%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT021-1 : 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 : n016.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 08:02:08 AM UTC 2026
% Result : Unsatisfiable 0.06s 15.44s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 13 unt; 0 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 125 ( 65 ~; 60 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_l3_35,axiom,
environment(sk1),
file('theBenchmark.p',prove_l3_35) ).
cnf(c_1,plain,
environment(sk1),
inference(clausify,[status(thm)],[prove_l3_35]) ).
fof(l4_34,axiom,
! [VAR_0,VAR_1] :
( ~ decreases(difference(disbanding_rate(first_movers,VAR_1),disbanding_rate(efficient_producers,VAR_1)))
| ~ constant(resources(VAR_0,VAR_1))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l4_34) ).
cnf(c_2,plain,
( ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l4_34]) ).
fof(l4_33,axiom,
! [VAR_0,VAR_1] :
( increases(difference(disbanding_rate(first_movers,VAR_1),disbanding_rate(efficient_producers,VAR_1)))
| ~ decreases(resources(VAR_0,VAR_1))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l4_33) ).
cnf(c_3,plain,
( increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l4_33]) ).
fof(a3_32,axiom,
! [VAR_0,VAR_1] :
( constant(resources(VAR_0,VAR_1))
| greater(equilibrium(VAR_0),VAR_1)
| ~ greater(number_of_organizations(VAR_0,VAR_1),zero)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',a3_32) ).
cnf(c_4,plain,
( constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a3_32]) ).
fof(a3_31,axiom,
! [VAR_0,VAR_1] :
( decreases(resources(VAR_0,VAR_1))
| ~ greater(equilibrium(VAR_0),VAR_1)
| ~ greater(number_of_organizations(VAR_0,VAR_1),zero)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',a3_31) ).
cnf(c_5,plain,
( decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a3_31]) ).
fof(mp_environment_not_empty_28,axiom,
! [VAR_0,VAR_1] :
( greater(number_of_organizations(VAR_0,VAR_1),zero)
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_environment_not_empty_28) ).
cnf(c_6,plain,
( greater(number_of_organizations(A,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_environment_not_empty_28]) ).
fof(mp_time_point_in_environment_27,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_in_environment_27) ).
cnf(c_7,plain,
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_time_point_in_environment_27]) ).
fof(mp_increase_not_decrease_29,axiom,
! [VAR_0] :
( ~ decreases(VAR_0)
| ~ increases(VAR_0) ),
file('theBenchmark.p',mp_increase_not_decrease_29) ).
cnf(c_8,plain,
( ~ decreases(A)
| ~ increases(A) ),
inference(clausify,[status(thm)],[mp_increase_not_decrease_29]) ).
cnf(c_9,plain,
( increases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| ~ decreases(resources(sk1,A))
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_10,plain,
( in_environment(sk1,A)
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_11,plain,
( greater(number_of_organizations(sk1,A),zero)
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_12,plain,
( decreases(resources(sk1,A))
| ~ greater(equilibrium(sk1),A)
| ~ greater(number_of_organizations(sk1,A),zero)
| ~ in_environment(sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_13,plain,
( constant(resources(sk1,A))
| greater(equilibrium(sk1),A)
| ~ greater(number_of_organizations(sk1,A),zero)
| ~ in_environment(sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_14,plain,
( ~ decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| ~ constant(resources(sk1,A))
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_l3_37,axiom,
decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
file('theBenchmark.p',prove_l3_37) ).
cnf(c_15,plain,
decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
inference(clausify,[status(thm)],[prove_l3_37]) ).
fof(prove_l3_36,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('theBenchmark.p',prove_l3_36) ).
cnf(c_16,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(clausify,[status(thm)],[prove_l3_36]) ).
cnf(c_17,plain,
( ~ decreases(resources(sk1,A))
| ~ subpopulations(first_movers,efficient_producers,sk1,A)
| ~ decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A))) ),
inference(resolve,[status(thm)],[c_8,c_9]) ).
cnf(c_24,plain,
( ~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ constant(resources(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_16,c_14]) ).
cnf(c_18,plain,
~ constant(resources(sk1,sk2)),
inference(resolve,[status(thm)],[c_15,c_24]) ).
cnf(c_19,plain,
greater(number_of_organizations(sk1,sk2),zero),
inference(resolve,[status(thm)],[c_16,c_11]) ).
cnf(c_20,plain,
in_environment(sk1,sk2),
inference(resolve,[status(thm)],[c_16,c_10]) ).
cnf(c_25,plain,
( ~ decreases(resources(sk1,sk2))
| ~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
inference(resolve,[status(thm)],[c_17,c_16]) ).
cnf(c_21,plain,
~ decreases(resources(sk1,sk2)),
inference(resolve,[status(thm)],[c_15,c_25]) ).
cnf(c_26,plain,
( constant(resources(sk1,sk2))
| greater(equilibrium(sk1),sk2)
| ~ greater(number_of_organizations(sk1,sk2),zero) ),
inference(resolve,[status(thm)],[c_20,c_13]) ).
cnf(c_27,plain,
( constant(resources(sk1,sk2))
| greater(equilibrium(sk1),sk2) ),
inference(resolve,[status(thm)],[c_19,c_26]) ).
cnf(c_22,plain,
greater(equilibrium(sk1),sk2),
inference(resolve,[status(thm)],[c_18,c_27]) ).
cnf(c_28,plain,
( decreases(resources(sk1,sk2))
| ~ greater(equilibrium(sk1),sk2)
| ~ greater(number_of_organizations(sk1,sk2),zero) ),
inference(resolve,[status(thm)],[c_20,c_12]) ).
cnf(c_29,plain,
( decreases(resources(sk1,sk2))
| ~ greater(equilibrium(sk1),sk2) ),
inference(resolve,[status(thm)],[c_19,c_28]) ).
cnf(c_30,plain,
decreases(resources(sk1,sk2)),
inference(resolve,[status(thm)],[c_22,c_29]) ).
cnf(c_23,plain,
$false,
inference(resolve,[status(thm)],[c_21,c_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT021-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.06/15.42 % CPULimit : 300
% 0.06/15.42 % WCLimit : 300
% 0.06/15.42 % DateTime : Sat Sep 26 00:04:14 UTC 2026
% 0.06/15.42 % CPUTime :
% 0.06/15.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/15.42 % Process 4074243 was started by sandbox on n006,
% 0.06/15.42 % Sat Sep 26 00:04:14 2026
% 0.06/15.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.06/15.42
% 0.06/15.42 % From the command line: assign(max_seconds, 300).
% 0.06/15.44
% 0.06/15.44 % SZS status Unsatisfiable for theBenchmark
% 0.06/15.44
% 0.06/15.44 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.06/15.44 % Length of proof is 23.
% 0.06/15.44 % Level of proof is 4.
% 0.06/15.44 % Maximum clause weight is 17.000.
% 0.06/15.44 % Given clauses 11.
% 0.06/15.44
% 0.06/15.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------