%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT023+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 : Fri Sep 25 02:11:20 PM UTC 2026
% Result : Theorem 4.11s 1.15s
% Output : Proof 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 8 unt; 0 def)
% Number of atoms : 137 ( 22 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 149 ( 53 ~; 68 |; 22 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 15 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,conjecture,
! [E] :
( ( stable(E)
& environment(E) )
=> in_environment(E,critical_point(E)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5) ).
fof(f2_neg,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> in_environment(E,critical_point(E)) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f2_nnf,plain,
? [E] :
( ~ in_environment(E,critical_point(E))
& stable(E)
& environment(E) ),
inference(nnf_transformation,[status(thm)],[f2_neg]) ).
fof(f2_sk,plain,
( ~ in_environment(sk2,critical_point(sk2))
& stable(sk2)
& environment(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f2_nnf]) ).
cnf(c6,plain,
environment(sk2),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f1,hypothesis,
! [E] :
( ( stable(E)
& 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)) )
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12) ).
fof(f1_nnf,plain,
! [E] :
( ? [To] :
( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To) )
| ~ stable(E)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [E,T] :
( ( ( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,sk1(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,sk1(E)),growth_rate(first_movers,sk1(E)))
& in_environment(E,sk1(E)) )
| ~ stable(E)
| ~ environment(E) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f1_nnf]) ).
cnf(c3,plain,
( in_environment(X0,sk1(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p12,plain,
( in_environment(sk2,sk1(sk2))
| ~ stable(sk2) ),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(c7,plain,
stable(sk2),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p15,plain,
in_environment(sk2,sk1(sk2)),
inference(resolution,[status(thm)],[p12,c7]) ).
fof(f0,hypothesis,
! [E,To] :
( ( ! [T] :
( ( greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To)
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& environment(E) )
=> To = critical_point(E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(f0_nnf,plain,
! [E,To] :
( To = critical_point(E)
| ? [T] :
( ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
& greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ in_environment(E,To)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [E,To] :
( To = critical_point(E)
| ( ~ greater(growth_rate(efficient_producers,sk0(E,To)),growth_rate(first_movers,sk0(E,To)))
& greater(sk0(E,To),To)
& subpopulations(first_movers,efficient_producers,E,sk0(E,To)) )
| ~ in_environment(E,To)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ~ environment(E) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c0,plain,
( X1 = critical_point(X0)
| subpopulations(first_movers,efficient_producers,X0,sk0(X0,X1))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p9,plain,
( X0 = critical_point(sk2)
| subpopulations(first_movers,efficient_producers,sk2,sk0(sk2,X0))
| ~ in_environment(sk2,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(p18,plain,
( sk1(sk2) = critical_point(sk2)
| subpopulations(first_movers,efficient_producers,sk2,sk0(sk2,sk1(sk2)))
| greater(growth_rate(efficient_producers,sk1(sk2)),growth_rate(first_movers,sk1(sk2))) ),
inference(resolution,[status(thm)],[p15,p9]) ).
cnf(c4,plain,
( ~ greater(growth_rate(efficient_producers,sk1(X0)),growth_rate(first_movers,sk1(X0)))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p13,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk2)),growth_rate(first_movers,sk1(sk2)))
| ~ stable(sk2) ),
inference(resolution,[status(thm)],[c6,c4]) ).
cnf(p16,plain,
~ greater(growth_rate(efficient_producers,sk1(sk2)),growth_rate(first_movers,sk1(sk2))),
inference(resolution,[status(thm)],[p13,c7]) ).
cnf(p21,plain,
( sk1(sk2) = critical_point(sk2)
| subpopulations(first_movers,efficient_producers,sk2,sk0(sk2,sk1(sk2))) ),
inference(resolution,[status(thm)],[p18,p16]) ).
cnf(c5,plain,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sk1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p14,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk1(sk2))
| ~ subpopulations(first_movers,efficient_producers,sk2,X0)
| ~ stable(sk2) ),
inference(resolution,[status(thm)],[c6,c5]) ).
