
& ( ~ environment(E)
| ~ in_environment(E,T)
| subpopulation(first_movers,E,T) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [E,T] :
( ~ environment(E)
| ~ in_environment(E,T)
| subpopulation(first_movers,E,T) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
environment(skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,plain,
! [E,S1,S2,T] :
( cardinality_at_time(S2,T) != zero
| ~ environment(E)
| ~ greater(cardinality_at_time(S1,T),zero)
| ~ subpopulation(S1,E,T)
| ~ subpopulation(S2,E,T)
| selection_favors(S1,S2,T) ),
inference(canonicalize,[],[mp2_favour_members]) ).
fof(normalize_0_9,plain,
! [E,S1,S2,T] :
( cardinality_at_time(S2,T) != zero
| ~ environment(E)
| ~ greater(cardinality_at_time(S1,T),zero)
| ~ subpopulation(S1,E,T)
| ~ subpopulation(S2,E,T)
| selection_favors(S1,S2,T) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
greater(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ greater_or_equal(X,Y)
<=> ( X != Y
& ~ greater(X,Y) ) ),
inference(canonicalize,[],[mp_greater_or_equal]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ greater_or_equal(X,Y)
<=> ( X != Y
& ~ greater(X,Y) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ( X != Y
| greater_or_equal(X,Y) )
& ( ~ greater(X,Y)
| greater_or_equal(X,Y) )
& ( ~ greater_or_equal(X,Y)
| X = Y
| greater(X,Y) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ greater(X,Y)
| greater_or_equal(X,Y) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [E,T] :
( ~ environment(E)
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ in_environment(E,T)
| greater(cardinality_at_time(efficient_producers,T),zero) ),
inference(canonicalize,[],[t6]) ).
fof(normalize_0_16,plain,
! [E,T] :
( ~ environment(E)
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ in_environment(E,T)
| greater(cardinality_at_time(efficient_producers,T),zero) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [E] :
( ~ environment(E)
| greater_or_equal(critical_point(E),appear(efficient_producers,E)) ),
inference(canonicalize,[],[mp_critical_point_after_EP]) ).
fof(normalize_0_18,plain,
! [E] :
( ~ environment(E)
| greater_or_equal(critical_point(E),appear(efficient_producers,E)) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ greater_or_equal(X,Y)
| X = Y
| greater(X,Y) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_20,plain,
! [X,Y,Z] :
( ~ greater(X,Y)
| ~ greater(Y,Z)
| greater(X,Z) ),
inference(canonicalize,[],[mp_greater_transitivity]) ).
fof(normalize_0_21,plain,
! [X,Y,Z] :
( ~ greater(X,Y)
| ~ greater(Y,Z)
| greater(X,Z) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [E,T] :
( ~ environment(E)
| ~ in_environment(E,T)
| subpopulation(efficient_producers,E,T) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_23,plain,
~ selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_24,plain,
! [E,T] :
( ~ environment(E)
| ~ in_environment(E,T)
| greater_or_equal(cardinality_at_time(first_movers,T),zero) ),
inference(canonicalize,[],[mp_first_movers_exist]) ).
fof(normalize_0_25,plain,
! [E,T] :
( ~ environment(E)
| ~ in_environment(E,T)
| greater_or_equal(cardinality_at_time(first_movers,T),zero) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [E,T] :
( ~ environment(E)
| ~ greater(cardinality_at_time(efficient_producers,T),zero)
| ~ greater(cardinality_at_time(first_movers,T),zero)
| ~ in_environment(E,T)
| subpopulations(first_movers,efficient_producers,E,T) ),
inference(canonicalize,[],[mp_non_empty_fm_and_ep]) ).
fof(normalize_0_27,plain,
! [E,T] :
( ~ environment(E)
| ~ greater(cardinality_at_time(efficient_producers,T),zero)
| ~ greater(cardinality_at_time(first_movers,T),zero)
| ~ in_environment(E,T)
| subpopulations(first_movers,efficient_producers,E,T) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [E,Tc] :
( Tc != critical_point(E)
| ~ environment(E)
| ( ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc))
& ! [T] :
( ~ greater(T,Tc)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
inference(canonicalize,[],[d1]) ).
