%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT022-2 : 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 : 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 08:02:09 AM UTC 2026
% Result : Unsatisfiable 0.15s 10.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 10 unt; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 77 ( 37 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_l4_5,axiom,
environment(sk1),
file('theBenchmark.p',prove_l4_5) ).
cnf(c_1,plain,
environment(sk1),
inference(clausify,[status(thm)],[prove_l4_5]) ).
fof(a6_3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( constant(difference(disbanding_rate(VAR_1,VAR_3),disbanding_rate(VAR_2,VAR_3)))
| ~ constant(resources(VAR_0,VAR_3))
| ~ greater(resilience(VAR_2),resilience(VAR_1))
| ~ subpopulations(VAR_1,VAR_2,VAR_0,VAR_3)
| ~ environment(VAR_0) ),
file('theBenchmark.p',a6_3) ).
cnf(c_2,plain,
( constant(difference(disbanding_rate(B,D),disbanding_rate(C,D)))
| ~ constant(resources(A,D))
| ~ greater(resilience(C),resilience(B))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a6_3]) ).
fof(a6_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( increases(difference(disbanding_rate(VAR_1,VAR_3),disbanding_rate(VAR_2,VAR_3)))
| ~ decreases(resources(VAR_0,VAR_3))
| ~ greater(resilience(VAR_2),resilience(VAR_1))
| ~ subpopulations(VAR_1,VAR_2,VAR_0,VAR_3)
| ~ environment(VAR_0) ),
file('theBenchmark.p',a6_2) ).
cnf(c_3,plain,
( increases(difference(disbanding_rate(B,D),disbanding_rate(C,D)))
| ~ decreases(resources(A,D))
| ~ greater(resilience(C),resilience(B))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a6_2]) ).
fof(prove_l4_6,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('theBenchmark.p',prove_l4_6) ).
cnf(c_4,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(clausify,[status(thm)],[prove_l4_6]) ).
cnf(c_5,plain,
( constant(difference(disbanding_rate(A,C),disbanding_rate(B,C)))
| ~ constant(resources(sk1,C))
| ~ greater(resilience(B),resilience(A))
| ~ subpopulations(A,B,sk1,C) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
( increases(difference(disbanding_rate(A,C),disbanding_rate(B,C)))
| ~ decreases(resources(sk1,C))
| ~ greater(resilience(B),resilience(A))
| ~ subpopulations(A,B,sk1,C) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
fof(a2_4,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('theBenchmark.p',a2_4) ).
cnf(c_7,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(clausify,[status(thm)],[a2_4]) ).
cnf(c_8,plain,
( constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ constant(resources(sk1,sk2))
| ~ greater(resilience(efficient_producers),resilience(first_movers)) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_9,plain,
( increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ decreases(resources(sk1,sk2))
| ~ greater(resilience(efficient_producers),resilience(first_movers)) ),
inference(resolve,[status(thm)],[c_4,c_6]) ).
cnf(c_11,plain,
( increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ decreases(resources(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_7,c_9]) ).
fof(prove_l4_9,axiom,
( constant(resources(sk1,sk2))
| ~ increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
file('theBenchmark.p',prove_l4_9) ).
cnf(c_12,plain,
( constant(resources(sk1,sk2))
| ~ increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
inference(clausify,[status(thm)],[prove_l4_9]) ).
cnf(c_13,plain,
( ~ decreases(resources(sk1,sk2))
| constant(resources(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_12,c_11]) ).
fof(mp_constant_not_decrease_1,axiom,
! [VAR_0] :
( ~ decreases(VAR_0)
| ~ constant(VAR_0) ),
file('theBenchmark.p',mp_constant_not_decrease_1) ).
cnf(c_15,plain,
( ~ decreases(A)
| ~ constant(A) ),
inference(clausify,[status(thm)],[mp_constant_not_decrease_1]) ).
fof(prove_l4_7,axiom,
( constant(resources(sk1,sk2))
| decreases(resources(sk1,sk2)) ),
file('theBenchmark.p',prove_l4_7) ).
cnf(c_16,plain,
( constant(resources(sk1,sk2))
| decreases(resources(sk1,sk2)) ),
inference(clausify,[status(thm)],[prove_l4_7]) ).
fof(prove_l4_8,axiom,
( decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| decreases(resources(sk1,sk2)) ),
file('theBenchmark.p',prove_l4_8) ).
cnf(c_17,plain,
( decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| decreases(resources(sk1,sk2)) ),
inference(clausify,[status(thm)],[prove_l4_8]) ).
cnf(c_18,plain,
( constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ constant(resources(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_19,plain,
( decreases(resources(sk1,sk2))
| constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
inference(resolve,[status(thm)],[c_18,c_16]) ).
cnf(c_20,plain,
( ~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| decreases(resources(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_19,c_15]) ).
cnf(c_26,plain,
( decreases(resources(sk1,sk2))
| decreases(resources(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_20,c_17]) ).
cnf(c_21,plain,
decreases(resources(sk1,sk2)),
inference(copy,[status(thm)],[c_26]) ).
cnf(c_23,plain,
constant(resources(sk1,sk2)),
inference(resolve,[status(thm)],[c_21,c_13]) ).
cnf(c_27,plain,
~ constant(resources(sk1,sk2)),
inference(resolve,[status(thm)],[c_15,c_21]) ).
cnf(c_25,plain,
$false,
inference(resolve,[status(thm)],[c_23,c_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : MGT022-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/10.43 % Computer : n016.cluster.edu
% 0.15/10.43 % Model : x86_64 x86_64
% 0.15/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.43 % Memory : 8046.5625MB
% 0.15/10.43 % OS : Linux 6.8.0-71-generic
% 0.15/10.43 % CPULimit : 300
% 0.15/10.43 % WCLimit : 300
% 0.15/10.43 % DateTime : Sat Sep 26 00:09:10 UTC 2026
% 0.15/10.43 % CPUTime :
% 0.15/10.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/10.44 % Process 3626170 was started by sandbox2 on n016,
% 0.15/10.44 % Sat Sep 26 00:09:10 2026
% 0.15/10.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/10.44
% 0.15/10.44 % From the command line: assign(max_seconds, 300).
% 0.15/10.45
% 0.15/10.45 % SZS status Unsatisfiable for theBenchmark
% 0.15/10.45
% 0.15/10.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/10.45 % Length of proof is 21.
% 0.15/10.45 % Level of proof is 8.
% 0.15/10.45 % Maximum clause weight is 12.000.
% 0.15/10.45 % Given clauses 9.
% 0.15/10.45
% 0.15/10.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------