%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT036-2 : 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 : n013.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 0.18s 5.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 13 unt; 0 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 138 ( 72 ~; 66 |; 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 : 98 ( 24 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_growth_rate_relationships_3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ greater(zero,growth_rate(VAR_1,VAR_2))
| environment(VAR_0) ),
file('theBenchmark.p',mp_growth_rate_relationships_3) ).
cnf(c_1,plain,
( ~ greater(zero,growth_rate(B,C))
| environment(A) ),
inference(clausify,[status(thm)],[mp_growth_rate_relationships_3]) ).
fof(mp_time_point_occur_2,axiom,
! [VAR_0,VAR_1] :
( in_environment(VAR_0,VAR_1)
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_time_point_occur_2) ).
cnf(c_2,plain,
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_time_point_occur_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_3,plain,
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_symmetry_of_subpopulations_1]) ).
fof(d2_8,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( greater_or_equal(growth_rate(VAR_2,VAR_3),zero)
| ~ outcompetes(VAR_2,VAR_1,VAR_3)
| ~ subpopulations(VAR_1,VAR_2,VAR_0,VAR_3)
| ~ environment(VAR_0) ),
file('theBenchmark.p',d2_8) ).
cnf(c_6,plain,
( greater_or_equal(growth_rate(C,D),zero)
| ~ outcompetes(C,B,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[d2_8]) ).
fof(d2_9,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( greater(zero,growth_rate(VAR_1,VAR_3))
| ~ outcompetes(VAR_2,VAR_1,VAR_3)
| ~ subpopulations(VAR_1,VAR_2,VAR_0,VAR_3)
| ~ environment(VAR_0) ),
file('theBenchmark.p',d2_9) ).
cnf(c_7,plain,
( greater(zero,growth_rate(B,D))
| ~ outcompetes(C,B,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[d2_9]) ).
fof(a13_11,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ greater(zero,growth_rate(VAR_3,VAR_1))
| ~ greater(resilience(VAR_3),resilience(VAR_2))
| greater(zero,growth_rate(VAR_2,VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',a13_11) ).
cnf(c_8,plain,
( ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a13_11]) ).
fof(prove_t5_12,axiom,
environment(sk1),
file('theBenchmark.p',prove_t5_12) ).
cnf(c_9,plain,
environment(sk1),
inference(clausify,[status(thm)],[prove_t5_12]) ).
cnf(c_10,plain,
( ~ greater(zero,growth_rate(E,F))
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) ),
inference(resolve,[status(thm)],[c_8,c_1]) ).
cnf(c_12,plain,
( in_environment(C,D)
| ~ subpopulations(first_movers,efficient_producers,C,D)
| ~ greater(zero,growth_rate(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(mp_growth_rate_relationships_5,axiom,
! [VAR_0,VAR_1] :
( ~ greater(zero,growth_rate(VAR_0,VAR_1))
| ~ greater_or_equal(growth_rate(VAR_0,VAR_1),zero) ),
file('theBenchmark.p',mp_growth_rate_relationships_5) ).
cnf(c_14,plain,
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) ),
inference(clausify,[status(thm)],[mp_growth_rate_relationships_5]) ).
cnf(c_16,plain,
( ~ greater(zero,growth_rate(E,F))
| greater_or_equal(growth_rate(B,D),zero)
| ~ outcompetes(B,A,D)
| ~ subpopulations(A,B,C,D) ),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_19,plain,
( ~ greater(zero,growth_rate(B,D))
| ~ greater(zero,growth_rate(E,F))
| ~ outcompetes(B,A,D)
| ~ subpopulations(A,B,C,D) ),
inference(resolve,[status(thm)],[c_16,c_14]) ).
cnf(c_22,plain,
( subpopulations(B,A,sk1,C)
| ~ subpopulations(A,B,sk1,C) ),
inference(resolve,[status(thm)],[c_9,c_3]) ).
cnf(c_23,plain,
( greater(zero,growth_rate(A,C))
| ~ outcompetes(B,A,C)
| ~ subpopulations(A,B,sk1,C) ),
inference(resolve,[status(thm)],[c_9,c_7]) ).
