TSTP Solution File: MGT023+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT023+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 22:18:55 EDT 2022
% Result : Theorem 0.21s 0.35s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 4
% Syntax : Number of formulae : 63 ( 10 unt; 0 def)
% Number of atoms : 238 ( 36 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 286 ( 111 ~; 141 |; 27 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 30 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1,hypothesis,
! [E,To] :
( ( environment(E)
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater(T,To) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) )
=> To = critical_point(E) ) ).
fof(l12,hypothesis,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( in_environment(E,To)
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater(T,To) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ) ).
fof(prove_l5,conjecture,
! [E] :
( ( environment(E)
& stable(E) )
=> in_environment(E,critical_point(E)) ) ).
fof(subgoal_0,plain,
! [E] :
( ( environment(E)
& stable(E) )
=> in_environment(E,critical_point(E)) ),
inference(strip,[],[prove_l5]) ).
fof(negate_0_0,plain,
~ ! [E] :
( ( environment(E)
& stable(E) )
=> in_environment(E,critical_point(E)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [E] :
( ~ in_environment(E,critical_point(E))
& environment(E)
& stable(E) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ in_environment(skolemFOFtoCNF_E,critical_point(skolemFOFtoCNF_E))
& environment(skolemFOFtoCNF_E)
& stable(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(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To)
& ! [T] :
( ~ greater(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
inference(canonicalize,[],[l12]) ).
fof(normalize_0_4,plain,
! [E] :
( ~ environment(E)
| ~ stable(E)
| ? [To] :
( ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To)
& ! [T] :
( ~ greater(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [E,T] :
( ( ~ environment(E)
| ~ greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(E)),growth_rate(first_movers,skolemFOFtoCNF_To(E)))
| ~ stable(E) )
& ( ~ environment(E)
| ~ stable(E)
| in_environment(E,skolemFOFtoCNF_To(E)) )
& ( ~ environment(E)
| ~ greater(T,skolemFOFtoCNF_To(E))
| ~ stable(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [E] :
( ~ environment(E)
| ~ stable(E)
| in_environment(E,skolemFOFtoCNF_To(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)
| ~ greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(E)),growth_rate(first_movers,skolemFOFtoCNF_To(E)))
| ~ stable(E) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_9,plain,
! [E,To] :
( ~ environment(E)
| ~ in_environment(E,To)
| To = critical_point(E)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ? [T] :
( ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
& greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) ) ),
inference(canonicalize,[],[d1]) ).
fof(normalize_0_10,plain,
! [E,To] :
( ~ environment(E)
| ~ in_environment(E,To)
| To = critical_point(E)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ? [T] :
( ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
& greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [E,To] :
( ( ~ environment(E)
| ~ greater(growth_rate(efficient_producers,skolemFOFtoCNF_T(E,To)),growth_rate(first_movers,skolemFOFtoCNF_T(E,To)))
| ~ in_environment(E,To)
| To = critical_point(E)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To)) )
& ( ~ environment(E)
| ~ in_environment(E,To)
| To = critical_point(E)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| greater(skolemFOFtoCNF_T(E,To),To) )
& ( ~ environment(E)
| ~ in_environment(E,To)
| To = critical_point(E)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| subpopulations(first_movers,efficient_producers,E,skolemFOFtoCNF_T(E,To)) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [E,To] :
( ~ environment(E)
| ~ in_environment(E,To)
| To = critical_point(E)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| greater(skolemFOFtoCNF_T(E,To),To) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [E,T] :
( ~ environment(E)
| ~ greater(T,skolemFOFtoCNF_To(E))
| ~ stable(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_14,plain,
! [E,To] :
( ~ environment(E)
| ~ in_environment(E,To)
| To = critical_point(E)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| subpopulations(first_movers,efficient_producers,E,skolemFOFtoCNF_T(E,To)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_15,plain,
! [E,To] :
( ~ environment(E)
| ~ greater(growth_rate(efficient_producers,skolemFOFtoCNF_T(E,To)),growth_rate(first_movers,skolemFOFtoCNF_T(E,To)))
| ~ in_environment(E,To)
| To = critical_point(E)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_16,plain,
~ in_environment(skolemFOFtoCNF_E,critical_point(skolemFOFtoCNF_E)),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
stable(skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ environment(E)
| ~ stable(E)
| in_environment(E,skolemFOFtoCNF_To(E)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ stable(skolemFOFtoCNF_E)
| in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_1:[bind(E,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_3,plain,
( ~ environment(skolemFOFtoCNF_E)
| in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(resolve,[$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,
in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ environment(E)
| ~ greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(E)),growth_rate(first_movers,skolemFOFtoCNF_To(E)))
| ~ stable(E) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| ~ stable(skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_6:[bind(E,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_8,plain,
( ~ environment(E)
| ~ in_environment(E,To)
| To = critical_point(E)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| greater(skolemFOFtoCNF_T(E,To),To) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_9,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| greater(skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_8:[bind(E,$fot(skolemFOFtoCNF_E)),bind(To,$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_10,plain,
( ~ environment(skolemFOFtoCNF_E)
| skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| greater(skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| greater(skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ stable(skolemFOFtoCNF_E)
| skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) )],[refute_0_11,refute_0_7]) ).