fof(normalize_0_29,plain,
! [E,Tc] :
( Tc != critical_point(E)
| ~ environment(E)
| ( ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc))
& ! [T] :
( ~ greater(T,Tc)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [E,T,Tc] :
( ( Tc != critical_point(E)
| ~ environment(E)
| ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc)) )
& ( Tc != critical_point(E)
| ~ environment(E)
| ~ greater(T,Tc)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ),
inference(clausify,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [E,T,Tc] :
( Tc != critical_point(E)
| ~ environment(E)
| ~ greater(T,Tc)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ),
inference(conjunct,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ greater(growth_rate(S2,T),growth_rate(S1,T))
| ~ subpopulations(S1,S2,E,T)
| selection_favors(S2,S1,T) ),
inference(canonicalize,[],[mp1_high_growth_rates]) ).
fof(normalize_0_33,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ greater(growth_rate(S2,T),growth_rate(S1,T))
| ~ subpopulations(S1,S2,E,T)
| selection_favors(S2,S1,T) ),
inference(specialize,[],[normalize_0_32]) ).
cnf(refute_0_0,plain,
in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ environment(E)
| ~ in_environment(E,T)
| subpopulation(first_movers,E,T) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| subpopulation(first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_1:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_3,plain,
( ~ environment(skolemFOFtoCNF_E)
| subpopulation(first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
environment(skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
subpopulation(first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( cardinality_at_time(S2,T) != zero
| ~ environment(E)
| ~ greater(cardinality_at_time(S1,T),zero)
| ~ subpopulation(S1,E,T)
| ~ subpopulation(S2,E,T)
| selection_favors(S1,S2,T) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( cardinality_at_time(S2,skolemFOFtoCNF_T) != zero
| ~ environment(E)
| ~ greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T),zero)
| ~ subpopulation(S2,E,skolemFOFtoCNF_T)
| ~ subpopulation(efficient_producers,E,skolemFOFtoCNF_T)
| selection_favors(efficient_producers,S2,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_6:[bind(S1,$fot(efficient_producers)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_8,plain,
greater(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( ~ greater(X,Y)
| greater_or_equal(X,Y) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_10,plain,
( ~ greater(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E))
| greater_or_equal(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_T)),bind(Y,$fot(critical_point(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_11,plain,
greater_or_equal(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E)),
inference(resolve,[$cnf( greater(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E)) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ environment(E)
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ in_environment(E,T)
| greater(cardinality_at_time(efficient_producers,T),zero) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_13,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater_or_equal(T,appear(efficient_producers,skolemFOFtoCNF_E))
| ~ in_environment(skolemFOFtoCNF_E,T)
| greater(cardinality_at_time(efficient_producers,T),zero) ),
inference(subst,[],[refute_0_12:[bind(E,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_14,plain,
( ~ greater(skolemFOFtoCNF_T,appear(efficient_producers,skolemFOFtoCNF_E))
| greater_or_equal(skolemFOFtoCNF_T,appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_T)),bind(Y,$fot(appear(efficient_producers,skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_15,plain,
( ~ environment(E)
| greater_or_equal(critical_point(E),appear(efficient_producers,E)) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_16,plain,
( ~ environment(skolemFOFtoCNF_E)
| greater_or_equal(critical_point(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_15:[bind(E,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_17,plain,
greater_or_equal(critical_point(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ greater_or_equal(X,Y)
| X = Y
| greater(X,Y) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_19,plain,
( ~ greater_or_equal(critical_point(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E))
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| greater(critical_point(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(critical_point(skolemFOFtoCNF_E))),bind(Y,$fot(appear(efficient_producers,skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_20,plain,
( critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| greater(critical_point(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( greater_or_equal(critical_point(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ greater(X,Y)
| ~ greater(Y,Z)
| greater(X,Z) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_22,plain,
( ~ greater(X_13,critical_point(skolemFOFtoCNF_E))
| ~ greater(critical_point(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E))
| greater(X_13,appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(X_13)),bind(Y,$fot(critical_point(skolemFOFtoCNF_E))),bind(Z,$fot(appear(efficient_producers,skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_23,plain,
( ~ greater(X_13,critical_point(skolemFOFtoCNF_E))
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| greater(X_13,appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( greater(critical_point(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ greater(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E))
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| greater(skolemFOFtoCNF_T,appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_23:[bind(X_13,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_25,plain,
( critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| greater(skolemFOFtoCNF_T,appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( greater(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E)) )],[refute_0_8,refute_0_24]) ).
