%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : MGT022+2 : 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 : n020.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 06:02:53 AM UTC 2026
% Result : Theorem 3.38s 2.25s
% Output : CNFRefutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 68 ( 32 ~; 24 |; 5 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulations > greater > increases > environment > decreases > constant > resources > disbanding_rate > difference > #nlpp > resilience > 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(constant,type,
constant: $i > $o ).
tff(efficient_producers,type,
efficient_producers: $i ).
tff(disbanding_rate,type,
disbanding_rate: ( $i * $i ) > $i ).
tff(resilience,type,
resilience: $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(difference,type,
difference: ( $i * $i ) > $i ).
tff(resources,type,
resources: ( $i * $i ) > $i ).
tff(increases,type,
increases: $i > $o ).
tff(f_70,negated_conjecture,
~ ! [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',prove_l4) ).
tff(f_53,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
tff(f_51,hypothesis,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T)
& greater(resilience(S2),resilience(S1)) )
=> ( ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) )
& ( constant(resources(E,T))
=> constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6) ).
tff(f_35,axiom,
! [X] :
( constant(X)
=> ~ decreases(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_constant_not_decrease) ).
tff(c_10,plain,
subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_8,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_12,plain,
environment('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_20,plain,
( decreases(resources('#skF_1','#skF_2'))
| constant(resources('#skF_1','#skF_2')) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_22,plain,
constant(resources('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_31,plain,
! [S1_11,T_12,S2_13,E_14] :
( constant(difference(disbanding_rate(S1_11,T_12),disbanding_rate(S2_13,T_12)))
| ~ constant(resources(E_14,T_12))
| ~ greater(resilience(S2_13),resilience(S1_11))
| ~ subpopulations(S1_11,S2_13,E_14,T_12)
| ~ environment(E_14) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_33,plain,
! [S1_11,S2_13] :
( constant(difference(disbanding_rate(S1_11,'#skF_2'),disbanding_rate(S2_13,'#skF_2')))
| ~ greater(resilience(S2_13),resilience(S1_11))
| ~ subpopulations(S1_11,S2_13,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_22,c_31]) ).
tff(c_37,plain,
! [S1_15,S2_16] :
( constant(difference(disbanding_rate(S1_15,'#skF_2'),disbanding_rate(S2_16,'#skF_2')))
| ~ greater(resilience(S2_16),resilience(S1_15))
| ~ subpopulations(S1_15,S2_16,'#skF_1','#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_33]) ).
tff(c_16,plain,
( decreases(resources('#skF_1','#skF_2'))
| decreases(difference(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2'))) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_24,plain,
decreases(difference(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2'))),
inference(splitLeft,[status(thm)],[c_16]) ).
tff(c_2,plain,
! [X_1] :
( ~ decreases(X_1)
| ~ constant(X_1) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_28,plain,
~ constant(difference(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2'))),
inference(resolution,[status(thm)],[c_24,c_2]) ).
tff(c_40,plain,
( ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2') ),
inference(resolution,[status(thm)],[c_37,c_28]) ).
tff(c_44,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8,c_40]) ).
tff(c_45,plain,
decreases(resources('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_49,plain,
~ constant(resources('#skF_1','#skF_2')),
inference(resolution,[status(thm)],[c_45,c_2]) ).
tff(c_53,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22,c_49]) ).
tff(c_54,plain,
decreases(resources('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_62,plain,
! [S1_17,T_18,S2_19,E_20] :
( increases(difference(disbanding_rate(S1_17,T_18),disbanding_rate(S2_19,T_18)))
| ~ decreases(resources(E_20,T_18))
| ~ greater(resilience(S2_19),resilience(S1_17))
| ~ subpopulations(S1_17,S2_19,E_20,T_18)
| ~ environment(E_20) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_64,plain,
! [S1_17,S2_19] :
( increases(difference(disbanding_rate(S1_17,'#skF_2'),disbanding_rate(S2_19,'#skF_2')))
| ~ greater(resilience(S2_19),resilience(S1_17))
| ~ subpopulations(S1_17,S2_19,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_54,c_62]) ).
tff(c_68,plain,
! [S1_21,S2_22] :
( increases(difference(disbanding_rate(S1_21,'#skF_2'),disbanding_rate(S2_22,'#skF_2')))
| ~ greater(resilience(S2_22),resilience(S1_21))
| ~ subpopulations(S1_21,S2_22,'#skF_1','#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_64]) ).
tff(c_55,plain,
~ constant(resources('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_18,plain,
( ~ increases(difference(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2')))
| constant(resources('#skF_1','#skF_2')) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_60,plain,
~ increases(difference(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2'))),
inference(negUnitSimplification,[status(thm)],[c_55,c_18]) ).
tff(c_71,plain,
( ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2') ),
inference(resolution,[status(thm)],[c_68,c_60]) ).
tff(c_75,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8,c_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT022+2 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.05 % 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
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 7 12:05:58 UTC 2026
% 0.14/0.38 % CPUTime :
% 3.38/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.38/2.25
% 3.38/2.25 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------