TSTP Solution File: MGT027+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT027+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 16
% Syntax : Number of formulae : 158 ( 22 unt; 0 def)
% Number of atoms : 514 ( 44 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 641 ( 285 ~; 301 |; 40 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 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 : 143 ( 0 sgn 80 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_contracts_from,axiom,
! [E,To] :
( ( environment(E)
& stable(E)
& in_environment(E,To)
& ! [T] :
( ( greater(cardinality_at_time(first_movers,T),zero)
& greater_or_equal(T,To) )
=> greater(zero,growth_rate(first_movers,T)) ) )
=> contracts_from(To,first_movers) ) ).
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_long_stable_environments,axiom,
! [E,T1,T2] :
( ( environment(E)
& stable(E)
& in_environment(E,T1)
& greater(T2,T1) )
=> in_environment(E,T2) ) ).
fof(mp_EP_in_stable_environments,axiom,
! [E] :
( ( environment(E)
& stable(E) )
=> in_environment(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(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(l10,hypothesis,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( greater(To,appear(efficient_producers,E))
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> greater(zero,growth_rate(first_movers,T)) ) ) ) ).
fof(prove_l9,conjecture,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( greater(To,appear(efficient_producers,E))
& contracts_from(To,first_movers) ) ) ).
fof(subgoal_0,plain,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( greater(To,appear(efficient_producers,E))
& contracts_from(To,first_movers) ) ),
inference(strip,[],[prove_l9]) ).
fof(negate_0_0,plain,
~ ! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( greater(To,appear(efficient_producers,E))
& contracts_from(To,first_movers) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [E] :
( environment(E)
& stable(E)
& ! [To] :
( ~ contracts_from(To,first_movers)
| ~ greater(To,appear(efficient_producers,E)) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( environment(skolemFOFtoCNF_E)
& stable(skolemFOFtoCNF_E)
& ! [To] :
( ~ contracts_from(To,first_movers)
| ~ greater(To,appear(efficient_producers,skolemFOFtoCNF_E)) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
stable(skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [E] :
( ~ environment(E)
| ~ stable(E)
| ? [To] :
( greater(To,appear(efficient_producers,E))
& ! [T] :
( ~ greater_or_equal(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(zero,growth_rate(first_movers,T)) ) ) ),
inference(canonicalize,[],[l10]) ).
fof(normalize_0_4,plain,
! [E] :
( ~ environment(E)
| ~ stable(E)
| ? [To] :
( greater(To,appear(efficient_producers,E))
& ! [T] :
( ~ greater_or_equal(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(zero,growth_rate(first_movers,T)) ) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [E,T] :
( ( ~ environment(E)
| ~ stable(E)
| greater(skolemFOFtoCNF_To(E),appear(efficient_producers,E)) )
& ( ~ environment(E)
| ~ greater_or_equal(T,skolemFOFtoCNF_To(E))
| ~ stable(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(zero,growth_rate(first_movers,T)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [E] :
( ~ environment(E)
| ~ stable(E)
| greater(skolemFOFtoCNF_To(E),appear(efficient_producers,E)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
environment(skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,plain,
! [E] :
( ~ environment(E)
| ~ stable(E)
| in_environment(E,appear(efficient_producers,E)) ),
inference(canonicalize,[],[mp_EP_in_stable_environments]) ).
fof(normalize_0_9,plain,
! [E] :
( ~ environment(E)
| ~ stable(E)
| in_environment(E,appear(efficient_producers,E)) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [E,T1,T2] :
( ~ environment(E)
| ~ greater(T2,T1)
| ~ in_environment(E,T1)
| ~ stable(E)
| in_environment(E,T2) ),
inference(canonicalize,[],[mp_long_stable_environments]) ).
fof(normalize_0_11,plain,
! [E,T1,T2] :
( ~ environment(E)
| ~ greater(T2,T1)
| ~ in_environment(E,T1)
| ~ stable(E)
| in_environment(E,T2) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [E,To] :
( ~ environment(E)
| ~ in_environment(E,To)
| ~ stable(E)
| contracts_from(To,first_movers)
| ? [T] :
( ~ greater(zero,growth_rate(first_movers,T))
& greater(cardinality_at_time(first_movers,T),zero)
& greater_or_equal(T,To) ) ),
inference(canonicalize,[],[mp_contracts_from]) ).