cnf(refute_0_26,plain,
( critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| greater_or_equal(skolemFOFtoCNF_T,appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( greater(skolemFOFtoCNF_T,appear(efficient_producers,skolemFOFtoCNF_E)) )],[refute_0_25,refute_0_14]) ).
cnf(refute_0_27,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater_or_equal(skolemFOFtoCNF_T,appear(efficient_producers,skolemFOFtoCNF_E))
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T),zero) ),
inference(subst,[],[refute_0_12:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_28,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T),zero) ),
inference(resolve,[$cnf( greater_or_equal(skolemFOFtoCNF_T,appear(efficient_producers,skolemFOFtoCNF_E)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T),zero) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_28]) ).
cnf(refute_0_30,plain,
( critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T),zero) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_0,refute_0_29]) ).
cnf(refute_0_31,plain,
( cardinality_at_time(X_47,skolemFOFtoCNF_T) != zero
| ~ environment(X_45)
| ~ greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T),zero)
| ~ subpopulation(X_47,X_45,skolemFOFtoCNF_T)
| ~ subpopulation(efficient_producers,X_45,skolemFOFtoCNF_T)
| selection_favors(efficient_producers,X_47,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_6:[bind(E,$fot(X_45)),bind(S1,$fot(efficient_producers)),bind(S2,$fot(X_47)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_32,plain,
( cardinality_at_time(X_47,skolemFOFtoCNF_T) != zero
| ~ environment(X_45)
| ~ subpopulation(X_47,X_45,skolemFOFtoCNF_T)
| ~ subpopulation(efficient_producers,X_45,skolemFOFtoCNF_T)
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| selection_favors(efficient_producers,X_47,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T),zero) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( cardinality_at_time(first_movers,skolemFOFtoCNF_T) != zero
| ~ environment(skolemFOFtoCNF_E)
| ~ subpopulation(efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| ~ subpopulation(first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_32:[bind(X_45,$fot(skolemFOFtoCNF_E)),bind(X_47,$fot(first_movers))]]) ).
cnf(refute_0_34,plain,
( cardinality_at_time(first_movers,skolemFOFtoCNF_T) != zero
| ~ environment(skolemFOFtoCNF_E)
| ~ subpopulation(efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( subpopulation(first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_5,refute_0_33]) ).
cnf(refute_0_35,plain,
( cardinality_at_time(first_movers,skolemFOFtoCNF_T) != zero
| ~ subpopulation(efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ environment(E)
| ~ in_environment(E,T)
| subpopulation(efficient_producers,E,T) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_37,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| subpopulation(efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_36:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_38,plain,
( ~ environment(skolemFOFtoCNF_E)
| subpopulation(efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_0,refute_0_37]) ).
cnf(refute_0_39,plain,
subpopulation(efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_38]) ).
cnf(refute_0_40,plain,
( cardinality_at_time(first_movers,skolemFOFtoCNF_T) != zero
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( subpopulation(efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_39,refute_0_35]) ).
cnf(refute_0_41,plain,
~ selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_42,plain,
( cardinality_at_time(first_movers,skolemFOFtoCNF_T) != zero
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ greater_or_equal(cardinality_at_time(first_movers,skolemFOFtoCNF_T),zero)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| greater(cardinality_at_time(first_movers,skolemFOFtoCNF_T),zero) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(cardinality_at_time(first_movers,skolemFOFtoCNF_T))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_44,plain,
( ~ environment(E)
| ~ in_environment(E,T)
| greater_or_equal(cardinality_at_time(first_movers,T),zero) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_45,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| greater_or_equal(cardinality_at_time(first_movers,skolemFOFtoCNF_T),zero) ),
inference(subst,[],[refute_0_44:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_46,plain,
( ~ environment(skolemFOFtoCNF_E)
| greater_or_equal(cardinality_at_time(first_movers,skolemFOFtoCNF_T),zero) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_0,refute_0_45]) ).
