TSTP Solution File: MGT034+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : MGT034+2 : TPTP v8.1.2. 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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:49:38 EDT 2023
% Result : Theorem 6.35s 2.56s
% Output : CNFRefutation 6.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 38
% Syntax : Number of formulae : 127 ( 37 unt; 20 typ; 0 def)
% Number of atoms : 290 ( 8 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 332 ( 149 ~; 131 |; 32 &)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 15 >; 14 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 104 (; 104 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulations > selection_favors > in_environment > greater_or_equal > greater > environment > decreases > growth_rate > founding_rate > disbanding_rate > difference > cardinality_at_time > appear > #nlpp > start_time > critical_point > 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(in_environment,type,
in_environment: ( $i * $i ) > $o ).
tff(founding_rate,type,
founding_rate: ( $i * $i ) > $i ).
tff(appear,type,
appear: ( $i * $i ) > $i ).
tff(efficient_producers,type,
efficient_producers: $i ).
tff(disbanding_rate,type,
disbanding_rate: ( $i * $i ) > $i ).
tff(cardinality_at_time,type,
cardinality_at_time: ( $i * $i ) > $i ).
tff(critical_point,type,
critical_point: $i > $i ).
tff(growth_rate,type,
growth_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(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(selection_favors,type,
selection_favors: ( $i * $i * $i ) > $o ).
tff(zero,type,
zero: $i ).
tff(f_243,negated_conjecture,
~ ! [E,T] :
( ( environment(E)
& in_environment(E,critical_point(E))
& greater_or_equal(T,appear(efficient_producers,E))
& greater(critical_point(E),T) )
=> selection_favors(first_movers,efficient_producers,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3) ).
tff(f_57,axiom,
! [E] :
( ( environment(E)
& in_environment(E,critical_point(E)) )
=> subpopulations(first_movers,efficient_producers,E,critical_point(E)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_means_FM_and_EP) ).
tff(f_173,axiom,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater_or_equal(T,appear(efficient_producers,E)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_members_EP_appeared) ).
tff(f_180,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( greater(X,Y)
| ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
tff(f_143,axiom,
! [E,T] :
( ( environment(E)
& in_environment(E,critical_point(E))
& greater_or_equal(T,appear(efficient_producers,E))
& greater(critical_point(E),T) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_time_points) ).
tff(f_119,axiom,
! [E,T1,T2,T] :
( ( environment(E)
& in_environment(E,T1)
& in_environment(E,T2)
& greater_or_equal(T2,T)
& greater_or_equal(T,T1) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_durations_are_time_intervals) ).
tff(f_64,axiom,
! [E] :
( ( environment(E)
& in_environment(E,appear(efficient_producers,E)) )
=> subpopulations(first_movers,efficient_producers,E,appear(efficient_producers,E)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_when_EP_appears) ).
tff(f_222,hypothesis,
! [E,T1,T2,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T1)
& subpopulations(first_movers,efficient_producers,E,T2)
& greater_or_equal(T,T1)
& greater_or_equal(T2,T) )
=> subpopulations(first_movers,efficient_producers,E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a10) ).
tff(f_165,axiom,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> subpopulations(efficient_producers,first_movers,E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
tff(f_230,hypothesis,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a12) ).
tff(f_74,axiom,
! [T] :
( ( decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T)))
& ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
=> decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_difference_between_founding_rates) ).
tff(f_190,axiom,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& ~ greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))) )
=> greater_or_equal(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_relationship_of_growth_rates) ).
tff(f_92,axiom,
! [E,T,To] :
( ( environment(E)
& in_environment(E,To)
& greater_or_equal(difference(growth_rate(first_movers,To),growth_rate(efficient_producers,To)),zero)
& greater_or_equal(T,appear(efficient_producers,E))
& greater(To,T) )
=> ( decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
=> greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_decreasing_function) ).
tff(f_99,axiom,
! [T] :
( greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
<=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_negative_growth_rate_difference) ).
tff(f_207,hypothesis,
! [E,Tc] :
( ( environment(E)
& ( Tc = critical_point(E) ) )
=> ( ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc))
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater(T,Tc) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
tff(f_49,axiom,
! [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/sandbox/benchmark/theBenchmark.p',l3) ).
tff(f_106,axiom,
! [T] :
( greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero)
<=> greater(growth_rate(first_movers,T),growth_rate(efficient_producers,T)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_growth_rate_difference) ).