cnf(refute_0_13,plain,
( ~ stable(skolemFOFtoCNF_E)
| skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
( skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( stable(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ environment(E)
| ~ greater(T,skolemFOFtoCNF_To(E))
| ~ stable(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_16,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater(skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))),growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),
inference(subst,[],[refute_0_15:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))))]]) ).
cnf(refute_0_17,plain,
( ~ environment(E)
| ~ in_environment(E,To)
| To = critical_point(E)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| subpopulations(first_movers,efficient_producers,E,skolemFOFtoCNF_T(E,To)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_18,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(subst,[],[refute_0_17:[bind(E,$fot(skolemFOFtoCNF_E)),bind(To,$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_19,plain,
( ~ environment(skolemFOFtoCNF_E)
| skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_5,refute_0_18]) ).
cnf(refute_0_20,plain,
( skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ stable(skolemFOFtoCNF_E)
| skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) )],[refute_0_20,refute_0_7]) ).
cnf(refute_0_22,plain,
( ~ stable(skolemFOFtoCNF_E)
| skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_21]) ).
cnf(refute_0_23,plain,
( skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( stable(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater(skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))),growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) )],[refute_0_23,refute_0_16]) ).
cnf(refute_0_25,plain,
( ~ greater(skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))),growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ greater(skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))),growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),
inference(resolve,[$cnf( stable(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_25]) ).
cnf(refute_0_27,plain,
( skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))),growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),
inference(resolve,[$cnf( greater(skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_14,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ environment(E)
| ~ greater(growth_rate(efficient_producers,skolemFOFtoCNF_T(E,To)),growth_rate(first_movers,skolemFOFtoCNF_T(E,To)))
| ~ in_environment(E,To)
| To = critical_point(E)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To)) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_29,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater(growth_rate(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))),growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))))
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),growth_rate(first_movers,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)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( greater(growth_rate(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))),growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) )],[refute_0_27,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_30]) ).
cnf(refute_0_32,plain,
( skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_5,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ stable(skolemFOFtoCNF_E)
| skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( greater(growth_rate(efficient_producers,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),growth_rate(first_movers,skolemFOFtoCNF_To(skolemFOFtoCNF_E))) )],[refute_0_32,refute_0_7]) ).
cnf(refute_0_34,plain,
( ~ stable(skolemFOFtoCNF_E)
| skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_33]) ).
cnf(refute_0_35,plain,
skolemFOFtoCNF_To(skolemFOFtoCNF_E) = critical_point(skolemFOFtoCNF_E),
inference(resolve,[$cnf( stable(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_34]) ).
cnf(refute_0_36,plain,
( skolemFOFtoCNF_To(skolemFOFtoCNF_E) != critical_point(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| in_environment(skolemFOFtoCNF_E,critical_point(skolemFOFtoCNF_E)) ),
introduced(tautology,[equality,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),[1],$fot(critical_point(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_37,plain,
( ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| in_environment(skolemFOFtoCNF_E,critical_point(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_To(skolemFOFtoCNF_E),critical_point(skolemFOFtoCNF_E)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
in_environment(skolemFOFtoCNF_E,critical_point(skolemFOFtoCNF_E)),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_5,refute_0_37]) ).
cnf(refute_0_39,plain,
~ in_environment(skolemFOFtoCNF_E,critical_point(skolemFOFtoCNF_E)),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_40,plain,
$false,
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,critical_point(skolemFOFtoCNF_E)) )],[refute_0_38,refute_0_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT023+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jun 9 09:50:12 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.35
% 0.21/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.36
%------------------------------------------------------------------------------