cnf(refute_0_47,plain,
greater_or_equal(cardinality_at_time(first_movers,skolemFOFtoCNF_T),zero),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_46]) ).
cnf(refute_0_48,plain,
( cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| greater(cardinality_at_time(first_movers,skolemFOFtoCNF_T),zero) ),
inference(resolve,[$cnf( greater_or_equal(cardinality_at_time(first_movers,skolemFOFtoCNF_T),zero) )],[refute_0_47,refute_0_43]) ).
cnf(refute_0_49,plain,
( ~ environment(E)
| ~ greater(cardinality_at_time(efficient_producers,T),zero)
| ~ greater(cardinality_at_time(first_movers,T),zero)
| ~ in_environment(E,T)
| subpopulations(first_movers,efficient_producers,E,T) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_50,plain,
( ~ environment(X_29)
| ~ greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T),zero)
| ~ greater(cardinality_at_time(first_movers,skolemFOFtoCNF_T),zero)
| ~ in_environment(X_29,skolemFOFtoCNF_T)
| subpopulations(first_movers,efficient_producers,X_29,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_49:[bind(E,$fot(X_29)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_51,plain,
( ~ environment(X_29)
| ~ greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T),zero)
| ~ in_environment(X_29,skolemFOFtoCNF_T)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| subpopulations(first_movers,efficient_producers,X_29,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( greater(cardinality_at_time(first_movers,skolemFOFtoCNF_T),zero) )],[refute_0_48,refute_0_50]) ).
cnf(refute_0_52,plain,
( ~ environment(X_31)
| ~ greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T),zero)
| ~ in_environment(X_31,skolemFOFtoCNF_T)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| subpopulations(first_movers,efficient_producers,X_31,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_51:[bind(X_29,$fot(X_31))]]) ).
cnf(refute_0_53,plain,
( ~ environment(X_31)
| ~ in_environment(X_31,skolemFOFtoCNF_T)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| subpopulations(first_movers,efficient_producers,X_31,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T),zero) )],[refute_0_30,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_53:[bind(X_31,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_55,plain,
( ~ environment(skolemFOFtoCNF_E)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_0,refute_0_54]) ).
cnf(refute_0_56,plain,
( cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_55]) ).
cnf(refute_0_57,plain,
( Tc != critical_point(E)
| ~ environment(E)
| ~ greater(T,Tc)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_58,plain,
( critical_point(E) != critical_point(E)
| ~ environment(E)
| ~ greater(T,critical_point(E))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ),
inference(subst,[],[refute_0_57:[bind(Tc,$fot(critical_point(E)))]]) ).
cnf(refute_0_59,plain,
critical_point(E) = critical_point(E),
introduced(tautology,[refl,[$fot(critical_point(E))]]) ).
cnf(refute_0_60,plain,
( ~ environment(E)
| ~ greater(T,critical_point(E))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ),
inference(resolve,[$cnf( $equal(critical_point(E),critical_point(E)) )],[refute_0_59,refute_0_58]) ).
cnf(refute_0_61,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E))
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_T),growth_rate(first_movers,skolemFOFtoCNF_T)) ),
inference(subst,[],[refute_0_60:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_62,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E))
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_T),growth_rate(first_movers,skolemFOFtoCNF_T)) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
( ~ greater(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E))
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_T),growth_rate(first_movers,skolemFOFtoCNF_T)) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_62]) ).
cnf(refute_0_64,plain,
( cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_T),growth_rate(first_movers,skolemFOFtoCNF_T)) ),
inference(resolve,[$cnf( greater(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E)) )],[refute_0_8,refute_0_63]) ).
