%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : MGT021+1 : TPTP v9.3.0. Released v2.0.0.
% 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 : n029.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 : Theorem 3.27s 2.29s
% Output : CNFRefutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 113 ( 51 ~; 44 |; 8 &)
% ( 0 <=>; 10 =>; 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 : 35 ( 35 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulations > in_environment > greater_or_equal > greater > increases > environment > decreases > constant > resources > number_of_organizations > disbanding_rate > difference > #nlpp > equilibrium > zero > first_movers > efficient_producers > #skF_2 > #skF_1
%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(constant,type,
constant: $i > $o ).
tff(efficient_producers,type,
efficient_producers: $i ).
tff(disbanding_rate,type,
disbanding_rate: ( $i * $i ) > $i ).
tff(decreases,type,
decreases: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
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_103,negated_conjecture,
~ ! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l3) ).
tff(f_40,axiom,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_in_environment) ).
tff(f_49,axiom,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(number_of_organizations(E,T),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_not_empty) ).
tff(f_78,hypothesis,
! [E,T] :
( ( environment(E)
& in_environment(E,T)
& greater(number_of_organizations(E,T),zero) )
=> ( ( greater(equilibrium(E),T)
=> decreases(resources(E,T)) )
& ( ~ greater(equilibrium(E),T)
=> constant(resources(E,T)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
tff(f_93,hypothesis,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ( ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
& ( constant(resources(E,T))
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4) ).
tff(f_55,axiom,
! [X] :
( increases(X)
=> ~ decreases(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_increase_not_decrease) ).
tff(c_18,plain,
decreases(difference(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2'))),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_22,plain,
environment('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_20,plain,
subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_25,plain,
! [E_15,T_16] :
( in_environment(E_15,T_16)
| ~ subpopulations(first_movers,efficient_producers,E_15,T_16)
| ~ environment(E_15) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_28,plain,
( in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_20,c_25]) ).
tff(c_31,plain,
in_environment('#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_28]) ).
tff(c_4,plain,
! [E_3,T_4] :
( greater(number_of_organizations(E_3,T_4),zero)
| ~ subpopulations(first_movers,efficient_producers,E_3,T_4)
| ~ environment(E_3) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_33,plain,
! [E_19,T_20] :
( constant(resources(E_19,T_20))
| greater(equilibrium(E_19),T_20)
| ~ greater(number_of_organizations(E_19,T_20),zero)
| ~ in_environment(E_19,T_20)
| ~ environment(E_19) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_37,plain,
! [E_3,T_4] :
( constant(resources(E_3,T_4))
| greater(equilibrium(E_3),T_4)
| ~ in_environment(E_3,T_4)
| ~ subpopulations(first_movers,efficient_producers,E_3,T_4)
| ~ environment(E_3) ),
inference(resolution,[status(thm)],[c_4,c_33]) ).
tff(c_38,plain,
! [E_21,T_22] :
( decreases(resources(E_21,T_22))
| ~ greater(equilibrium(E_21),T_22)
| ~ greater(number_of_organizations(E_21,T_22),zero)
| ~ in_environment(E_21,T_22)
| ~ environment(E_21) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_44,plain,
! [E_25,T_26] :
( decreases(resources(E_25,T_26))
| ~ greater(equilibrium(E_25),T_26)
| ~ in_environment(E_25,T_26)
| ~ subpopulations(first_movers,efficient_producers,E_25,T_26)
| ~ environment(E_25) ),
inference(resolution,[status(thm)],[c_4,c_38]) ).
tff(c_48,plain,
! [E_3,T_4] :
( decreases(resources(E_3,T_4))
| constant(resources(E_3,T_4))
| ~ in_environment(E_3,T_4)
| ~ subpopulations(first_movers,efficient_producers,E_3,T_4)
| ~ environment(E_3) ),
inference(resolution,[status(thm)],[c_37,c_44]) ).
tff(c_50,plain,
! [T_29,E_30] :
( increases(difference(disbanding_rate(first_movers,T_29),disbanding_rate(efficient_producers,T_29)))
| ~ decreases(resources(E_30,T_29))
| ~ subpopulations(first_movers,efficient_producers,E_30,T_29)
| ~ environment(E_30) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_59,plain,
! [T_34,E_35] :
( increases(difference(disbanding_rate(first_movers,T_34),disbanding_rate(efficient_producers,T_34)))
| constant(resources(E_35,T_34))
| ~ in_environment(E_35,T_34)
| ~ subpopulations(first_movers,efficient_producers,E_35,T_34)
| ~ environment(E_35) ),
inference(resolution,[status(thm)],[c_48,c_50]) ).
tff(c_54,plain,
! [T_31,E_32] :
( ~ decreases(difference(disbanding_rate(first_movers,T_31),disbanding_rate(efficient_producers,T_31)))
| ~ constant(resources(E_32,T_31))
| ~ subpopulations(first_movers,efficient_producers,E_32,T_31)
| ~ environment(E_32) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_57,plain,
! [E_32] :
( ~ constant(resources(E_32,'#skF_2'))
| ~ subpopulations(first_movers,efficient_producers,E_32,'#skF_2')
| ~ environment(E_32) ),
inference(resolution,[status(thm)],[c_18,c_54]) ).
tff(c_68,plain,
! [E_35] :
( increases(difference(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2')))
| ~ in_environment(E_35,'#skF_2')
| ~ subpopulations(first_movers,efficient_producers,E_35,'#skF_2')
| ~ environment(E_35) ),
inference(resolution,[status(thm)],[c_59,c_57]) ).
tff(c_70,plain,
! [E_36] :
( ~ in_environment(E_36,'#skF_2')
| ~ subpopulations(first_movers,efficient_producers,E_36,'#skF_2')
| ~ environment(E_36) ),
inference(splitLeft,[status(thm)],[c_68]) ).
tff(c_73,plain,
( ~ in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_20,c_70]) ).
tff(c_77,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22,c_31,c_73]) ).
tff(c_78,plain,
increases(difference(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2'))),
inference(splitRight,[status(thm)],[c_68]) ).
tff(c_6,plain,
! [X_5] :
( ~ decreases(X_5)
| ~ increases(X_5) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_81,plain,
~ decreases(difference(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2'))),
inference(resolution,[status(thm)],[c_78,c_6]) ).
tff(c_85,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_18,c_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT021+1 : TPTP v9.3.0. Released v2.0.0.
% 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
% 0.08/0.35 % Computer : n029.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 7 12:04:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 3.27/2.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.27/2.29
% 3.27/2.29 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------