%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : MGT021-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n028.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 : Tue Sep 8 06:02:52 AM UTC 2026
% Result : Unsatisfiable 3.31s 2.17s
% Output : CNFRefutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 129 ( 66 ~; 63 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulations > in_environment > greater_or_equal > greater > increases > environment > decreases > constant > resources > number_of_organizations > disbanding_rate > difference > #nlpp > equilibrium > zero > sk2 > sk1 > first_movers > efficient_producers
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(subpopulations,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(greater,type,
greater: ( $i * $i ) > $o ).
tff(number_of_organizations,type,
number_of_organizations: ( $i * $i ) > $i ).
tff(in_environment,type,
in_environment: ( $i * $i ) > $o ).
tff(sk2,type,
sk2: $i ).
tff(constant,type,
constant: $i > $o ).
tff(sk1,type,
sk1: $i ).
tff(efficient_producers,type,
efficient_producers: $i ).
tff(disbanding_rate,type,
disbanding_rate: ( $i * $i ) > $i ).
tff(decreases,type,
decreases: $i > $o ).
tff(environment,type,
environment: $i > $o ).
tff(first_movers,type,
first_movers: $i ).
tff(equilibrium,type,
equilibrium: $i > $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff(greater_or_equal,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(resources,type,
resources: ( $i * $i ) > $i ).
tff(zero,type,
zero: $i ).
tff(increases,type,
increases: $i > $o ).
tff(f_108,axiom,
decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
file(unknown,unknown) ).
tff(f_106,axiom,
environment(sk1),
file(unknown,unknown) ).
tff(f_107,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file(unknown,unknown) ).
tff(f_34,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| in_environment(A,B) ),
file(unknown,unknown) ).
tff(f_42,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| greater(number_of_organizations(A,B),zero) ),
file(unknown,unknown) ).
tff(f_82,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero)
| greater(equilibrium(A),B)
| constant(resources(A,B)) ),
file(unknown,unknown) ).
tff(f_69,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ greater(equilibrium(A),B)
| decreases(resources(A,B)) ),
file(unknown,unknown) ).
tff(f_93,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ decreases(resources(A,B))
| increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) ),
file(unknown,unknown) ).
tff(f_105,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ constant(resources(A,B))
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) ),
file(unknown,unknown) ).
tff(f_48,axiom,
! [A] :
( ~ increases(A)
| ~ decreases(A) ),
file(unknown,unknown) ).
tff(c_22,plain,
decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_18,plain,
environment(sk1),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_20,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_25,plain,
! [A_19,B_20] :
( in_environment(A_19,B_20)
| ~ subpopulations(first_movers,efficient_producers,A_19,B_20)
| ~ environment(A_19) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_28,plain,
( in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_20,c_25]) ).
tff(c_31,plain,
in_environment(sk1,sk2),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_28]) ).
tff(c_4,plain,
! [A_3,B_4] :
( greater(number_of_organizations(A_3,B_4),zero)
| ~ subpopulations(first_movers,efficient_producers,A_3,B_4)
| ~ environment(A_3) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_38,plain,
! [A_25,B_26] :
( constant(resources(A_25,B_26))
| greater(equilibrium(A_25),B_26)
| ~ greater(number_of_organizations(A_25,B_26),zero)
| ~ in_environment(A_25,B_26)
| ~ environment(A_25) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_44,plain,
! [A_29,B_30] :
( constant(resources(A_29,B_30))
| greater(equilibrium(A_29),B_30)
| ~ in_environment(A_29,B_30)
| ~ subpopulations(first_movers,efficient_producers,A_29,B_30)
| ~ environment(A_29) ),
inference(resolution,[status(thm)],[c_4,c_38]) ).
tff(c_33,plain,
! [A_23,B_24] :
( decreases(resources(A_23,B_24))
| ~ greater(equilibrium(A_23),B_24)
| ~ greater(number_of_organizations(A_23,B_24),zero)
| ~ in_environment(A_23,B_24)
| ~ environment(A_23) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_37,plain,
! [A_3,B_4] :
( decreases(resources(A_3,B_4))
| ~ greater(equilibrium(A_3),B_4)
| ~ in_environment(A_3,B_4)
| ~ subpopulations(first_movers,efficient_producers,A_3,B_4)
| ~ environment(A_3) ),
inference(resolution,[status(thm)],[c_4,c_33]) ).
tff(c_48,plain,
! [A_29,B_30] :
( decreases(resources(A_29,B_30))
| constant(resources(A_29,B_30))
| ~ in_environment(A_29,B_30)
| ~ subpopulations(first_movers,efficient_producers,A_29,B_30)
| ~ environment(A_29) ),
inference(resolution,[status(thm)],[c_44,c_37]) ).
tff(c_50,plain,
! [B_33,A_34] :
( increases(difference(disbanding_rate(first_movers,B_33),disbanding_rate(efficient_producers,B_33)))
| ~ decreases(resources(A_34,B_33))
| ~ subpopulations(first_movers,efficient_producers,A_34,B_33)
| ~ environment(A_34) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_59,plain,
! [B_38,A_39] :
( increases(difference(disbanding_rate(first_movers,B_38),disbanding_rate(efficient_producers,B_38)))
| constant(resources(A_39,B_38))
| ~ in_environment(A_39,B_38)
| ~ subpopulations(first_movers,efficient_producers,A_39,B_38)
| ~ environment(A_39) ),
inference(resolution,[status(thm)],[c_48,c_50]) ).
tff(c_54,plain,
! [B_35,A_36] :
( ~ decreases(difference(disbanding_rate(first_movers,B_35),disbanding_rate(efficient_producers,B_35)))
| ~ constant(resources(A_36,B_35))
| ~ subpopulations(first_movers,efficient_producers,A_36,B_35)
| ~ environment(A_36) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_57,plain,
! [A_36] :
( ~ constant(resources(A_36,sk2))
| ~ subpopulations(first_movers,efficient_producers,A_36,sk2)
| ~ environment(A_36) ),
inference(resolution,[status(thm)],[c_22,c_54]) ).
tff(c_68,plain,
! [A_39] :
( increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ in_environment(A_39,sk2)
| ~ subpopulations(first_movers,efficient_producers,A_39,sk2)
| ~ environment(A_39) ),
inference(resolution,[status(thm)],[c_59,c_57]) ).
tff(c_70,plain,
! [A_40] :
( ~ in_environment(A_40,sk2)
| ~ subpopulations(first_movers,efficient_producers,A_40,sk2)
| ~ environment(A_40) ),
inference(splitLeft,[status(thm)],[c_68]) ).
tff(c_73,plain,
( ~ in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_20,c_70]) ).
tff(c_77,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_18,c_31,c_73]) ).
tff(c_78,plain,
increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
inference(splitRight,[status(thm)],[c_68]) ).
tff(c_6,plain,
! [A_5] :
( ~ decreases(A_5)
| ~ increases(A_5) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_85,plain,
~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
inference(resolution,[status(thm)],[c_78,c_6]) ).
tff(c_89,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22,c_85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT021-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.10/0.36 % Computer : n028.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 7 12:05:32 UTC 2026
% 0.10/0.36 % CPUTime :
% 3.31/2.17 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.31/2.17
% 3.31/2.17 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------