tff(f_40,axiom,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T)
& greater(growth_rate(S2,T),growth_rate(S1,T)) )
=> selection_favors(S2,S1,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
tff(c_60,plain,
environment('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_243]) ).
tff(c_54,plain,
greater(critical_point('#skF_1'),'#skF_2'),
inference(cnfTransformation,[status(thm)],[f_243]) ).
tff(c_58,plain,
in_environment('#skF_1',critical_point('#skF_1')),
inference(cnfTransformation,[status(thm)],[f_243]) ).
tff(c_6,plain,
! [E_7] :
( subpopulations(first_movers,efficient_producers,E_7,critical_point(E_7))
| ~ in_environment(E_7,critical_point(E_7))
| ~ environment(E_7) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_85,plain,
! [T_51,E_52] :
( greater_or_equal(T_51,appear(efficient_producers,E_52))
| ~ subpopulations(first_movers,efficient_producers,E_52,T_51)
| ~ environment(E_52) ),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_36,plain,
! [Y_30,X_29] :
( ( Y_30 = X_29 )
| greater(X_29,Y_30)
| ~ greater_or_equal(X_29,Y_30) ),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_89,plain,
! [E_52,T_51] :
( ( appear(efficient_producers,E_52) = T_51 )
| greater(T_51,appear(efficient_producers,E_52))
| ~ subpopulations(first_movers,efficient_producers,E_52,T_51)
| ~ environment(E_52) ),
inference(resolution,[status(thm)],[c_85,c_36]) ).
tff(c_38,plain,
! [Y_30] : greater_or_equal(Y_30,Y_30),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_222,plain,
! [E_100,T_101] :
( in_environment(E_100,T_101)
| ~ greater(critical_point(E_100),T_101)
| ~ greater_or_equal(T_101,appear(efficient_producers,E_100))
| ~ in_environment(E_100,critical_point(E_100))
| ~ environment(E_100) ),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_419,plain,
! [E_121] :
( in_environment(E_121,appear(efficient_producers,E_121))
| ~ greater(critical_point(E_121),appear(efficient_producers,E_121))
| ~ in_environment(E_121,critical_point(E_121))
| ~ environment(E_121) ),
inference(resolution,[status(thm)],[c_38,c_222]) ).
tff(c_627,plain,
! [E_164] :
( in_environment(E_164,appear(efficient_producers,E_164))
| ~ in_environment(E_164,critical_point(E_164))
| ( appear(efficient_producers,E_164) = critical_point(E_164) )
| ~ subpopulations(first_movers,efficient_producers,E_164,critical_point(E_164))
| ~ environment(E_164) ),
inference(resolution,[status(thm)],[c_89,c_419]) ).
tff(c_632,plain,
! [E_165] :
( in_environment(E_165,appear(efficient_producers,E_165))
| ( appear(efficient_producers,E_165) = critical_point(E_165) )
| ~ in_environment(E_165,critical_point(E_165))
| ~ environment(E_165) ),
inference(resolution,[status(thm)],[c_6,c_627]) ).
tff(c_56,plain,
greater_or_equal('#skF_2',appear(efficient_producers,'#skF_1')),
inference(cnfTransformation,[status(thm)],[f_243]) ).
tff(c_126,plain,
! [E_71,T_72,T1_73,T2_74] :
( in_environment(E_71,T_72)
| ~ greater_or_equal(T_72,T1_73)
| ~ greater_or_equal(T2_74,T_72)
| ~ in_environment(E_71,T2_74)
| ~ in_environment(E_71,T1_73)
| ~ environment(E_71) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_142,plain,
! [E_75,T2_76] :
( in_environment(E_75,'#skF_2')
| ~ greater_or_equal(T2_76,'#skF_2')
| ~ in_environment(E_75,T2_76)
| ~ in_environment(E_75,appear(efficient_producers,'#skF_1'))
| ~ environment(E_75) ),
inference(resolution,[status(thm)],[c_56,c_126]) ).
tff(c_146,plain,
( in_environment('#skF_1','#skF_2')
| ~ greater_or_equal(critical_point('#skF_1'),'#skF_2')
| ~ in_environment('#skF_1',appear(efficient_producers,'#skF_1'))
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_58,c_142]) ).
tff(c_150,plain,
( in_environment('#skF_1','#skF_2')
| ~ greater_or_equal(critical_point('#skF_1'),'#skF_2')
| ~ in_environment('#skF_1',appear(efficient_producers,'#skF_1')) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_146]) ).
