TSTP Solution File: MGT032+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT032+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 22:19:20 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 50 ( 11 unt; 0 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 194 ( 82 ~; 72 |; 31 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 37 !; 11 ?)
% 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(l1,hypothesis,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ) ).
fof(prove_t1,conjecture,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> selection_favors(efficient_producers,first_movers,T) ) ) ) ).
fof(subgoal_0,plain,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> selection_favors(efficient_producers,first_movers,T) ) ) ),
inference(strip,[],[prove_t1]) ).
fof(negate_0_0,plain,
~ ! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> selection_favors(efficient_producers,first_movers,T) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [E] :
( environment(E)
& stable(E)
& ! [To] :
( ~ in_environment(E,To)
| ? [T] :
( ~ selection_favors(efficient_producers,first_movers,T)
& greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( environment(skolemFOFtoCNF_E)
& stable(skolemFOFtoCNF_E)
& ! [To] :
( ~ in_environment(skolemFOFtoCNF_E,To)
| ? [T] :
( ~ selection_favors(efficient_producers,first_movers,T)
& greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,T) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [To] :
( ~ in_environment(skolemFOFtoCNF_E,To)
| ? [T] :
( ~ selection_favors(efficient_producers,first_movers,T)
& greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,T) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [To] :
( ~ in_environment(skolemFOFtoCNF_E,To)
| ? [T] :
( ~ selection_favors(efficient_producers,first_movers,T)
& greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,T) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [To] :
( ( ~ in_environment(skolemFOFtoCNF_E,To)
| ~ selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T(To)) )
& ( ~ in_environment(skolemFOFtoCNF_E,To)
| greater_or_equal(skolemFOFtoCNF_T(To),To) )
& ( ~ in_environment(skolemFOFtoCNF_E,To)
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(To)) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [To] :
( ~ in_environment(skolemFOFtoCNF_E,To)
| ~ selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T(To)) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [To] :
( ~ in_environment(skolemFOFtoCNF_E,To)
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(To)) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_7,plain,
stable(skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,plain,
! [E] :
( ~ environment(E)
| ~ stable(E)
| ? [To] :
( in_environment(E,To)
& ! [T] :
( ~ greater_or_equal(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
inference(canonicalize,[],[l1]) ).
fof(normalize_0_9,plain,
! [E] :
( ~ environment(E)
| ~ stable(E)
| ? [To] :
( in_environment(E,To)
& ! [T] :
( ~ greater_or_equal(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [E,T] :
( ( ~ environment(E)
| ~ stable(E)
| in_environment(E,skolemFOFtoCNF_To(E)) )
& ( ~ environment(E)
| ~ greater_or_equal(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_9]) ).
fof(normalize_0_11,plain,
! [E] :
( ~ environment(E)
| ~ stable(E)
| in_environment(E,skolemFOFtoCNF_To(E)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
environment(skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_13,plain,
! [E,T] :
( ~ environment(E)
| ~ greater_or_equal(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_10]) ).
fof(normalize_0_14,plain,
! [To] :
( ~ in_environment(skolemFOFtoCNF_E,To)
| greater_or_equal(skolemFOFtoCNF_T(To),To) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_15,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_16,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_15]) ).
cnf(refute_0_0,plain,
( ~ in_environment(skolemFOFtoCNF_E,To)
| ~ selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T(To)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
( ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(subst,[],[refute_0_0:[bind(To,$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_2,plain,
( ~ in_environment(skolemFOFtoCNF_E,To)
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(To)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(subst,[],[refute_0_2:[bind(To,$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_4,plain,
stable(skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ environment(E)
| ~ stable(E)
| in_environment(E,skolemFOFtoCNF_To(E)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_6,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ stable(skolemFOFtoCNF_E)
| in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_5:[bind(E,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_7,plain,
( ~ environment(skolemFOFtoCNF_E)
| in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( stable(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
environment(skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_9,plain,
in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_9,refute_0_3]) ).
cnf(refute_0_11,plain,
( ~ environment(E)
| ~ greater_or_equal(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_12,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(growth_rate(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),
inference(subst,[],[refute_0_11:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))))]]) ).
cnf(refute_0_13,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| ~ stable(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_8,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ in_environment(skolemFOFtoCNF_E,To)
| greater_or_equal(skolemFOFtoCNF_T(To),To) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_16,plain,
( ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E))
| greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_15:[bind(To,$fot(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_17,plain,
greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_9,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ stable(skolemFOFtoCNF_E)
| greater(growth_rate(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) ),
inference(resolve,[$cnf( greater_or_equal(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)),skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_17,refute_0_14]) ).
cnf(refute_0_19,plain,
greater(growth_rate(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))),
inference(resolve,[$cnf( stable(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_18]) ).
cnf(refute_0_20,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_16]) ).
cnf(refute_0_21,plain,
( ~ environment(X_6)
| ~ greater(growth_rate(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))))
| ~ subpopulations(first_movers,efficient_producers,X_6,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(subst,[],[refute_0_20:[bind(E,$fot(X_6)),bind(S1,$fot(first_movers)),bind(S2,$fot(efficient_producers)),bind(T,$fot(skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))))]]) ).
cnf(refute_0_22,plain,
( ~ environment(X_6)
| ~ subpopulations(first_movers,efficient_producers,X_6,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( greater(growth_rate(efficient_producers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),growth_rate(first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E)))
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(subst,[],[refute_0_22:[bind(X_6,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_24,plain,
( ~ environment(skolemFOFtoCNF_E)
| selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) )],[refute_0_10,refute_0_23]) ).
cnf(refute_0_25,plain,
selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_8,refute_0_24]) ).
cnf(refute_0_26,plain,
~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)),
inference(resolve,[$cnf( selection_favors(efficient_producers,first_movers,skolemFOFtoCNF_T(skolemFOFtoCNF_To(skolemFOFtoCNF_E))) )],[refute_0_25,refute_0_1]) ).
cnf(refute_0_27,plain,
$false,
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_To(skolemFOFtoCNF_E)) )],[refute_0_9,refute_0_26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : MGT032+2 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n022.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 12:04:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------