fof(normalize_0_13,plain,
! [E,To] :
( ~ environment(E)
| ~ in_environment(E,To)
| ~ stable(E)
| contracts_from(To,first_movers)
| ? [T] :
( ~ greater(zero,growth_rate(first_movers,T))
& greater(cardinality_at_time(first_movers,T),zero)
& greater_or_equal(T,To) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [E,To] :
( ( ~ environment(E)
| ~ greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T(To)))
| ~ in_environment(E,To)
| ~ stable(E)
| contracts_from(To,first_movers) )
& ( ~ environment(E)
| ~ in_environment(E,To)
| ~ stable(E)
| contracts_from(To,first_movers)
| greater(cardinality_at_time(first_movers,skolemFOFtoCNF_T(To)),zero) )
& ( ~ environment(E)
| ~ in_environment(E,To)
| ~ stable(E)
| contracts_from(To,first_movers)
| greater_or_equal(skolemFOFtoCNF_T(To),To) ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [E,To] :
( ~ environment(E)
| ~ greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T(To)))
| ~ in_environment(E,To)
| ~ stable(E)
| contracts_from(To,first_movers) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [E,T] :
( ~ environment(E)
| ~ greater_or_equal(T,skolemFOFtoCNF_To(E))
| ~ stable(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(zero,growth_rate(first_movers,T)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_17,plain,
! [X,Y,Z] :
( ~ greater(X,Y)
| ~ greater(Y,Z)
| greater(X,Z) ),
inference(canonicalize,[],[mp_greater_transitivity]) ).
fof(normalize_0_18,plain,
! [X,Y,Z] :
( ~ greater(X,Y)
| ~ greater(Y,Z)
| greater(X,Z) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ greater_or_equal(X,Y)
<=> ( X != Y
& ~ greater(X,Y) ) ),
inference(canonicalize,[],[mp_greater_or_equal]) ).
fof(normalize_0_20,plain,
! [X,Y] :
( ~ greater_or_equal(X,Y)
<=> ( X != Y
& ~ greater(X,Y) ) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,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_20]) ).
fof(normalize_0_22,plain,
! [X,Y] :
( ~ greater_or_equal(X,Y)
| X = Y
| greater(X,Y) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [E,To] :
( ~ environment(E)
| ~ in_environment(E,To)
| ~ stable(E)
| contracts_from(To,first_movers)
| greater_or_equal(skolemFOFtoCNF_T(To),To) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_24,plain,
! [To] :
( ~ contracts_from(To,first_movers)
| ~ greater(To,appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_25,plain,
! [To] :
( ~ contracts_from(To,first_movers)
| ~ greater(To,appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,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_27,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_26]) ).
fof(normalize_0_28,plain,
! [X,Y] :
( ~ greater(X,Y)
| greater_or_equal(X,Y) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_29,plain,
! [E,To] :
( ~ environment(E)
| ~ in_environment(E,To)
| ~ stable(E)
| contracts_from(To,first_movers)
| greater(cardinality_at_time(first_movers,skolemFOFtoCNF_T(To)),zero) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_30,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_31,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_30]) ).
fof(normalize_0_32,plain,
! [X,Y] :
( X != Y
| greater_or_equal(X,Y) ),
inference(conjunct,[],[normalize_0_21]) ).
cnf(refute_0_0,plain,
stable(skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ environment(E)
| ~ stable(E)
| greater(skolemFOFtoCNF_To(E),appear(efficient_producers,E)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ stable(skolemFOFtoCNF_E)
| greater(skolemFOFtoCNF_To(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_1:[bind(E,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_3,plain,
( ~ environment(skolemFOFtoCNF_E)
| greater(skolemFOFtoCNF_To(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( stable(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
environment(skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
greater(skolemFOFtoCNF_To(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ environment(E)
| ~ stable(E)
| in_environment(E,appear(efficient_producers,E)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ stable(skolemFOFtoCNF_E)
| in_environment(skolemFOFtoCNF_E,appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_6:[bind(E,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_8,plain,
( ~ environment(skolemFOFtoCNF_E)
| in_environment(skolemFOFtoCNF_E,appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( stable(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_7]) ).
