%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : MGT020-1 : 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 : n008.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 6.36s 3.06s
% Output : CNFRefutation 6.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 144 ( 5 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 188 ( 95 ~; 93 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulations > in_environment > greater_or_equal > greater > environment > decreases > disbanding_rate > difference > #nlpp > start_time > initial_FM_EP > 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(in_environment,type,
in_environment: ( $i * $i ) > $o ).
tff(sk2,type,
sk2: $i ).
tff(sk1,type,
sk1: $i ).
tff(efficient_producers,type,
efficient_producers: $i ).
tff(disbanding_rate,type,
disbanding_rate: ( $i * $i ) > $i ).
tff(initial_FM_EP,type,
initial_FM_EP: $i > $i ).
tff(decreases,type,
decreases: $i > $o ).
tff(environment,type,
environment: $i > $o ).
tff(start_time,type,
start_time: $i > $i ).
tff(first_movers,type,
first_movers: $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff(greater_or_equal,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(f_134,axiom,
environment(sk1),
file(unknown,unknown) ).
tff(f_135,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file(unknown,unknown) ).
tff(f_50,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| greater_or_equal(B,initial_FM_EP(A)) ),
file(unknown,unknown) ).
tff(f_137,axiom,
~ greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)),
file(unknown,unknown) ).
tff(f_111,axiom,
! [A,B] :
( ~ greater_or_equal(A,B)
| greater(A,B)
| ( A = B ) ),
file(unknown,unknown) ).
tff(f_82,axiom,
! [A] :
( ~ environment(A)
| greater_or_equal(initial_FM_EP(A),start_time(A)) ),
file(unknown,unknown) ).
tff(f_77,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| in_environment(A,B) ),
file(unknown,unknown) ).
tff(f_96,axiom,
! [A,B,C] :
( ~ environment(A)
| ~ greater_or_equal(B,start_time(A))
| ~ greater(C,B)
| ~ in_environment(A,C)
| in_environment(A,B) ),
file(unknown,unknown) ).
tff(f_116,axiom,
! [A] :
( ~ environment(A)
| greater(disbanding_rate(first_movers,initial_FM_EP(A)),disbanding_rate(efficient_producers,initial_FM_EP(A))) ),
file(unknown,unknown) ).
tff(f_42,axiom,
! [A] :
( ~ environment(A)
| ~ in_environment(A,initial_FM_EP(A))
| subpopulations(first_movers,efficient_producers,A,initial_FM_EP(A)) ),
file(unknown,unknown) ).
tff(f_69,axiom,
! [A,B,C,D] :
( ~ environment(A)
| ~ greater_or_equal(B,C)
| ~ greater_or_equal(D,B)
| ~ subpopulations(first_movers,efficient_producers,A,D)
| ~ greater(disbanding_rate(first_movers,C),disbanding_rate(efficient_producers,C))
| decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| greater(disbanding_rate(first_movers,D),disbanding_rate(efficient_producers,D)) ),
file(unknown,unknown) ).
tff(f_34,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) ),
file(unknown,unknown) ).
tff(c_24,plain,
environment(sk1),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_26,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_6,plain,
! [B_5,A_4] :
( greater_or_equal(B_5,initial_FM_EP(A_4))
| ~ subpopulations(first_movers,efficient_producers,A_4,B_5)
| ~ environment(A_4) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_28,plain,
~ greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_47,plain,
! [B_35,A_36] :
( greater_or_equal(B_35,initial_FM_EP(A_36))
| ~ subpopulations(first_movers,efficient_producers,A_36,B_35)
| ~ environment(A_36) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_18,plain,
! [B_20,A_19] :
( ( B_20 = A_19 )
| greater(A_19,B_20)
| ~ greater_or_equal(A_19,B_20) ),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_51,plain,
! [A_36,B_35] :
( ( initial_FM_EP(A_36) = B_35 )
| greater(B_35,initial_FM_EP(A_36))
| ~ subpopulations(first_movers,efficient_producers,A_36,B_35)
| ~ environment(A_36) ),
inference(resolution,[status(thm)],[c_47,c_18]) ).