fof(prove_t5_14,axiom,
outcompetes(first_movers,efficient_producers,sk2),
file('theBenchmark.p',prove_t5_14) ).
cnf(c_26,plain,
outcompetes(first_movers,efficient_producers,sk2),
inference(clausify,[status(thm)],[prove_t5_14]) ).
fof(prove_t5_13,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('theBenchmark.p',prove_t5_13) ).
cnf(c_27,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(clausify,[status(thm)],[prove_t5_13]) ).
fof(a2_10,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('theBenchmark.p',a2_10) ).
cnf(c_28,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(clausify,[status(thm)],[a2_10]) ).
cnf(c_31,plain,
( ~ greater(zero,growth_rate(V6,V7))
| ~ greater(zero,growth_rate(F,D))
| ~ greater(resilience(F),resilience(E))
| greater(zero,growth_rate(E,D))
| ~ subpopulations(first_movers,efficient_producers,C,D)
| ~ greater(zero,growth_rate(A,B)) ),
inference(resolve,[status(thm)],[c_12,c_10]) ).
cnf(c_32,plain,
( ~ greater(zero,growth_rate(B,D))
| ~ outcompetes(B,A,D)
| ~ subpopulations(A,B,C,D) ),
inference(factor,[status(thm)],[c_19]) ).
cnf(c_36,plain,
( ~ greater(zero,growth_rate(E,F))
| ~ greater(resilience(A),resilience(D))
| greater(zero,growth_rate(D,B))
| ~ subpopulations(first_movers,efficient_producers,C,B)
| ~ greater(zero,growth_rate(A,B)) ),
inference(factor,[status(thm)],[c_31]) ).
cnf(c_39,plain,
( ~ greater(resilience(A),resilience(D))
| greater(zero,growth_rate(D,B))
| ~ subpopulations(first_movers,efficient_producers,C,B)
| ~ greater(zero,growth_rate(A,B)) ),
inference(factor,[status(thm)],[c_36]) ).
cnf(c_43,plain,
subpopulations(efficient_producers,first_movers,sk1,sk2),
inference(resolve,[status(thm)],[c_27,c_22]) ).
cnf(c_49,plain,
( ~ greater(resilience(A),resilience(B))
| greater(zero,growth_rate(B,sk2))
| ~ greater(zero,growth_rate(A,sk2)) ),
inference(resolve,[status(thm)],[c_39,c_27]) ).
cnf(c_57,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ outcompetes(first_movers,efficient_producers,sk2) ),
inference(resolve,[status(thm)],[c_43,c_32]) ).
cnf(c_52,plain,
~ greater(zero,growth_rate(first_movers,sk2)),
inference(resolve,[status(thm)],[c_26,c_57]) ).
cnf(c_58,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ outcompetes(first_movers,efficient_producers,sk2) ),
inference(resolve,[status(thm)],[c_43,c_23]) ).
cnf(c_54,plain,
greater(zero,growth_rate(efficient_producers,sk2)),
inference(resolve,[status(thm)],[c_26,c_58]) ).
cnf(c_59,plain,
( greater(zero,growth_rate(first_movers,sk2))
| ~ greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_49,c_28]) ).
cnf(c_60,plain,
greater(zero,growth_rate(first_movers,sk2)),
inference(resolve,[status(thm)],[c_54,c_59]) ).
cnf(c_56,plain,
$false,
inference(resolve,[status(thm)],[c_52,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT036-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n013.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.46 % CPULimit : 300
% 0.18/5.46 % WCLimit : 300
% 0.18/5.46 % DateTime : Sat Sep 26 00:06:12 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.18/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.46 % Process 1508515 was started by sandbox on n013,
% 0.18/5.46 % Sat Sep 26 00:06:12 2026
% 0.18/5.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/5.47
% 0.18/5.47 % From the command line: assign(max_seconds, 300).
% 0.18/5.48
% 0.18/5.48 % SZS status Unsatisfiable for theBenchmark
% 0.18/5.48
% 0.18/5.48 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/5.48 % Length of proof is 26.
% 0.18/5.48 % Level of proof is 6.
% 0.18/5.48 % Maximum clause weight is 40.000.
% 0.18/5.48 % Given clauses 15.
% 0.18/5.48
% 0.18/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------