%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT036-2 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 : Unsatisfiable 5.18s 6.11s
% Output : Proof 5.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 64 ( 22 unt; 0 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 171 ( 88 ~; 83 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 135 ( 17 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,hypothesis,
( greater(zero,growth_rate(B,D))
| ~ outcompetes(C,B,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_9) ).
fof(f8_nnf,plain,
! [A,B,C,D] :
( greater(zero,growth_rate(B,D))
| ~ outcompetes(C,B,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D] :
( greater(zero,growth_rate(B,D))
| ~ outcompetes(C,B,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( greater(zero,growth_rate(X1,X3))
| ~ outcompetes(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(f11,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_12) ).
fof(f11_nnf,plain,
environment(sk1),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
environment(sk1),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(p26,plain,
( greater(zero,growth_rate(X0,X2))
| ~ outcompetes(X1,X0,X2)
| ~ subpopulations(X0,X1,sk1,X2) ),
inference(resolution,[status(thm)],[c8,c11]) ).
cnf(f0,axiom,
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_1) ).
fof(f0_nnf,plain,
! [A,B,C,D] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C,D] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
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(p14,plain,
( subpopulations(X1,X0,sk1,X2)
| ~ subpopulations(X0,X1,sk1,X2) ),
inference(resolution,[status(thm)],[c0,c11]) ).
cnf(f12,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_13) ).
fof(f12_nnf,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(p15,plain,
subpopulations(efficient_producers,first_movers,sk1,sk2),
inference(resolution,[status(thm)],[p14,c12]) ).
cnf(p28,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ outcompetes(first_movers,efficient_producers,sk2) ),
inference(resolution,[status(thm)],[p26,p15]) ).
cnf(f13,negated_conjecture,
outcompetes(first_movers,efficient_producers,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_14) ).
fof(f13_nnf,plain,
outcompetes(first_movers,efficient_producers,sk2),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
outcompetes(first_movers,efficient_producers,sk2),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(p29,plain,
greater(zero,growth_rate(efficient_producers,sk2)),
inference(resolution,[status(thm)],[p28,c13]) ).
cnf(f2,axiom,
( ~ greater(zero,growth_rate(B,C))
| environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships_3) ).
fof(f2_nnf,plain,
! [A,B,C] :
( ~ greater(zero,growth_rate(B,C))
| environment(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] :
( ~ greater(zero,growth_rate(B,C))
| environment(A) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ greater(zero,growth_rate(X1,X2))
| environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p30,plain,
environment(X0),
inference(resolution,[status(thm)],[p29,c2]) ).
cnf(f10,hypothesis,
( ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a13_11) ).
fof(f10_nnf,plain,
! [A,B,C,D] :
( ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A,B,C,D] :
( ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( ~ greater(zero,growth_rate(X3,X1))
| ~ greater(resilience(X3),resilience(X2))
| greater(zero,growth_rate(X2,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p38,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)],[p30,c10]) ).
cnf(p32,plain,
( subpopulations(X1,X0,X2,X3)
| ~ subpopulations(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[p30,c0]) ).
cnf(f3,axiom,
( ~ greater(zero,growth_rate(A,D))
| subpopulations(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships_4) ).
fof(f3_nnf,plain,
! [A,B,C,D] :
( ~ greater(zero,growth_rate(A,D))
| subpopulations(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( ~ greater(zero,growth_rate(A,D))
| subpopulations(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ greater(zero,growth_rate(X0,X3))
| subpopulations(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p31,plain,
subpopulations(efficient_producers,X0,X1,sk2),
inference(resolution,[status(thm)],[p29,c3]) ).
cnf(p39,plain,
subpopulations(X0,efficient_producers,X1,sk2),
inference(resolution,[status(thm)],[p32,p31]) ).
cnf(f1,axiom,
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur_2) ).
fof(f1_nnf,plain,
! [A,B] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
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(p33,plain,
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(resolution,[status(thm)],[p30,c1]) ).
cnf(p41,plain,
in_environment(X0,sk2),
inference(resolution,[status(thm)],[p39,p33]) ).
cnf(p45,plain,
( ~ greater(zero,growth_rate(X1,sk2))
| ~ greater(resilience(X1),resilience(X0))
| greater(zero,growth_rate(X0,sk2)) ),
inference(resolution,[status(thm)],[p38,p41]) ).
cnf(f9,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2_10) ).
fof(f9_nnf,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(p51,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p45,c9]) ).
cnf(p58,plain,
greater(zero,growth_rate(first_movers,sk2)),
inference(resolution,[status(thm)],[p51,p29]) ).
cnf(f7,hypothesis,
( greater_or_equal(growth_rate(C,D),zero)
| ~ outcompetes(C,B,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_8) ).
fof(f7_nnf,plain,
! [A,B,C,D] :
( greater_or_equal(growth_rate(C,D),zero)
| ~ outcompetes(C,B,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C,D] :
( greater_or_equal(growth_rate(C,D),zero)
| ~ outcompetes(C,B,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( greater_or_equal(growth_rate(X2,X3),zero)
| ~ outcompetes(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p18,plain,
( greater_or_equal(growth_rate(X1,X2),zero)
| ~ outcompetes(X1,X0,X2)
| ~ subpopulations(X0,X1,sk1,X2) ),
inference(resolution,[status(thm)],[c7,c11]) ).
cnf(p21,plain,
( greater_or_equal(growth_rate(first_movers,sk2),zero)
| ~ outcompetes(first_movers,efficient_producers,sk2) ),
inference(resolution,[status(thm)],[p18,p15]) ).
cnf(p22,plain,
greater_or_equal(growth_rate(first_movers,sk2),zero),
inference(resolution,[status(thm)],[p21,c13]) ).
cnf(f4,axiom,
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships_5) ).
fof(f4_nnf,plain,
! [A,B] :
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( ~ greater(zero,growth_rate(X0,X1))
| ~ greater_or_equal(growth_rate(X0,X1),zero) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p23,plain,
~ greater(zero,growth_rate(first_movers,sk2)),
inference(resolution,[status(thm)],[p22,c4]) ).
cnf(p60,plain,
$false,
inference(resolution,[status(thm)],[p58,p23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.38 % Computer : n007.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Thu Sep 24 01:06:12 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.18/6.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.18/6.11 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------