tff(c_151,plain,
~ in_environment('#skF_1',appear(efficient_producers,'#skF_1')),
inference(splitLeft,[status(thm)],[c_150]) ).
tff(c_656,plain,
( ( appear(efficient_producers,'#skF_1') = critical_point('#skF_1') )
| ~ in_environment('#skF_1',critical_point('#skF_1'))
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_632,c_151]) ).
tff(c_677,plain,
appear(efficient_producers,'#skF_1') = critical_point('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_58,c_656]) ).
tff(c_229,plain,
( in_environment('#skF_1','#skF_2')
| ~ greater(critical_point('#skF_1'),'#skF_2')
| ~ in_environment('#skF_1',critical_point('#skF_1'))
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_56,c_222]) ).
tff(c_237,plain,
in_environment('#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_58,c_54,c_229]) ).
tff(c_40,plain,
! [X_29,Y_30] :
( ~ greater(X_29,Y_30)
| greater_or_equal(X_29,Y_30) ),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_153,plain,
! [E_78,X_79,T2_80,Y_81] :
( in_environment(E_78,X_79)
| ~ greater_or_equal(T2_80,X_79)
| ~ in_environment(E_78,T2_80)
| ~ in_environment(E_78,Y_81)
| ~ environment(E_78)
| ~ greater(X_79,Y_81) ),
inference(resolution,[status(thm)],[c_40,c_126]) ).
tff(c_167,plain,
! [E_78,Y_81] :
( in_environment(E_78,appear(efficient_producers,'#skF_1'))
| ~ in_environment(E_78,'#skF_2')
| ~ in_environment(E_78,Y_81)
| ~ environment(E_78)
| ~ greater(appear(efficient_producers,'#skF_1'),Y_81) ),
inference(resolution,[status(thm)],[c_56,c_153]) ).
tff(c_242,plain,
( in_environment('#skF_1',appear(efficient_producers,'#skF_1'))
| ~ in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1')
| ~ greater(appear(efficient_producers,'#skF_1'),'#skF_2') ),
inference(resolution,[status(thm)],[c_237,c_167]) ).
tff(c_254,plain,
( in_environment('#skF_1',appear(efficient_producers,'#skF_1'))
| ~ greater(appear(efficient_producers,'#skF_1'),'#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_237,c_242]) ).
tff(c_255,plain,
~ greater(appear(efficient_producers,'#skF_1'),'#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_151,c_254]) ).
tff(c_691,plain,
~ greater(critical_point('#skF_1'),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_677,c_255]) ).
tff(c_701,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_691]) ).
tff(c_703,plain,
in_environment('#skF_1',appear(efficient_producers,'#skF_1')),
inference(splitRight,[status(thm)],[c_150]) ).
tff(c_8,plain,
! [E_8] :
( subpopulations(first_movers,efficient_producers,E_8,appear(efficient_producers,E_8))
| ~ in_environment(E_8,appear(efficient_producers,E_8))
| ~ environment(E_8) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_702,plain,
( ~ greater_or_equal(critical_point('#skF_1'),'#skF_2')
| in_environment('#skF_1','#skF_2') ),
inference(splitRight,[status(thm)],[c_150]) ).
tff(c_709,plain,
~ greater_or_equal(critical_point('#skF_1'),'#skF_2'),
inference(splitLeft,[status(thm)],[c_702]) ).
tff(c_712,plain,
~ greater(critical_point('#skF_1'),'#skF_2'),
inference(resolution,[status(thm)],[c_40,c_709]) ).
tff(c_716,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_712]) ).
tff(c_718,plain,
greater_or_equal(critical_point('#skF_1'),'#skF_2'),
inference(splitRight,[status(thm)],[c_702]) ).
tff(c_1113,plain,
! [E_227,T_228,T2_229,T1_230] :
( subpopulations(first_movers,efficient_producers,E_227,T_228)
| ~ greater_or_equal(T2_229,T_228)
| ~ greater_or_equal(T_228,T1_230)
| ~ subpopulations(first_movers,efficient_producers,E_227,T2_229)
| ~ subpopulations(first_movers,efficient_producers,E_227,T1_230)
| ~ environment(E_227) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_1447,plain,
! [E_283,T1_284] :
( subpopulations(first_movers,efficient_producers,E_283,'#skF_2')
| ~ greater_or_equal('#skF_2',T1_284)
| ~ subpopulations(first_movers,efficient_producers,E_283,critical_point('#skF_1'))
| ~ subpopulations(first_movers,efficient_producers,E_283,T1_284)
| ~ environment(E_283) ),
inference(resolution,[status(thm)],[c_718,c_1113]) ).