cnf(refute_0_9,plain,
in_environment(skolemFOFtoCNF_E,appear(efficient_producers,skolemFOFtoCNF_E)),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ environment(E)
| ~ greater(T2,T1)
| ~ in_environment(E,T1)
| ~ stable(E)
| in_environment(E,T2) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater(X_28,appear(efficient_producers,skolemFOFtoCNF_E))
| ~ in_environment(skolemFOFtoCNF_E,appear(efficient_producers,skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| in_environment(skolemFOFtoCNF_E,X_28) ),
inference(subst,[],[refute_0_10:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T1,$fot(appear(efficient_producers,skolemFOFtoCNF_E))),bind(T2,$fot(X_28))]]) ).
cnf(refute_0_12,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater(X_28,appear(efficient_producers,skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| in_environment(skolemFOFtoCNF_E,X_28) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,appear(efficient_producers,skolemFOFtoCNF_E)) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ greater(X_28,appear(efficient_producers,skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| in_environment(skolemFOFtoCNF_E,X_28) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ greater(X_28,appear(efficient_producers,skolemFOFtoCNF_E))
| in_environment(skolemFOFtoCNF_E,X_28) ),
inference(resolve,[$cnf( stable(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ greater(skolemFOFtoCNF_To(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E))
| in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_14:[bind(X_28,$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_16,plain,
in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),
inference(resolve,[$cnf( greater(skolemFOFtoCNF_To(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)) )],[refute_0_5,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ environment(E)
| ~ greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T(To)))
| ~ in_environment(E,To)
| ~ stable(E)
| contracts_from(To,first_movers) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_18,plain,
( ~ environment(E)
| ~ greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))))
| ~ in_environment(E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(E)
| contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers) ),
inference(subst,[],[refute_0_17:[bind(To,$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_19,plain,
( ~ environment(E)
| ~ greater_or_equal(T,skolemFOFtoCNF_To(E))
| ~ stable(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(zero,growth_rate(first_movers,T)) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_20,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),
inference(subst,[],[refute_0_19:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))))]]) ).
cnf(refute_0_21,plain,
( ~ greater(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),appear(efficient_producers,skolemFOFtoCNF_E))
| in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(subst,[],[refute_0_14:[bind(X_28,$fot(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))))]]) ).
cnf(refute_0_22,plain,
( ~ greater(X,Y)
| ~ greater(Y,Z)
| greater(X,Z) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_23,plain,
( ~ greater(X_8,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ greater(skolemFOFtoCNF_To(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E))
| greater(X_8,appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(X_8)),bind(Y,$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),bind(Z,$fot(appear(efficient_producers,skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_24,plain,
( ~ greater(X_8,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| greater(X_8,appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( greater(skolemFOFtoCNF_To(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)) )],[refute_0_5,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ greater(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| greater(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_24:[bind(X_8,$fot(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))))]]) ).
cnf(refute_0_26,plain,
( ~ greater_or_equal(X,Y)
| X = Y
| greater(X,Y) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_27,plain,
( ~ greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| greater(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))),bind(Y,$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_28,plain,
( ~ environment(E)
| ~ in_environment(E,To)
| ~ stable(E)
| contracts_from(To,first_movers)
| greater_or_equal(skolemFOFtoCNF_T(To),To) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_29,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers)
| greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_28:[bind(E,$fot(skolemFOFtoCNF_E)),bind(To,$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_30,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ stable(skolemFOFtoCNF_E)
| contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers)
| greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_16,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ stable(skolemFOFtoCNF_E)
| contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers)
| greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_30]) ).
cnf(refute_0_32,plain,
( contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers)
| greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( stable(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ contracts_from(To,first_movers)
| ~ greater(To,appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_34,plain,
( ~ contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers)
| ~ greater(skolemFOFtoCNF_To(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_33:[bind(To,$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_35,plain,
~ contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers),
inference(resolve,[$cnf( greater(skolemFOFtoCNF_To(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)) )],[refute_0_5,refute_0_34]) ).
