%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : MGT036+3 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/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 06:02:57 AM UTC 2026
% Result : Theorem 3.93s 2.54s
% Output : CNFRefutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 49 ( 22 ~; 16 |; 8 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 26 ( 22 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulations > outcompetes > greater_or_equal > greater > environment > growth_rate > #nlpp > 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(efficient_producers,type,
efficient_producers: $i ).
tff(growth_rate,type,
growth_rate: ( $i * $i ) > $i ).
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(greater_or_equal,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(outcompetes,type,
outcompetes: ( $i * $i * $i ) > $o ).
tff(zero,type,
zero: $i ).
tff(f_56,hypothesis,
? [E,T] :
( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(growth_rate(first_movers,T),zero)
& greater(zero,growth_rate(efficient_producers,T)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star) ).
tff(f_33,axiom,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T) )
=> subpopulations(S2,S1,E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
tff(f_65,negated_conjecture,
~ ? [E,T] :
( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& outcompetes(first_movers,efficient_producers,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_star) ).
tff(f_46,hypothesis,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T) )
=> ( ( greater_or_equal(growth_rate(S2,T),zero)
& greater(zero,growth_rate(S1,T)) )
<=> outcompetes(S2,S1,T) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
tff(c_16,plain,
environment('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_14,plain,
subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_26,plain,
! [S2_13,S1_14,E_15,T_16] :
( subpopulations(S2_13,S1_14,E_15,T_16)
| ~ subpopulations(S1_14,S2_13,E_15,T_16)
| ~ environment(E_15) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_28,plain,
( subpopulations(efficient_producers,first_movers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_14,c_26]) ).
tff(c_31,plain,
subpopulations(efficient_producers,first_movers,'#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_28]) ).
tff(c_19,plain,
! [T_11,E_12] :
( ~ outcompetes(first_movers,efficient_producers,T_11)
| ~ subpopulations(first_movers,efficient_producers,E_12,T_11)
| ~ environment(E_12) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_22,plain,
( ~ outcompetes(first_movers,efficient_producers,'#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_14,c_19]) ).
tff(c_25,plain,
~ outcompetes(first_movers,efficient_producers,'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_22]) ).
tff(c_12,plain,
greater_or_equal(growth_rate(first_movers,'#skF_2'),zero),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_10,plain,
greater(zero,growth_rate(efficient_producers,'#skF_2')),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_60,plain,
! [S2_25,S1_26,T_27,E_28] :
( outcompetes(S2_25,S1_26,T_27)
| ~ greater(zero,growth_rate(S1_26,T_27))
| ~ greater_or_equal(growth_rate(S2_25,T_27),zero)
| ~ subpopulations(S1_26,S2_25,E_28,T_27)
| ~ environment(E_28) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_64,plain,
! [S2_29,E_30] :
( outcompetes(S2_29,efficient_producers,'#skF_2')
| ~ greater_or_equal(growth_rate(S2_29,'#skF_2'),zero)
| ~ subpopulations(efficient_producers,S2_29,E_30,'#skF_2')
| ~ environment(E_30) ),
inference(resolution,[status(thm)],[c_10,c_60]) ).
tff(c_66,plain,
! [E_30] :
( outcompetes(first_movers,efficient_producers,'#skF_2')
| ~ subpopulations(efficient_producers,first_movers,E_30,'#skF_2')
| ~ environment(E_30) ),
inference(resolution,[status(thm)],[c_12,c_64]) ).
tff(c_70,plain,
! [E_31] :
( ~ subpopulations(efficient_producers,first_movers,E_31,'#skF_2')
| ~ environment(E_31) ),
inference(negUnitSimplification,[status(thm)],[c_25,c_66]) ).
tff(c_73,plain,
~ environment('#skF_1'),
inference(resolution,[status(thm)],[c_31,c_70]) ).
tff(c_77,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 7 12:42:53 UTC 2026
% 0.09/0.35 % CPUTime :
% 3.93/2.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.93/2.55
% 3.93/2.55 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------