tff(c_12,plain,
! [A_12] :
( greater_or_equal(initial_FM_EP(A_12),start_time(A_12))
| ~ environment(A_12) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_36,plain,
! [A_32,B_33] :
( in_environment(A_32,B_33)
| ~ subpopulations(first_movers,efficient_producers,A_32,B_33)
| ~ environment(A_32) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_39,plain,
( in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_26,c_36]) ).
tff(c_42,plain,
in_environment(sk1,sk2),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_39]) ).
tff(c_70,plain,
! [A_45,B_46,C_47] :
( in_environment(A_45,B_46)
| ~ in_environment(A_45,C_47)
| ~ greater(C_47,B_46)
| ~ greater_or_equal(B_46,start_time(A_45))
| ~ environment(A_45) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_72,plain,
! [B_46] :
( in_environment(sk1,B_46)
| ~ greater(sk2,B_46)
| ~ greater_or_equal(B_46,start_time(sk1))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_42,c_70]) ).
tff(c_76,plain,
! [B_48] :
( in_environment(sk1,B_48)
| ~ greater(sk2,B_48)
| ~ greater_or_equal(B_48,start_time(sk1)) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_72]) ).
tff(c_80,plain,
( in_environment(sk1,initial_FM_EP(sk1))
| ~ greater(sk2,initial_FM_EP(sk1))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_12,c_76]) ).
tff(c_83,plain,
( in_environment(sk1,initial_FM_EP(sk1))
| ~ greater(sk2,initial_FM_EP(sk1)) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_80]) ).
tff(c_84,plain,
~ greater(sk2,initial_FM_EP(sk1)),
inference(splitLeft,[status(thm)],[c_83]) ).
tff(c_87,plain,
( ( initial_FM_EP(sk1) = sk2 )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_51,c_84]) ).
tff(c_90,plain,
initial_FM_EP(sk1) = sk2,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_87]) ).
tff(c_20,plain,
! [A_21] :
( greater(disbanding_rate(first_movers,initial_FM_EP(A_21)),disbanding_rate(efficient_producers,initial_FM_EP(A_21)))
| ~ environment(A_21) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_111,plain,
( greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,initial_FM_EP(sk1)))
| ~ environment(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_90,c_20]) ).
tff(c_131,plain,
greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_90,c_111]) ).
tff(c_133,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_131]) ).
tff(c_134,plain,
in_environment(sk1,initial_FM_EP(sk1)),
inference(splitRight,[status(thm)],[c_83]) ).
tff(c_4,plain,
! [A_3] :
( subpopulations(first_movers,efficient_producers,A_3,initial_FM_EP(A_3))
| ~ in_environment(A_3,initial_FM_EP(A_3))
| ~ environment(A_3) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_278,plain,
! [D_71,B_72,C_73,A_74] :
( greater(disbanding_rate(first_movers,D_71),disbanding_rate(efficient_producers,D_71))
| decreases(difference(disbanding_rate(first_movers,B_72),disbanding_rate(efficient_producers,B_72)))
| ~ greater(disbanding_rate(first_movers,C_73),disbanding_rate(efficient_producers,C_73))
| ~ subpopulations(first_movers,efficient_producers,A_74,D_71)
| ~ greater_or_equal(D_71,B_72)
| ~ greater_or_equal(B_72,C_73)
| ~ environment(A_74) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_810,plain,
! [D_152,B_153,A_154,A_155] :
( greater(disbanding_rate(first_movers,D_152),disbanding_rate(efficient_producers,D_152))
| decreases(difference(disbanding_rate(first_movers,B_153),disbanding_rate(efficient_producers,B_153)))
| ~ subpopulations(first_movers,efficient_producers,A_154,D_152)
| ~ greater_or_equal(D_152,B_153)
| ~ greater_or_equal(B_153,initial_FM_EP(A_155))
| ~ environment(A_154)
| ~ environment(A_155) ),
inference(resolution,[status(thm)],[c_20,c_278]) ).