cnf(refute_0_36,plain,
greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)),
inference(resolve,[$cnf( contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
( skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| greater(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_36,refute_0_27]) ).
cnf(refute_0_38,plain,
( skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| greater(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( greater(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_37,refute_0_25]) ).
cnf(refute_0_39,plain,
( skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( greater(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),appear(efficient_producers,skolemFOFtoCNF_E)) )],[refute_0_38,refute_0_21]) ).
cnf(refute_0_40,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_27]) ).
cnf(refute_0_41,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),appear(efficient_producers,skolemFOFtoCNF_E))
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero) ),
inference(subst,[],[refute_0_40:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))))]]) ).
cnf(refute_0_42,plain,
( ~ greater(X,Y)
| greater_or_equal(X,Y) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_43,plain,
( ~ greater(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),appear(efficient_producers,skolemFOFtoCNF_E))
| greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_42:[bind(X,$fot(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))),bind(Y,$fot(appear(efficient_producers,skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_44,plain,
( skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( greater(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),appear(efficient_producers,skolemFOFtoCNF_E)) )],[refute_0_38,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero) ),
inference(resolve,[$cnf( greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),appear(efficient_producers,skolemFOFtoCNF_E)) )],[refute_0_44,refute_0_41]) ).
cnf(refute_0_46,plain,
( ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_45]) ).
cnf(refute_0_47,plain,
( skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) )],[refute_0_39,refute_0_46]) ).
cnf(refute_0_48,plain,
( ~ environment(E)
| ~ in_environment(E,To)
| ~ stable(E)
| contracts_from(To,first_movers)
| greater(cardinality_at_time(first_movers,skolemFOFtoCNF_T(To)),zero) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_49,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers)
| greater(cardinality_at_time(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero) ),
inference(subst,[],[refute_0_48:[bind(E,$fot(skolemFOFtoCNF_E)),bind(To,$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_50,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ stable(skolemFOFtoCNF_E)
| contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers)
| greater(cardinality_at_time(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_16,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ stable(skolemFOFtoCNF_E)
| contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers)
| greater(cardinality_at_time(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_50]) ).
cnf(refute_0_52,plain,
( contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers)
| greater(cardinality_at_time(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero) ),
inference(resolve,[$cnf( stable(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_51]) ).
cnf(refute_0_53,plain,
greater(cardinality_at_time(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero),
inference(resolve,[$cnf( contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers) )],[refute_0_52,refute_0_35]) ).
cnf(refute_0_54,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_31]) ).
cnf(refute_0_55,plain,
( ~ environment(X_45)
| ~ greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero)
| ~ greater(cardinality_at_time(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero)
| ~ in_environment(X_45,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| subpopulations(first_movers,efficient_producers,X_45,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(subst,[],[refute_0_54:[bind(E,$fot(X_45)),bind(T,$fot(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))))]]) ).
cnf(refute_0_56,plain,
( ~ environment(X_45)
| ~ greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero)
| ~ in_environment(X_45,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| subpopulations(first_movers,efficient_producers,X_45,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( greater(cardinality_at_time(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero) )],[refute_0_53,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ environment(X_47)
| ~ greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero)
| ~ in_environment(X_47,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| subpopulations(first_movers,efficient_producers,X_47,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(subst,[],[refute_0_56:[bind(X_45,$fot(X_47))]]) ).
cnf(refute_0_58,plain,
( ~ environment(X_47)
| ~ in_environment(X_47,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| subpopulations(first_movers,efficient_producers,X_47,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero) )],[refute_0_47,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(subst,[],[refute_0_58:[bind(X_47,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_60,plain,
( ~ environment(skolemFOFtoCNF_E)
| skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) )],[refute_0_39,refute_0_59]) ).
cnf(refute_0_61,plain,
( skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) )],[refute_0_61,refute_0_20]) ).
cnf(refute_0_63,plain,
( ~ greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_62]) ).
