%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT036+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:11:45 PM UTC 2026
% Result : Theorem 0.13s 5.97s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 16 unt; 0 def)
% Number of atoms : 152 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 173 ( 74 ~; 66 |; 24 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 114 ( 12 sgn 58 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,hypothesis,
! [E,S1,S2,T] :
( ( greater(resilience(S2),resilience(S1))
& ~ greater(zero,growth_rate(S1,T))
& in_environment(E,T)
& environment(E) )
=> ~ greater(zero,growth_rate(S2,T)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13) ).
fof(f5_nnf,plain,
! [E,S1,S2,T] :
( ~ greater(zero,growth_rate(S2,T))
| ~ greater(resilience(S2),resilience(S1))
| greater(zero,growth_rate(S1,T))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [E,T,S1,S2] :
( ~ greater(zero,growth_rate(S2,T))
| ~ greater(resilience(S2),resilience(S1))
| greater(zero,growth_rate(S1,T))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c10,plain,
( ~ greater(zero,growth_rate(X2,X3))
| ~ greater(resilience(X2),resilience(X1))
| greater(zero,growth_rate(X1,X3))
| ~ in_environment(X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f3,hypothesis,
! [E,S1,S2,T] :
( ( subpopulations(S1,S2,E,T)
& environment(E) )
=> ( ( greater(zero,growth_rate(S1,T))
& greater_or_equal(growth_rate(S2,T),zero) )
<=> outcompetes(S2,S1,T) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
fof(f3_nnf,plain,
! [E,S1,S2,T] :
( ( ( ~ outcompetes(S2,S1,T)
| ( greater(zero,growth_rate(S1,T))
& greater_or_equal(growth_rate(S2,T),zero) ) )
& ( outcompetes(S2,S1,T)
| ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S2,T),zero) ) )
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [E,S1,S2,T] :
( ( ( ~ outcompetes(S2,S1,T)
| ( greater(zero,growth_rate(S1,T))
& greater_or_equal(growth_rate(S2,T),zero) ) )
& ( outcompetes(S2,S1,T)
| ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S2,T),zero) ) )
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c8,plain,
( ~ outcompetes(X2,X1,X3)
| greater(zero,growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f6,conjecture,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ outcompetes(first_movers,efficient_producers,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5) ).
fof(f6_neg,negated_conjecture,
~ ! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ outcompetes(first_movers,efficient_producers,T) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [E,T] :
( outcompetes(first_movers,efficient_producers,T)
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( outcompetes(first_movers,efficient_producers,sk1)
& subpopulations(first_movers,efficient_producers,sk0,sk1)
& environment(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f6_nnf]) ).
cnf(c11,plain,
environment(sk0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p23,plain,
( ~ outcompetes(X1,X0,X2)
| greater(zero,growth_rate(X0,X2))
| ~ subpopulations(X0,X1,sk0,X2) ),
inference(resolution,[status(thm)],[c8,c11]) ).
fof(f0,axiom,
! [E,S1,S2,T] :
( ( subpopulations(S1,S2,E,T)
& environment(E) )
=> subpopulations(S2,S1,E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(f0_nnf,plain,
! [E,S1,S2,T] :
( subpopulations(S2,S1,E,T)
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [E,S1,S2,T] :
( subpopulations(S2,S1,E,T)
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( subpopulations(X2,X1,X0,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p16,plain,
( subpopulations(X1,X0,sk0,X2)
| ~ subpopulations(X0,X1,sk0,X2) ),
inference(resolution,[status(thm)],[c0,c11]) ).
cnf(c12,plain,
subpopulations(first_movers,efficient_producers,sk0,sk1),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p17,plain,
subpopulations(efficient_producers,first_movers,sk0,sk1),
inference(resolution,[status(thm)],[p16,c12]) ).
cnf(p25,plain,
( ~ outcompetes(first_movers,efficient_producers,sk1)
| greater(zero,growth_rate(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p23,p17]) ).
cnf(c13,plain,
outcompetes(first_movers,efficient_producers,sk1),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p26,plain,
greater(zero,growth_rate(efficient_producers,sk1)),
inference(resolution,[status(thm)],[p25,c13]) ).