tff(c_1450,plain,
! [T1_284] :
( subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ greater_or_equal('#skF_2',T1_284)
| ~ subpopulations(first_movers,efficient_producers,'#skF_1',T1_284)
| ~ in_environment('#skF_1',critical_point('#skF_1'))
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_6,c_1447]) ).
tff(c_1453,plain,
! [T1_284] :
( subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ greater_or_equal('#skF_2',T1_284)
| ~ subpopulations(first_movers,efficient_producers,'#skF_1',T1_284) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_58,c_1450]) ).
tff(c_1978,plain,
! [T1_322] :
( ~ greater_or_equal('#skF_2',T1_322)
| ~ subpopulations(first_movers,efficient_producers,'#skF_1',T1_322) ),
inference(splitLeft,[status(thm)],[c_1453]) ).
tff(c_1982,plain,
( ~ greater_or_equal('#skF_2',appear(efficient_producers,'#skF_1'))
| ~ in_environment('#skF_1',appear(efficient_producers,'#skF_1'))
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_8,c_1978]) ).
tff(c_1990,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_60,c_703,c_56,c_1982]) ).
tff(c_1991,plain,
subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2'),
inference(splitRight,[status(thm)],[c_1453]) ).
tff(c_32,plain,
! [E_25,T_26] :
( subpopulations(efficient_producers,first_movers,E_25,T_26)
| ~ subpopulations(first_movers,efficient_producers,E_25,T_26)
| ~ environment(E_25) ),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_2047,plain,
( subpopulations(efficient_producers,first_movers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_1991,c_32]) ).
tff(c_2061,plain,
subpopulations(efficient_producers,first_movers,'#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_2047]) ).
tff(c_52,plain,
~ selection_favors(first_movers,efficient_producers,'#skF_2'),
inference(cnfTransformation,[status(thm)],[f_243]) ).
tff(c_1887,plain,
! [T1_314] :
( ~ greater_or_equal('#skF_2',T1_314)
| ~ subpopulations(first_movers,efficient_producers,'#skF_1',T1_314) ),
inference(splitLeft,[status(thm)],[c_1453]) ).
tff(c_1891,plain,
( ~ greater_or_equal('#skF_2',appear(efficient_producers,'#skF_1'))
| ~ in_environment('#skF_1',appear(efficient_producers,'#skF_1'))
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_8,c_1887]) ).
tff(c_1899,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_60,c_703,c_56,c_1891]) ).
tff(c_1900,plain,
subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2'),
inference(splitRight,[status(thm)],[c_1453]) ).
tff(c_50,plain,
! [T_42,E_41] :
( decreases(difference(founding_rate(first_movers,T_42),founding_rate(efficient_producers,T_42)))
| ~ subpopulations(first_movers,efficient_producers,E_41,T_42)
| ~ environment(E_41) ),
inference(cnfTransformation,[status(thm)],[f_230]) ).
tff(c_1909,plain,
( decreases(difference(founding_rate(first_movers,'#skF_2'),founding_rate(efficient_producers,'#skF_2')))
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_1900,c_50]) ).
tff(c_1923,plain,
decreases(difference(founding_rate(first_movers,'#skF_2'),founding_rate(efficient_producers,'#skF_2'))),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_1909]) ).
tff(c_10,plain,
! [T_9] :
( decreases(difference(growth_rate(first_movers,T_9),growth_rate(efficient_producers,T_9)))
| decreases(difference(disbanding_rate(first_movers,T_9),disbanding_rate(efficient_producers,T_9)))
| ~ decreases(difference(founding_rate(first_movers,T_9),founding_rate(efficient_producers,T_9))) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_1313,plain,
! [T_258,E_259] :
( greater_or_equal(difference(growth_rate(first_movers,T_258),growth_rate(efficient_producers,T_258)),zero)
| greater(zero,difference(growth_rate(first_movers,T_258),growth_rate(efficient_producers,T_258)))
| ~ subpopulations(first_movers,efficient_producers,E_259,T_258)
| ~ environment(E_259) ),
inference(cnfTransformation,[status(thm)],[f_190]) ).