cnf(refute_0_64,plain,
( ~ stable(skolemFOFtoCNF_E)
| skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),
inference(resolve,[$cnf( greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_36,refute_0_63]) ).
cnf(refute_0_65,plain,
( skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),
inference(resolve,[$cnf( stable(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_64]) ).
cnf(refute_0_66,plain,
( ~ environment(E)
| ~ in_environment(E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(E)
| skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers) ),
inference(resolve,[$cnf( greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) )],[refute_0_65,refute_0_18]) ).
cnf(refute_0_67,plain,
( ~ environment(E)
| ~ in_environment(E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(E)
| skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers) )],[refute_0_66,refute_0_35]) ).
cnf(refute_0_68,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_67:[bind(E,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_69,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ stable(skolemFOFtoCNF_E)
| skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_16,refute_0_68]) ).
cnf(refute_0_70,plain,
( ~ stable(skolemFOFtoCNF_E)
| skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_69]) ).
cnf(refute_0_71,plain,
skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) = skolemFOFtoCNF_To(skolemFOFtoCNF_E),
inference(resolve,[$cnf( stable(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_70]) ).
cnf(refute_0_72,plain,
( skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) != skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| ~ greater(zero,growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),
introduced(tautology,[equality,[$cnf( ~ greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),[1,1],$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_73,plain,
( ~ greater(zero,growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( ~ environment(E)
| ~ greater(zero,growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| ~ in_environment(E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(E)
| contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers) ),
inference(resolve,[$cnf( greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) )],[refute_0_73,refute_0_18]) ).
cnf(refute_0_75,plain,
( ~ environment(E)
| ~ greater(zero,growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| ~ in_environment(E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(E) ),
inference(resolve,[$cnf( contracts_from(skolemFOFtoCNF_To(skolemFOFtoCNF_E),first_movers) )],[refute_0_74,refute_0_35]) ).
cnf(refute_0_76,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater_or_equal(skolemFOFtoCNF_To(skolemFOFtoCNF_E),skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| greater(zero,growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(subst,[],[refute_0_19:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_77,plain,
cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) = cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),
introduced(tautology,[refl,[$fot(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))))]]) ).
cnf(refute_0_78,plain,
( cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) != cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) != skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) = cardinality_at_time(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
introduced(tautology,[equality,[$cnf( $equal(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),[1,1],$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_79,plain,
( skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) != skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) = cardinality_at_time(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( $equal(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) = cardinality_at_time(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_71,refute_0_79]) ).
cnf(refute_0_81,plain,
( cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) != cardinality_at_time(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),zero)
| greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero) ),
introduced(tautology,[equality,[$cnf( ~ greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero) ),[0],$fot(cardinality_at_time(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_82,plain,
( ~ greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),zero)
| greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero) ),
inference(resolve,[$cnf( $equal(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),cardinality_at_time(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
( ~ environment(X_45)
| ~ greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),zero)
| ~ in_environment(X_45,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| subpopulations(first_movers,efficient_producers,X_45,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),zero) )],[refute_0_82,refute_0_56]) ).
cnf(refute_0_84,plain,
( skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) != skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| ~ in_environment(X_45,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| in_environment(X_45,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
introduced(tautology,[equality,[$cnf( ~ in_environment(X_45,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),[1],$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_85,plain,
( ~ in_environment(X_45,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| in_environment(X_45,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_71,refute_0_84]) ).
cnf(refute_0_86,plain,
( ~ environment(X_45)
| ~ greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),zero)
| ~ in_environment(X_45,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| subpopulations(first_movers,efficient_producers,X_45,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( in_environment(X_45,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) )],[refute_0_85,refute_0_83]) ).
cnf(refute_0_87,plain,
( skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)) != skolemFOFtoCNF_To(skolemFOFtoCNF_E)
| ~ subpopulations(first_movers,efficient_producers,X_45,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| subpopulations(first_movers,efficient_producers,X_45,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
introduced(tautology,[equality,[$cnf( subpopulations(first_movers,efficient_producers,X_45,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),[3],$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_88,plain,
( ~ subpopulations(first_movers,efficient_producers,X_45,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| subpopulations(first_movers,efficient_producers,X_45,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_71,refute_0_87]) ).