cnf(p17,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk1(sk2))
| ~ subpopulations(first_movers,efficient_producers,sk2,X0) ),
inference(resolution,[status(thm)],[p14,c7]) ).
cnf(p23,plain,
( greater(growth_rate(efficient_producers,sk0(sk2,sk1(sk2))),growth_rate(first_movers,sk0(sk2,sk1(sk2))))
| ~ greater(sk0(sk2,sk1(sk2)),sk1(sk2))
| sk1(sk2) = critical_point(sk2) ),
inference(resolution,[status(thm)],[p21,p17]) ).
cnf(c1,plain,
( X1 = critical_point(X0)
| greater(sk0(X0,X1),X1)
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p10,plain,
( X0 = critical_point(sk2)
| greater(sk0(sk2,X0),X0)
| ~ in_environment(sk2,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(p19,plain,
( sk1(sk2) = critical_point(sk2)
| greater(sk0(sk2,sk1(sk2)),sk1(sk2))
| greater(growth_rate(efficient_producers,sk1(sk2)),growth_rate(first_movers,sk1(sk2))) ),
inference(resolution,[status(thm)],[p15,p10]) ).
cnf(p22,plain,
( sk1(sk2) = critical_point(sk2)
| greater(sk0(sk2,sk1(sk2)),sk1(sk2)) ),
inference(resolution,[status(thm)],[p19,p16]) ).
cnf(p24,plain,
( sk1(sk2) = critical_point(sk2)
| greater(growth_rate(efficient_producers,sk0(sk2,sk1(sk2))),growth_rate(first_movers,sk0(sk2,sk1(sk2))))
| sk1(sk2) = critical_point(sk2) ),
inference(resolution,[status(thm)],[p23,p22]) ).
cnf(p25,plain,
( greater(growth_rate(efficient_producers,sk0(sk2,sk1(sk2))),growth_rate(first_movers,sk0(sk2,sk1(sk2))))
| sk1(sk2) = critical_point(sk2) ),
inference(factoring,[status(thm)],[p24]) ).
cnf(c2,plain,
( X1 = critical_point(X0)
| ~ greater(growth_rate(efficient_producers,sk0(X0,X1)),growth_rate(first_movers,sk0(X0,X1)))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p11,plain,
( X0 = critical_point(sk2)
| ~ greater(growth_rate(efficient_producers,sk0(sk2,X0)),growth_rate(first_movers,sk0(sk2,X0)))
| ~ in_environment(sk2,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(resolution,[status(thm)],[c6,c2]) ).
cnf(p20,plain,
( sk1(sk2) = critical_point(sk2)
| ~ greater(growth_rate(efficient_producers,sk0(sk2,sk1(sk2))),growth_rate(first_movers,sk0(sk2,sk1(sk2))))
| greater(growth_rate(efficient_producers,sk1(sk2)),growth_rate(first_movers,sk1(sk2))) ),
inference(resolution,[status(thm)],[p15,p11]) ).
cnf(p26,plain,
( sk1(sk2) = critical_point(sk2)
| greater(growth_rate(efficient_producers,sk1(sk2)),growth_rate(first_movers,sk1(sk2)))
| sk1(sk2) = critical_point(sk2) ),
inference(resolution,[status(thm)],[p25,p20]) ).
cnf(p27,plain,
( greater(growth_rate(efficient_producers,sk1(sk2)),growth_rate(first_movers,sk1(sk2)))
| sk1(sk2) = critical_point(sk2) ),
inference(factoring,[status(thm)],[p26]) ).
cnf(p28,plain,
sk1(sk2) = critical_point(sk2),
inference(resolution,[status(thm)],[p27,p16]) ).
cnf(p29,plain,
in_environment(sk2,critical_point(sk2)),
inference(demodulation,[status(thm)],[p28,p15]) ).
cnf(c8,plain,
~ in_environment(sk2,critical_point(sk2)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p32,plain,
$false,
inference(resolution,[status(thm)],[p29,c8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT023+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 01:02:34 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.11/1.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.11/1.15 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------