%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT036-3 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 08:02:54 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.37s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 55 ( 30 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a13_star_5,axiom,
environment(sk1),
file('theBenchmark.p',a13_star_5) ).
cnf(c_1,plain,
environment(sk1),
inference(clausify,[status(thm)],[a13_star_5]) ).
fof(d2_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( outcompetes(VAR_2,VAR_1,VAR_3)
| ~ greater(zero,growth_rate(VAR_1,VAR_3))
| ~ greater_or_equal(growth_rate(VAR_2,VAR_3),zero)
| ~ subpopulations(VAR_1,VAR_2,VAR_0,VAR_3)
| ~ environment(VAR_0) ),
file('theBenchmark.p',d2_2) ).
cnf(c_4,plain,
( outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[d2_2]) ).
fof(mp_symmetry_of_subpopulations_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( subpopulations(VAR_2,VAR_1,VAR_0,VAR_3)
| ~ subpopulations(VAR_1,VAR_2,VAR_0,VAR_3)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_symmetry_of_subpopulations_1) ).
cnf(c_5,plain,
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_symmetry_of_subpopulations_1]) ).
fof(prove_t5_star_9,axiom,
! [VAR_0,VAR_1] :
( ~ outcompetes(first_movers,efficient_producers,VAR_1)
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',prove_t5_star_9) ).
cnf(c_6,plain,
( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[prove_t5_star_9]) ).
cnf(c_8,plain,
( outcompetes(B,A,C)
| ~ greater(zero,growth_rate(A,C))
| ~ greater_or_equal(growth_rate(B,C),zero)
| ~ subpopulations(A,B,sk1,C) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
fof(a13_star_7,axiom,
greater_or_equal(growth_rate(first_movers,sk2),zero),
file('theBenchmark.p',a13_star_7) ).
cnf(c_9,plain,
greater_or_equal(growth_rate(first_movers,sk2),zero),
inference(clausify,[status(thm)],[a13_star_7]) ).
fof(a13_star_8,axiom,
greater(zero,growth_rate(efficient_producers,sk2)),
file('theBenchmark.p',a13_star_8) ).
cnf(c_10,plain,
greater(zero,growth_rate(efficient_producers,sk2)),
inference(clausify,[status(thm)],[a13_star_8]) ).
cnf(c_12,plain,
( outcompetes(first_movers,A,sk2)
| ~ greater(zero,growth_rate(A,sk2))
| ~ subpopulations(A,first_movers,sk1,sk2) ),
inference(resolve,[status(thm)],[c_9,c_8]) ).
cnf(c_16,plain,
( outcompetes(first_movers,efficient_producers,sk2)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2) ),
inference(resolve,[status(thm)],[c_10,c_12]) ).
cnf(c_18,plain,
( ~ outcompetes(first_movers,efficient_producers,A)
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_19,plain,
( subpopulations(B,A,sk1,C)
| ~ subpopulations(A,B,sk1,C) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
fof(a13_star_6,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('theBenchmark.p',a13_star_6) ).
cnf(c_20,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(clausify,[status(thm)],[a13_star_6]) ).
cnf(c_27,plain,
( ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2) ),
inference(resolve,[status(thm)],[c_18,c_16]) ).
cnf(c_22,plain,
~ subpopulations(efficient_producers,first_movers,sk1,sk2),
inference(resolve,[status(thm)],[c_20,c_27]) ).
cnf(c_28,plain,
subpopulations(efficient_producers,first_movers,sk1,sk2),
inference(resolve,[status(thm)],[c_19,c_20]) ).
cnf(c_26,plain,
$false,
inference(resolve,[status(thm)],[c_22,c_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT036-3 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 00:07:19 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 4154910 was started by sandbox on n020,
% 0.10/0.35 % Sat Sep 26 00:07:19 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.10/0.37
% 0.10/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.37
% 0.10/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.37 % Length of proof is 14.
% 0.10/0.37 % Level of proof is 5.
% 0.10/0.37 % Maximum clause weight is 10.000.
% 0.10/0.37 % Given clauses 7.
% 0.10/0.37
% 0.10/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------