%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT032-2 : 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 : 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 08:02:32 AM UTC 2026
% Result : Unsatisfiable 0.17s 5.67s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 7 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 112 ( 60 ~; 52 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_t1_4,axiom,
environment(sk2),
file('theBenchmark.p',prove_t1_4) ).
cnf(c_1,plain,
environment(sk2),
inference(clausify,[status(thm)],[prove_t1_4]) ).
fof(l1_3,axiom,
! [VAR_0,VAR_1] :
( greater(growth_rate(efficient_producers,VAR_1),growth_rate(first_movers,VAR_1))
| ~ greater_or_equal(VAR_1,sk1(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ stable(VAR_0)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l1_3) ).
cnf(c_2,plain,
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l1_3]) ).
fof(l1_2,axiom,
! [VAR_0] :
( in_environment(VAR_0,sk1(VAR_0))
| ~ stable(VAR_0)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l1_2) ).
cnf(c_3,plain,
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l1_2]) ).
fof(mp1_high_growth_rates_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( selection_favors(VAR_2,VAR_1,VAR_3)
| ~ greater(growth_rate(VAR_2,VAR_3),growth_rate(VAR_1,VAR_3))
| ~ subpopulations(VAR_1,VAR_2,VAR_0,VAR_3)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp1_high_growth_rates_1) ).
cnf(c_4,plain,
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp1_high_growth_rates_1]) ).
fof(prove_t1_6,axiom,
! [VAR_0] :
( subpopulations(first_movers,efficient_producers,sk2,sk3(VAR_0))
| ~ in_environment(sk2,VAR_0) ),
file('theBenchmark.p',prove_t1_6) ).
cnf(c_5,plain,
( subpopulations(first_movers,efficient_producers,sk2,sk3(A))
| ~ in_environment(sk2,A) ),
inference(clausify,[status(thm)],[prove_t1_6]) ).
cnf(c_6,plain,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater_or_equal(A,sk1(sk2))
| ~ subpopulations(first_movers,efficient_producers,sk2,A)
| ~ stable(sk2) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_7,plain,
( selection_favors(B,A,C)
| ~ greater(growth_rate(B,C),growth_rate(A,C))
| ~ subpopulations(A,B,sk2,C) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_8,plain,
( greater(growth_rate(efficient_producers,sk3(A)),growth_rate(first_movers,sk3(A)))
| ~ greater_or_equal(sk3(A),sk1(sk2))
| ~ stable(sk2)
| ~ in_environment(sk2,A) ),
inference(resolve,[status(thm)],[c_5,c_6]) ).
cnf(c_9,plain,
( selection_favors(efficient_producers,first_movers,sk3(A))
| ~ greater(growth_rate(efficient_producers,sk3(A)),growth_rate(first_movers,sk3(A)))
| ~ in_environment(sk2,A) ),
inference(resolve,[status(thm)],[c_5,c_7]) ).
fof(prove_t1_8,axiom,
! [VAR_0] :
( ~ selection_favors(efficient_producers,first_movers,sk3(VAR_0))
| ~ in_environment(sk2,VAR_0) ),
file('theBenchmark.p',prove_t1_8) ).
cnf(c_10,plain,
( ~ selection_favors(efficient_producers,first_movers,sk3(A))
| ~ in_environment(sk2,A) ),
inference(clausify,[status(thm)],[prove_t1_8]) ).
cnf(c_11,plain,
( selection_favors(efficient_producers,first_movers,sk3(A))
| ~ in_environment(sk2,A)
| ~ greater_or_equal(sk3(A),sk1(sk2))
| ~ stable(sk2)
| ~ in_environment(sk2,A) ),
inference(resolve,[status(thm)],[c_8,c_9]) ).
fof(prove_t1_5,axiom,
stable(sk2),
file('theBenchmark.p',prove_t1_5) ).
cnf(c_12,plain,
stable(sk2),
inference(clausify,[status(thm)],[prove_t1_5]) ).
cnf(c_13,plain,
( ~ in_environment(sk2,A)
| ~ greater_or_equal(sk3(A),sk1(sk2))
| ~ stable(sk2)
| ~ in_environment(sk2,A)
| ~ in_environment(sk2,A) ),
inference(resolve,[status(thm)],[c_10,c_11]) ).
cnf(c_14,plain,
( in_environment(sk2,sk1(sk2))
| ~ stable(sk2) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
fof(prove_t1_7,axiom,
! [VAR_0] :
( greater_or_equal(sk3(VAR_0),VAR_0)
| ~ in_environment(sk2,VAR_0) ),
file('theBenchmark.p',prove_t1_7) ).
cnf(c_15,plain,
( greater_or_equal(sk3(A),A)
| ~ in_environment(sk2,A) ),
inference(clausify,[status(thm)],[prove_t1_7]) ).
cnf(c_16,plain,
( ~ in_environment(sk2,A)
| ~ greater_or_equal(sk3(A),sk1(sk2))
| ~ in_environment(sk2,A)
| ~ in_environment(sk2,A) ),
inference(resolve,[status(thm)],[c_12,c_13]) ).
cnf(c_17,plain,
( ~ in_environment(sk2,sk1(sk2))
| ~ in_environment(sk2,sk1(sk2))
| ~ in_environment(sk2,sk1(sk2))
| ~ in_environment(sk2,sk1(sk2)) ),
inference(resolve,[status(thm)],[c_15,c_16]) ).
cnf(c_21,plain,
( ~ in_environment(sk2,sk1(sk2))
| ~ in_environment(sk2,sk1(sk2))
| ~ in_environment(sk2,sk1(sk2)) ),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_22,plain,
( ~ in_environment(sk2,sk1(sk2))
| ~ in_environment(sk2,sk1(sk2)) ),
inference(copy,[status(thm)],[c_21]) ).
cnf(c_18,plain,
~ in_environment(sk2,sk1(sk2)),
inference(copy,[status(thm)],[c_22]) ).
cnf(c_19,plain,
in_environment(sk2,sk1(sk2)),
inference(resolve,[status(thm)],[c_14,c_12]) ).
cnf(c_20,plain,
$false,
inference(resolve,[status(thm)],[c_18,c_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT032-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.64 % Computer : n020.cluster.edu
% 0.17/5.64 % Model : x86_64 x86_64
% 0.17/5.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.64 % Memory : 8046.5625MB
% 0.17/5.64 % OS : Linux 6.8.0-71-generic
% 0.17/5.64 % CPULimit : 300
% 0.17/5.64 % WCLimit : 300
% 0.17/5.64 % DateTime : Sat Sep 26 00:06:09 UTC 2026
% 0.17/5.64 % CPUTime :
% 0.17/5.65 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.65 % Process 4150411 was started by sandbox2 on n020,
% 0.17/5.65 % Sat Sep 26 00:06:09 2026
% 0.17/5.65 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.65
% 0.17/5.65 % From the command line: assign(max_seconds, 300).
% 0.17/5.67
% 0.17/5.67 % SZS status Unsatisfiable for theBenchmark
% 0.17/5.67
% 0.17/5.67 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/5.67 % Length of proof is 20.
% 0.17/5.67 % Level of proof is 8.
% 0.17/5.67 % Maximum clause weight is 4.000.
% 0.17/5.67 % Given clauses 0.
% 0.17/5.67
% 0.17/5.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------