%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT023-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 : Sun Sep 27 08:02:09 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 11 unt; 0 def)
% Number of atoms : 132 ( 28 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 141 ( 55 ~; 86 |; 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 : 28 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_l5_23,axiom,
environment(sk3),
file('theBenchmark.p',prove_l5_23) ).
cnf(c_1,plain,
environment(sk3),
inference(clausify,[status(thm)],[prove_l5_23]) ).
fof(l12_22,axiom,
! [VAR_0,VAR_1] :
( greater(growth_rate(efficient_producers,VAR_1),growth_rate(first_movers,VAR_1))
| ~ greater(VAR_1,sk2(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ stable(VAR_0)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l12_22) ).
cnf(c_2,plain,
( 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(clausify,[status(thm)],[l12_22]) ).
fof(l12_21,axiom,
! [VAR_0] :
( ~ greater(growth_rate(efficient_producers,sk2(VAR_0)),growth_rate(first_movers,sk2(VAR_0)))
| ~ stable(VAR_0)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l12_21) ).
cnf(c_3,plain,
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| ~ stable(A)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l12_21]) ).
fof(l12_20,axiom,
! [VAR_0] :
( in_environment(VAR_0,sk2(VAR_0))
| ~ stable(VAR_0)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l12_20) ).
cnf(c_4,plain,
( in_environment(A,sk2(A))
| ~ stable(A)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l12_20]) ).
fof(d1_19,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = critical_point(VAR_0)
| ~ greater(growth_rate(efficient_producers,sk1(VAR_1,VAR_0)),growth_rate(first_movers,sk1(VAR_1,VAR_0)))
| ~ in_environment(VAR_0,VAR_1)
| greater(growth_rate(efficient_producers,VAR_1),growth_rate(first_movers,VAR_1))
| ~ environment(VAR_0) ),
file('theBenchmark.p',d1_19) ).
cnf(c_5,plain,
( 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(clausify,[status(thm)],[d1_19]) ).
fof(d1_18,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = critical_point(VAR_0)
| greater(sk1(VAR_1,VAR_0),VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| greater(growth_rate(efficient_producers,VAR_1),growth_rate(first_movers,VAR_1))
| ~ environment(VAR_0) ),
file('theBenchmark.p',d1_18) ).
cnf(c_6,plain,
( 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(clausify,[status(thm)],[d1_18]) ).
fof(d1_17,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = critical_point(VAR_0)
| subpopulations(first_movers,efficient_producers,VAR_0,sk1(VAR_1,VAR_0))
| ~ in_environment(VAR_0,VAR_1)
| greater(growth_rate(efficient_producers,VAR_1),growth_rate(first_movers,VAR_1))
| ~ environment(VAR_0) ),
file('theBenchmark.p',d1_17) ).
cnf(c_7,plain,
( 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(clausify,[status(thm)],[d1_17]) ).
cnf(c_8,plain,
( A = critical_point(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(A,sk3))
| ~ in_environment(sk3,A)
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_9,plain,
( critical_point(sk3) = A
| subpopulations(first_movers,efficient_producers,sk3,sk1(A,sk3))
| ~ in_environment(sk3,A)
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) ),
inference(copy,[status(thm)],[c_8]) ).
cnf(c_10,plain,
( A = critical_point(sk3)
| greater(sk1(A,sk3),A)
| ~ in_environment(sk3,A)
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_11,plain,
( critical_point(sk3) = A
| greater(sk1(A,sk3),A)
| ~ in_environment(sk3,A)
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) ),
inference(copy,[status(thm)],[c_10]) ).
cnf(c_12,plain,
( A = critical_point(sk3)
| ~ greater(growth_rate(efficient_producers,sk1(A,sk3)),growth_rate(first_movers,sk1(A,sk3)))
| ~ in_environment(sk3,A)
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_13,plain,
( critical_point(sk3) = A
| ~ greater(growth_rate(efficient_producers,sk1(A,sk3)),growth_rate(first_movers,sk1(A,sk3)))
| ~ in_environment(sk3,A)
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) ),
inference(copy,[status(thm)],[c_12]) ).