tff(c_814,plain,
! [B_153,A_155] :
( greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))
| decreases(difference(disbanding_rate(first_movers,B_153),disbanding_rate(efficient_producers,B_153)))
| ~ greater_or_equal(sk2,B_153)
| ~ greater_or_equal(B_153,initial_FM_EP(A_155))
| ~ environment(sk1)
| ~ environment(A_155) ),
inference(resolution,[status(thm)],[c_26,c_810]) ).
tff(c_818,plain,
! [B_153,A_155] :
( greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))
| decreases(difference(disbanding_rate(first_movers,B_153),disbanding_rate(efficient_producers,B_153)))
| ~ greater_or_equal(sk2,B_153)
| ~ greater_or_equal(B_153,initial_FM_EP(A_155))
| ~ environment(A_155) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_814]) ).
tff(c_820,plain,
! [B_156,A_157] :
( decreases(difference(disbanding_rate(first_movers,B_156),disbanding_rate(efficient_producers,B_156)))
| ~ greater_or_equal(sk2,B_156)
| ~ greater_or_equal(B_156,initial_FM_EP(A_157))
| ~ environment(A_157) ),
inference(negUnitSimplification,[status(thm)],[c_28,c_818]) ).
tff(c_824,plain,
! [B_158,A_159] :
( decreases(difference(disbanding_rate(first_movers,B_158),disbanding_rate(efficient_producers,B_158)))
| ~ greater_or_equal(sk2,B_158)
| ~ subpopulations(first_movers,efficient_producers,A_159,B_158)
| ~ environment(A_159) ),
inference(resolution,[status(thm)],[c_6,c_820]) ).
tff(c_834,plain,
! [A_160] :
( decreases(difference(disbanding_rate(first_movers,initial_FM_EP(A_160)),disbanding_rate(efficient_producers,initial_FM_EP(A_160))))
| ~ greater_or_equal(sk2,initial_FM_EP(A_160))
| ~ in_environment(A_160,initial_FM_EP(A_160))
| ~ environment(A_160) ),
inference(resolution,[status(thm)],[c_4,c_824]) ).
tff(c_2,plain,
! [B_2,A_1] :
( ~ decreases(difference(disbanding_rate(first_movers,B_2),disbanding_rate(efficient_producers,B_2)))
| ~ subpopulations(first_movers,efficient_producers,A_1,B_2)
| ~ environment(A_1) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_848,plain,
! [A_163,A_164] :
( ~ subpopulations(first_movers,efficient_producers,A_163,initial_FM_EP(A_164))
| ~ environment(A_163)
| ~ greater_or_equal(sk2,initial_FM_EP(A_164))
| ~ in_environment(A_164,initial_FM_EP(A_164))
| ~ environment(A_164) ),
inference(resolution,[status(thm)],[c_834,c_2]) ).
tff(c_852,plain,
! [A_165] :
( ~ greater_or_equal(sk2,initial_FM_EP(A_165))
| ~ in_environment(A_165,initial_FM_EP(A_165))
| ~ environment(A_165) ),
inference(resolution,[status(thm)],[c_4,c_848]) ).
tff(c_855,plain,
( ~ greater_or_equal(sk2,initial_FM_EP(sk1))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_134,c_852]) ).
tff(c_858,plain,
~ greater_or_equal(sk2,initial_FM_EP(sk1)),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_855]) ).
tff(c_861,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_6,c_858]) ).
tff(c_865,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_861]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT020-1 : 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 : n008.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
% 0.11/0.36 % DateTime : Mon Sep 7 12:02:38 UTC 2026
% 0.11/0.36 % CPUTime :
% 6.36/3.06 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.36/3.07
% 6.36/3.07 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------