%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT023-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 02:11:21 PM UTC 2026
% Result : Unsatisfiable 5.15s 1.28s
% Output : Proof 5.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 15 unt; 0 def)
% Number of atoms : 168 ( 28 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 195 ( 83 ~; 112 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 45 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,hypothesis,
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater(B,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_22) ).
fof(f5_nnf,plain,
! [A,B] :
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater(B,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] :
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater(B,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f6,negated_conjecture,
environment(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_23) ).
fof(f6_nnf,plain,
environment(sk3),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
environment(sk3),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(p21,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk2(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0)
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c5,c6]) ).
cnf(f7,negated_conjecture,
stable(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_24) ).
fof(f7_nnf,plain,
stable(sk3),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
stable(sk3),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(p22,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk2(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0) ),
inference(resolution,[status(thm)],[p21,c7]) ).
cnf(f4,hypothesis,
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_21) ).
fof(f4_nnf,plain,
! [A] :
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A] :
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p15,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c4,c6]) ).
cnf(p16,plain,
~ greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))),
inference(resolution,[status(thm)],[p15,c7]) ).
cnf(f0,hypothesis,
( B = critical_point(A)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_17) ).
fof(f0_nnf,plain,
! [A,B] :
( B = critical_point(A)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( B = critical_point(A)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( X1 = critical_point(X0)
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ 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(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(X0,sk3))
| ~ in_environment(sk3,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(resolution,[status(thm)],[c0,c6]) ).
cnf(f3,hypothesis,
( in_environment(A,sk2(A))
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_20) ).
fof(f3_nnf,plain,
! [A] :
( in_environment(A,sk2(A))
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] :
( in_environment(A,sk2(A))
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( in_environment(X0,sk2(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p9,plain,
( in_environment(sk3,sk2(sk3))
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c3,c6]) ).
cnf(p11,plain,
in_environment(sk3,sk2(sk3)),
inference(resolution,[status(thm)],[p9,c7]) ).
cnf(p12,plain,
( sk2(sk3) = critical_point(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3))
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
inference(resolution,[status(thm)],[p10,p11]) ).
cnf(p18,plain,
( sk2(sk3) = critical_point(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(resolution,[status(thm)],[p16,p12]) ).
cnf(p23,plain,
( sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| ~ greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(resolution,[status(thm)],[p22,p18]) ).
cnf(f1,hypothesis,
( B = critical_point(A)
| greater(sk1(B,A),B)
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_18) ).
fof(f1_nnf,plain,
! [A,B] :
( B = critical_point(A)
| greater(sk1(B,A),B)
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( B = critical_point(A)
| greater(sk1(B,A),B)
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( X1 = critical_point(X0)
| greater(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p13,plain,
( X0 = critical_point(sk3)
| greater(sk1(X0,sk3),X0)
| ~ in_environment(sk3,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(resolution,[status(thm)],[c1,c6]) ).
cnf(p14,plain,
( sk2(sk3) = critical_point(sk3)
| greater(sk1(sk2(sk3),sk3),sk2(sk3))
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
inference(resolution,[status(thm)],[p13,p11]) ).
cnf(p19,plain,
( sk2(sk3) = critical_point(sk3)
| greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(resolution,[status(thm)],[p16,p14]) ).
cnf(p24,plain,
( sk2(sk3) = critical_point(sk3)
| sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(resolution,[status(thm)],[p23,p19]) ).
cnf(p25,plain,
( sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(factoring,[status(thm)],[p24]) ).
cnf(f2,hypothesis,
( B = critical_point(A)
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_19) ).
fof(f2_nnf,plain,
! [A,B] :
( B = critical_point(A)
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( B = critical_point(A)
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( X1 = critical_point(X0)
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p17,plain,
( X0 = critical_point(sk3)
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk3)),growth_rate(first_movers,sk1(X0,sk3)))
| ~ in_environment(sk3,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(resolution,[status(thm)],[c2,c6]) ).
cnf(p20,plain,
( sk2(sk3) = critical_point(sk3)
| ~ greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
inference(resolution,[status(thm)],[p17,p11]) ).
cnf(p26,plain,
( sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| sk2(sk3) = critical_point(sk3) ),
inference(resolution,[status(thm)],[p25,p20]) ).
cnf(p27,plain,
( greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| sk2(sk3) = critical_point(sk3) ),
inference(factoring,[status(thm)],[p26]) ).
cnf(p28,plain,
sk2(sk3) = critical_point(sk3),
inference(resolution,[status(thm)],[p27,p16]) ).
cnf(p29,plain,
in_environment(sk3,critical_point(sk3)),
inference(demodulation,[status(thm)],[p28,p11]) ).
cnf(f8,negated_conjecture,
~ in_environment(sk3,critical_point(sk3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_25) ).
fof(f8_nnf,plain,
~ in_environment(sk3,critical_point(sk3)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ in_environment(sk3,critical_point(sk3)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ in_environment(sk3,critical_point(sk3)),
inference(cnf_transformation,[status(esa)],[f8_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 v2.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 01:03:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.15/1.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.15/1.28 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------