cnf(refute_0_89,plain,
( ~ environment(X_45)
| ~ greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),zero)
| ~ in_environment(X_45,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| subpopulations(first_movers,efficient_producers,X_45,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,X_45,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) )],[refute_0_86,refute_0_88]) ).
cnf(refute_0_90,plain,
( ~ greater(skolemFOFtoCNF_To(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E))
| greater_or_equal(skolemFOFtoCNF_To(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_42:[bind(X,$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),bind(Y,$fot(appear(efficient_producers,skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_91,plain,
greater_or_equal(skolemFOFtoCNF_To(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)),
inference(resolve,[$cnf( greater(skolemFOFtoCNF_To(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)) )],[refute_0_5,refute_0_90]) ).
cnf(refute_0_92,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater_or_equal(skolemFOFtoCNF_To(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E))
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),zero) ),
inference(subst,[],[refute_0_40:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_93,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),zero) ),
inference(resolve,[$cnf( greater_or_equal(skolemFOFtoCNF_To(skolemFOFtoCNF_E),appear(efficient_producers,skolemFOFtoCNF_E)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
( ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),zero) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_93]) ).
cnf(refute_0_95,plain,
greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),zero),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_16,refute_0_94]) ).
cnf(refute_0_96,plain,
( ~ environment(X_45)
| ~ in_environment(X_45,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| subpopulations(first_movers,efficient_producers,X_45,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( greater(cardinality_at_time(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),zero) )],[refute_0_95,refute_0_89]) ).
cnf(refute_0_97,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_96:[bind(X_45,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_98,plain,
( ~ environment(skolemFOFtoCNF_E)
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_16,refute_0_97]) ).
cnf(refute_0_99,plain,
subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_98]) ).
cnf(refute_0_100,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater_or_equal(skolemFOFtoCNF_To(skolemFOFtoCNF_E),skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| greater(zero,growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_99,refute_0_76]) ).
cnf(refute_0_101,plain,
( ~ greater_or_equal(skolemFOFtoCNF_To(skolemFOFtoCNF_E),skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| greater(zero,growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_100]) ).
cnf(refute_0_102,plain,
( X != Y
| greater_or_equal(X,Y) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_103,plain,
( Y != Y
| greater_or_equal(Y,Y) ),
inference(subst,[],[refute_0_102:[bind(X,$fot(Y))]]) ).
cnf(refute_0_104,plain,
Y = Y,
introduced(tautology,[refl,[$fot(Y)]]) ).
cnf(refute_0_105,plain,
greater_or_equal(Y,Y),
inference(resolve,[$cnf( $equal(Y,Y) )],[refute_0_104,refute_0_103]) ).
cnf(refute_0_106,plain,
greater_or_equal(skolemFOFtoCNF_To(skolemFOFtoCNF_E),skolemFOFtoCNF_To(skolemFOFtoCNF_E)),
inference(subst,[],[refute_0_105:[bind(Y,$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_107,plain,
( ~ stable(skolemFOFtoCNF_E)
| greater(zero,growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( greater_or_equal(skolemFOFtoCNF_To(skolemFOFtoCNF_E),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_106,refute_0_101]) ).
cnf(refute_0_108,plain,
greater(zero,growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E))),
inference(resolve,[$cnf( stable(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_107]) ).
cnf(refute_0_109,plain,
( ~ environment(E)
| ~ in_environment(E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(E) ),
inference(resolve,[$cnf( greater(zero,growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) )],[refute_0_108,refute_0_75]) ).
cnf(refute_0_110,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_109:[bind(E,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_111,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ stable(skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_16,refute_0_110]) ).
cnf(refute_0_112,plain,
~ stable(skolemFOFtoCNF_E),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_111]) ).
cnf(refute_0_113,plain,
$false,
inference(resolve,[$cnf( stable(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : MGT027+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n029.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 11:52:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Theorem 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
% 0.18/0.39
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