fof(f2,axiom,
! [E,S1,S2,T] :
( ( ( subpopulations(S1,S2,E,T)
& environment(E) )
=> greater_or_equal(growth_rate(S1,T),zero) )
<=> ~ greater(zero,growth_rate(S1,T)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_relationships) ).
fof(f2_nnf,plain,
! [E,S1,S2,T] :
( ( greater(zero,growth_rate(S1,T))
| greater_or_equal(growth_rate(S1,T),zero)
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) )
& ( ~ greater(zero,growth_rate(S1,T))
| ( ~ greater_or_equal(growth_rate(S1,T),zero)
& subpopulations(S1,S2,E,T)
& environment(E) ) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [E,S1,S2,T] :
( ( greater(zero,growth_rate(S1,T))
| greater_or_equal(growth_rate(S1,T),zero)
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) )
& ( ~ greater(zero,growth_rate(S1,T))
| ( ~ greater_or_equal(growth_rate(S1,T),zero)
& subpopulations(S1,S2,E,T)
& environment(E) ) ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ greater(zero,growth_rate(X1,X3))
| environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p27,plain,
environment(X0),
inference(resolution,[status(thm)],[p26,c2]) ).
cnf(p48,plain,
( ~ greater(zero,growth_rate(X3,X1))
| ~ greater(resilience(X3),resilience(X2))
| greater(zero,growth_rate(X2,X1))
| ~ in_environment(X0,X1) ),
inference(resolution,[status(thm)],[c10,p27]) ).
cnf(p30,plain,
( subpopulations(X1,X0,X2,X3)
| ~ subpopulations(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[p27,c0]) ).
cnf(c3,plain,
( ~ greater(zero,growth_rate(X1,X3))
| subpopulations(X1,X2,X0,X3) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p28,plain,
subpopulations(efficient_producers,X0,X1,sk1),
inference(resolution,[status(thm)],[p26,c3]) ).
cnf(p33,plain,
subpopulations(X0,efficient_producers,X1,sk1),
inference(resolution,[status(thm)],[p30,p28]) ).
fof(f1,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur) ).
fof(f1_nnf,plain,
! [E,T] :
( in_environment(E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [E,T] :
( in_environment(E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p29,plain,
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(resolution,[status(thm)],[p27,c1]) ).
cnf(p34,plain,
in_environment(X0,sk1),
inference(resolution,[status(thm)],[p33,p29]) ).
cnf(p49,plain,
( ~ greater(zero,growth_rate(X1,sk1))
| ~ greater(resilience(X1),resilience(X0))
| greater(zero,growth_rate(X0,sk1)) ),
inference(resolution,[status(thm)],[p48,p34]) ).
fof(f4,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(f4_nnf,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c9,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(p50,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1))
| greater(zero,growth_rate(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p49,c9]) ).
cnf(p51,plain,
greater(zero,growth_rate(first_movers,sk1)),
inference(resolution,[status(thm)],[p50,p26]) ).
cnf(c7,plain,
( ~ outcompetes(X2,X1,X3)
| greater_or_equal(growth_rate(X2,X3),zero)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p18,plain,
( ~ outcompetes(X1,X0,X2)
| greater_or_equal(growth_rate(X1,X2),zero)
| ~ subpopulations(X0,X1,sk0,X2) ),
inference(resolution,[status(thm)],[c7,c11]) ).
cnf(p20,plain,
( ~ outcompetes(first_movers,efficient_producers,sk1)
| greater_or_equal(growth_rate(first_movers,sk1),zero) ),
inference(resolution,[status(thm)],[p18,p17]) ).
cnf(p21,plain,
greater_or_equal(growth_rate(first_movers,sk1),zero),
inference(resolution,[status(thm)],[p20,c13]) ).
cnf(c4,plain,
( ~ greater(zero,growth_rate(X1,X3))
| ~ greater_or_equal(growth_rate(X1,X3),zero) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p22,plain,
~ greater(zero,growth_rate(first_movers,sk1)),
inference(resolution,[status(thm)],[p21,c4]) ).
cnf(p53,plain,
$false,
inference(resolution,[status(thm)],[p51,p22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n003.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 01:10:11 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/5.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.97 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------