%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:16:06 AM UTC 2026
% Result : Theorem 0.10s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 12 unt; 0 def)
% Number of atoms : 116 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 140 ( 63 ~; 52 |; 20 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 36 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_symmetry_of_subpopulations,axiom,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T) )
=> subpopulations(S2,S1,E,T) ) ).
fof(d2,hypothesis,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T) )
=> ( ( greater_or_equal(growth_rate(S2,T),zero)
& greater(zero,growth_rate(S1,T)) )
<=> outcompetes(S2,S1,T) ) ) ).
fof(a13_star,hypothesis,
? [E,T] :
( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(growth_rate(first_movers,T),zero)
& greater(zero,growth_rate(efficient_producers,T)) ) ).
fof(prove_t5_star,conjecture,
? [E,T] :
( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& outcompetes(first_movers,efficient_producers,T) ) ).
fof(subgoal_0,plain,
? [E,T] :
( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& outcompetes(first_movers,efficient_producers,T) ),
inference(strip,[],[prove_t5_star]) ).
fof(negate_0_0,plain,
~ ? [E,T] :
( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& outcompetes(first_movers,efficient_producers,T) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [E,T] :
( environment(E)
& greater(zero,growth_rate(efficient_producers,T))
& greater_or_equal(growth_rate(first_movers,T),zero)
& subpopulations(first_movers,efficient_producers,E,T) ),
inference(canonicalize,[],[a13_star]) ).
fof(normalize_0_1,plain,
( environment(skolemFOFtoCNF_E)
& greater(zero,growth_rate(efficient_producers,skolemFOFtoCNF_T))
& greater_or_equal(growth_rate(first_movers,skolemFOFtoCNF_T),zero)
& subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ subpopulations(S1,S2,E,T)
| subpopulations(S2,S1,E,T) ),
inference(canonicalize,[],[mp_symmetry_of_subpopulations]) ).
fof(normalize_0_4,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ subpopulations(S1,S2,E,T)
| subpopulations(S2,S1,E,T) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
environment(skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_6,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ subpopulations(S1,S2,E,T)
| ( ~ outcompetes(S2,S1,T)
<=> ( ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S2,T),zero) ) ) ),
inference(canonicalize,[],[d2]) ).
fof(normalize_0_7,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ subpopulations(S1,S2,E,T)
| ( ~ outcompetes(S2,S1,T)
<=> ( ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S2,T),zero) ) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [E,S1,S2,T] :
( ( ~ environment(E)
| ~ outcompetes(S2,S1,T)
| ~ subpopulations(S1,S2,E,T)
| greater(zero,growth_rate(S1,T)) )
& ( ~ environment(E)
| ~ outcompetes(S2,S1,T)
| ~ subpopulations(S1,S2,E,T)
| greater_or_equal(growth_rate(S2,T),zero) )
& ( ~ environment(E)
| ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S2,T),zero)
| ~ subpopulations(S1,S2,E,T)
| outcompetes(S2,S1,T) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S2,T),zero)
| ~ subpopulations(S1,S2,E,T)
| outcompetes(S2,S1,T) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
greater(zero,growth_rate(efficient_producers,skolemFOFtoCNF_T)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_11,plain,
greater_or_equal(growth_rate(first_movers,skolemFOFtoCNF_T),zero),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_12,plain,
! [E,T] :
( ~ environment(E)
| ~ outcompetes(first_movers,efficient_producers,T)
| ~ subpopulations(first_movers,efficient_producers,E,T) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_13,plain,
! [E,T] :
( ~ environment(E)
| ~ outcompetes(first_movers,efficient_producers,T)
| ~ subpopulations(first_movers,efficient_producers,E,T) ),
inference(specialize,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ environment(E)
| ~ subpopulations(S1,S2,E,T)
| subpopulations(S2,S1,E,T) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| subpopulations(efficient_producers,first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_1:[bind(E,$fot(skolemFOFtoCNF_E)),bind(S1,$fot(first_movers)),bind(S2,$fot(efficient_producers)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_3,plain,
( ~ environment(skolemFOFtoCNF_E)
| subpopulations(efficient_producers,first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
environment(skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
subpopulations(efficient_producers,first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ environment(E)
| ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S2,T),zero)
| ~ subpopulations(S1,S2,E,T)
| outcompetes(S2,S1,T) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater(zero,growth_rate(efficient_producers,skolemFOFtoCNF_T))
| ~ greater_or_equal(growth_rate(first_movers,skolemFOFtoCNF_T),zero)
| ~ subpopulations(efficient_producers,first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_6:[bind(E,$fot(skolemFOFtoCNF_E)),bind(S1,$fot(efficient_producers)),bind(S2,$fot(first_movers)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_8,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater(zero,growth_rate(efficient_producers,skolemFOFtoCNF_T))
| ~ greater_or_equal(growth_rate(first_movers,skolemFOFtoCNF_T),zero)
| outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( subpopulations(efficient_producers,first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ greater(zero,growth_rate(efficient_producers,skolemFOFtoCNF_T))
| ~ greater_or_equal(growth_rate(first_movers,skolemFOFtoCNF_T),zero)
| outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
greater(zero,growth_rate(efficient_producers,skolemFOFtoCNF_T)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_11,plain,
( ~ greater_or_equal(growth_rate(first_movers,skolemFOFtoCNF_T),zero)
| outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( greater(zero,growth_rate(efficient_producers,skolemFOFtoCNF_T)) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
greater_or_equal(growth_rate(first_movers,skolemFOFtoCNF_T),zero),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_13,plain,
outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T),
inference(resolve,[$cnf( greater_or_equal(growth_rate(first_movers,skolemFOFtoCNF_T),zero) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
( ~ environment(E)
| ~ outcompetes(first_movers,efficient_producers,T)
| ~ subpopulations(first_movers,efficient_producers,E,T) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_15,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T)
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_14:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_16,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_0,refute_0_15]) ).
cnf(refute_0_17,plain,
~ outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_16]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T) )],[refute_0_13,refute_0_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 7 12:43:24 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.10/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37
% 0.10/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.37
%------------------------------------------------------------------------------