cnf(refute_0_65,plain,
( ~ environment(E)
| ~ greater(growth_rate(S2,T),growth_rate(S1,T))
| ~ subpopulations(S1,S2,E,T)
| selection_favors(S2,S1,T) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_66,plain,
( ~ environment(X_38)
| ~ greater(growth_rate(efficient_producers,skolemFOFtoCNF_T),growth_rate(first_movers,skolemFOFtoCNF_T))
| ~ subpopulations(first_movers,efficient_producers,X_38,skolemFOFtoCNF_T)
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_65:[bind(E,$fot(X_38)),bind(S1,$fot(first_movers)),bind(S2,$fot(efficient_producers)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_67,plain,
( ~ environment(X_38)
| ~ subpopulations(first_movers,efficient_producers,X_38,skolemFOFtoCNF_T)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E)
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( greater(growth_rate(efficient_producers,skolemFOFtoCNF_T),growth_rate(first_movers,skolemFOFtoCNF_T)) )],[refute_0_64,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ environment(X_38)
| ~ subpopulations(first_movers,efficient_producers,X_38,skolemFOFtoCNF_T)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) )],[refute_0_67,refute_0_41]) ).
cnf(refute_0_69,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_68:[bind(X_38,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_70,plain,
( ~ environment(skolemFOFtoCNF_E)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_56,refute_0_69]) ).
cnf(refute_0_71,plain,
( cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_70]) ).
cnf(refute_0_72,plain,
( cardinality_at_time(first_movers,skolemFOFtoCNF_T) != zero
| zero != zero
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(cardinality_at_time(first_movers,skolemFOFtoCNF_T),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_73,plain,
( zero != zero
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( $equal(cardinality_at_time(first_movers,skolemFOFtoCNF_T),zero) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( zero != zero
| critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( $equal(cardinality_at_time(first_movers,skolemFOFtoCNF_T),zero) )],[refute_0_73,refute_0_42]) ).
cnf(refute_0_75,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_76,plain,
critical_point(skolemFOFtoCNF_E) = appear(efficient_producers,skolemFOFtoCNF_E),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_75,refute_0_74]) ).
cnf(refute_0_77,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_78,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_79,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
( critical_point(skolemFOFtoCNF_E) != appear(efficient_producers,skolemFOFtoCNF_E)
| appear(efficient_producers,skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_79:[bind(X0,$fot(critical_point(skolemFOFtoCNF_E))),bind(Y0,$fot(appear(efficient_producers,skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_81,plain,
appear(efficient_producers,skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E),
inference(resolve,[$cnf( $equal(critical_point(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)) )],[refute_0_76,refute_0_80]) ).
cnf(refute_0_82,plain,
( appear(efficient_producers,skolemFOFtoCNF_E) != critical_point(skolemFOFtoCNF_E)
| ~ greater_or_equal(T,critical_point(skolemFOFtoCNF_E))
| greater_or_equal(T,appear(efficient_producers,skolemFOFtoCNF_E)) ),
introduced(tautology,[equality,[$cnf( ~ greater_or_equal(T,appear(efficient_producers,skolemFOFtoCNF_E)) ),[1],$fot(critical_point(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_83,plain,
( ~ greater_or_equal(T,critical_point(skolemFOFtoCNF_E))
| greater_or_equal(T,appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( $equal(appear(efficient_producers,skolemFOFtoCNF_E),critical_point(skolemFOFtoCNF_E)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater_or_equal(T,critical_point(skolemFOFtoCNF_E))
| ~ in_environment(skolemFOFtoCNF_E,T)
| greater(cardinality_at_time(efficient_producers,T),zero) ),
inference(resolve,[$cnf( greater_or_equal(T,appear(efficient_producers,skolemFOFtoCNF_E)) )],[refute_0_83,refute_0_13]) ).
cnf(refute_0_85,plain,
( ~ greater_or_equal(T,critical_point(skolemFOFtoCNF_E))
| ~ in_environment(skolemFOFtoCNF_E,T)
| greater(cardinality_at_time(efficient_producers,T),zero) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_84]) ).
cnf(refute_0_86,plain,
( ~ greater_or_equal(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E))
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T),zero) ),
inference(subst,[],[refute_0_85:[bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_87,plain,
( ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T),zero) ),
inference(resolve,[$cnf( greater_or_equal(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E)) )],[refute_0_11,refute_0_86]) ).
cnf(refute_0_88,plain,
greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T),zero),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_0,refute_0_87]) ).
cnf(refute_0_89,plain,
( cardinality_at_time(S2,skolemFOFtoCNF_T) != zero
| ~ environment(E)
| ~ subpopulation(S2,E,skolemFOFtoCNF_T)
| ~ subpopulation(efficient_producers,E,skolemFOFtoCNF_T)
| selection_favors(efficient_producers,S2,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T),zero) )],[refute_0_88,refute_0_7]) ).