cnf(c_14,plain,
( in_environment(sk3,sk2(sk3))
| ~ stable(sk3) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_15,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| ~ stable(sk3) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_16,plain,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater(A,sk2(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,A)
| ~ stable(sk3) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_l5_25,axiom,
~ in_environment(sk3,critical_point(sk3)),
file('theBenchmark.p',prove_l5_25) ).
cnf(c_17,plain,
~ in_environment(sk3,critical_point(sk3)),
inference(clausify,[status(thm)],[prove_l5_25]) ).
fof(prove_l5_24,axiom,
stable(sk3),
file('theBenchmark.p',prove_l5_24) ).
cnf(c_18,plain,
stable(sk3),
inference(clausify,[status(thm)],[prove_l5_24]) ).
cnf(c_19,plain,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater(A,sk2(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,A) ),
inference(resolve,[status(thm)],[c_18,c_16]) ).
cnf(c_20,plain,
~ greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))),
inference(resolve,[status(thm)],[c_18,c_15]) ).
cnf(c_21,plain,
in_environment(sk3,sk2(sk3)),
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_29,plain,
( critical_point(sk3) = sk2(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(resolve,[status(thm)],[c_21,c_13]) ).
cnf(c_30,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(copy,[status(thm)],[c_29]) ).
cnf(c_22,plain,
( sk2(sk3) = critical_point(sk3)
| ~ greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(resolve,[status(thm)],[c_20,c_30]) ).
cnf(c_31,plain,
( critical_point(sk3) = sk2(sk3)
| greater(sk1(sk2(sk3),sk3),sk2(sk3))
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
inference(resolve,[status(thm)],[c_21,c_11]) ).
cnf(c_32,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(copy,[status(thm)],[c_31]) ).
cnf(c_23,plain,
( sk2(sk3) = critical_point(sk3)
| greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(resolve,[status(thm)],[c_20,c_32]) ).
cnf(c_33,plain,
( critical_point(sk3) = sk2(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(resolve,[status(thm)],[c_21,c_9]) ).
cnf(c_34,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(copy,[status(thm)],[c_33]) ).
cnf(c_24,plain,
( sk2(sk3) = critical_point(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(resolve,[status(thm)],[c_20,c_34]) ).
cnf(c_25,plain,
( greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| ~ greater(sk1(sk2(sk3),sk3),sk2(sk3))
| sk2(sk3) = critical_point(sk3) ),
inference(resolve,[status(thm)],[c_24,c_19]) ).
cnf(c_35,plain,
( sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| sk2(sk3) = critical_point(sk3) ),
inference(resolve,[status(thm)],[c_25,c_23]) ).
cnf(c_26,plain,
( greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| sk2(sk3) = critical_point(sk3) ),
inference(copy,[status(thm)],[c_35]) ).
cnf(c_36,plain,
( sk2(sk3) = critical_point(sk3)
| sk2(sk3) = critical_point(sk3) ),
inference(resolve,[status(thm)],[c_26,c_22]) ).
cnf(c_27,plain,
sk2(sk3) = critical_point(sk3),
inference(copy,[status(thm)],[c_36]) ).
cnf(c_37,plain,
in_environment(sk3,critical_point(sk3)),
inference(paramod,[status(thm)],[c_27,c_21]) ).
cnf(c_28,plain,
$false,
inference(resolve,[status(thm)],[c_17,c_37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT023-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n017.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 00:00:03 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 3511437 was started by sandbox2 on n017,
% 0.17/0.44 % Sat Sep 26 00:00:03 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.17/0.46
% 0.17/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.46
% 0.17/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.46 % Length of proof is 28.
% 0.17/0.46 % Level of proof is 7.
% 0.17/0.46 % Maximum clause weight is 25.000.
% 0.17/0.46 % Given clauses 13.
% 0.17/0.46
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------