cnf(refute_0_90,plain,
( cardinality_at_time(first_movers,skolemFOFtoCNF_T) != zero
| ~ environment(skolemFOFtoCNF_E)
| ~ subpopulation(efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| ~ subpopulation(first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_89:[bind(E,$fot(skolemFOFtoCNF_E)),bind(S2,$fot(first_movers))]]) ).
cnf(refute_0_91,plain,
( cardinality_at_time(first_movers,skolemFOFtoCNF_T) != zero
| ~ environment(skolemFOFtoCNF_E)
| ~ subpopulation(efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( subpopulation(first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_5,refute_0_90]) ).
cnf(refute_0_92,plain,
( ~ environment(X_29)
| ~ in_environment(X_29,skolemFOFtoCNF_T)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| subpopulations(first_movers,efficient_producers,X_29,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T),zero) )],[refute_0_88,refute_0_51]) ).
cnf(refute_0_93,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_92:[bind(X_29,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_94,plain,
( ~ environment(skolemFOFtoCNF_E)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_0,refute_0_93]) ).
cnf(refute_0_95,plain,
( cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_94]) ).
cnf(refute_0_96,plain,
( ~ environment(E)
| ~ greater(growth_rate(efficient_producers,skolemFOFtoCNF_T),growth_rate(first_movers,skolemFOFtoCNF_T))
| ~ subpopulations(first_movers,efficient_producers,E,skolemFOFtoCNF_T)
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_65:[bind(S1,$fot(first_movers)),bind(S2,$fot(efficient_producers)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_97,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E))
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_T),growth_rate(first_movers,skolemFOFtoCNF_T)) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_95,refute_0_61]) ).
cnf(refute_0_98,plain,
( ~ greater(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E))
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_T),growth_rate(first_movers,skolemFOFtoCNF_T)) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_97]) ).
cnf(refute_0_99,plain,
( cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_T),growth_rate(first_movers,skolemFOFtoCNF_T)) ),
inference(resolve,[$cnf( greater(skolemFOFtoCNF_T,critical_point(skolemFOFtoCNF_E)) )],[refute_0_8,refute_0_98]) ).
cnf(refute_0_100,plain,
( ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,skolemFOFtoCNF_T)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( greater(growth_rate(efficient_producers,skolemFOFtoCNF_T),growth_rate(first_movers,skolemFOFtoCNF_T)) )],[refute_0_99,refute_0_96]) ).
cnf(refute_0_101,plain,
( ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,skolemFOFtoCNF_T)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero ),
inference(resolve,[$cnf( selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) )],[refute_0_100,refute_0_41]) ).
cnf(refute_0_102,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero ),
inference(subst,[],[refute_0_101:[bind(E,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_103,plain,
( ~ environment(skolemFOFtoCNF_E)
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_95,refute_0_102]) ).
cnf(refute_0_104,plain,
cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero,
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_103]) ).
cnf(refute_0_105,plain,
( zero != zero
| cardinality_at_time(first_movers,skolemFOFtoCNF_T) = zero ),
inference(resolve,[$cnf( $equal(cardinality_at_time(first_movers,skolemFOFtoCNF_T),zero) )],[refute_0_104,refute_0_72]) ).
cnf(refute_0_106,plain,
( zero != zero
| ~ environment(skolemFOFtoCNF_E)
| ~ subpopulation(efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( $equal(cardinality_at_time(first_movers,skolemFOFtoCNF_T),zero) )],[refute_0_105,refute_0_91]) ).
cnf(refute_0_107,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ subpopulation(efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_75,refute_0_106]) ).
cnf(refute_0_108,plain,
( ~ subpopulation(efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_107]) ).
cnf(refute_0_109,plain,
selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T),
inference(resolve,[$cnf( subpopulation(efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_39,refute_0_108]) ).
cnf(refute_0_110,plain,
$false,
inference(resolve,[$cnf( selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T) )],[refute_0_109,refute_0_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n021.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 12:36:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.36
% 0.19/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.38
%------------------------------------------------------------------------------