tff(c_1778,plain,
! [E_313] :
( greater_or_equal(difference(growth_rate(first_movers,critical_point(E_313)),growth_rate(efficient_producers,critical_point(E_313))),zero)
| greater(zero,difference(growth_rate(first_movers,critical_point(E_313)),growth_rate(efficient_producers,critical_point(E_313))))
| ~ in_environment(E_313,critical_point(E_313))
| ~ environment(E_313) ),
inference(resolution,[status(thm)],[c_6,c_1313]) ).
tff(c_1426,plain,
! [T_277,To_278,E_279] :
( greater(difference(growth_rate(first_movers,T_277),growth_rate(efficient_producers,T_277)),zero)
| ~ decreases(difference(growth_rate(first_movers,T_277),growth_rate(efficient_producers,T_277)))
| ~ greater(To_278,T_277)
| ~ greater_or_equal(T_277,appear(efficient_producers,E_279))
| ~ greater_or_equal(difference(growth_rate(first_movers,To_278),growth_rate(efficient_producers,To_278)),zero)
| ~ in_environment(E_279,To_278)
| ~ environment(E_279) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_1444,plain,
! [E_279] :
( greater(difference(growth_rate(first_movers,'#skF_2'),growth_rate(efficient_producers,'#skF_2')),zero)
| ~ decreases(difference(growth_rate(first_movers,'#skF_2'),growth_rate(efficient_producers,'#skF_2')))
| ~ greater_or_equal('#skF_2',appear(efficient_producers,E_279))
| ~ greater_or_equal(difference(growth_rate(first_movers,critical_point('#skF_1')),growth_rate(efficient_producers,critical_point('#skF_1'))),zero)
| ~ in_environment(E_279,critical_point('#skF_1'))
| ~ environment(E_279) ),
inference(resolution,[status(thm)],[c_54,c_1426]) ).
tff(c_1454,plain,
~ greater_or_equal(difference(growth_rate(first_movers,critical_point('#skF_1')),growth_rate(efficient_producers,critical_point('#skF_1'))),zero),
inference(splitLeft,[status(thm)],[c_1444]) ).
tff(c_1785,plain,
( greater(zero,difference(growth_rate(first_movers,critical_point('#skF_1')),growth_rate(efficient_producers,critical_point('#skF_1'))))
| ~ in_environment('#skF_1',critical_point('#skF_1'))
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_1778,c_1454]) ).
tff(c_1799,plain,
greater(zero,difference(growth_rate(first_movers,critical_point('#skF_1')),growth_rate(efficient_producers,critical_point('#skF_1')))),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_58,c_1785]) ).
tff(c_14,plain,
! [T_13] :
( greater(growth_rate(efficient_producers,T_13),growth_rate(first_movers,T_13))
| ~ greater(zero,difference(growth_rate(first_movers,T_13),growth_rate(efficient_producers,T_13))) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_1831,plain,
greater(growth_rate(efficient_producers,critical_point('#skF_1')),growth_rate(first_movers,critical_point('#skF_1'))),
inference(resolution,[status(thm)],[c_1799,c_14]) ).
tff(c_46,plain,
! [E_33] :
( ~ greater(growth_rate(efficient_producers,critical_point(E_33)),growth_rate(first_movers,critical_point(E_33)))
| ~ environment(E_33) ),
inference(cnfTransformation,[status(thm)],[f_207]) ).
tff(c_1852,plain,
~ environment('#skF_1'),
inference(resolution,[status(thm)],[c_1831,c_46]) ).
tff(c_1865,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_60,c_1852]) ).
tff(c_1866,plain,
! [E_279] :
( ~ decreases(difference(growth_rate(first_movers,'#skF_2'),growth_rate(efficient_producers,'#skF_2')))
| ~ greater_or_equal('#skF_2',appear(efficient_producers,E_279))
| ~ in_environment(E_279,critical_point('#skF_1'))
| ~ environment(E_279)
| greater(difference(growth_rate(first_movers,'#skF_2'),growth_rate(efficient_producers,'#skF_2')),zero) ),
inference(splitRight,[status(thm)],[c_1444]) ).
tff(c_1881,plain,
~ decreases(difference(growth_rate(first_movers,'#skF_2'),growth_rate(efficient_producers,'#skF_2'))),
inference(splitLeft,[status(thm)],[c_1866]) ).
tff(c_1885,plain,
( decreases(difference(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2')))
| ~ decreases(difference(founding_rate(first_movers,'#skF_2'),founding_rate(efficient_producers,'#skF_2'))) ),
inference(resolution,[status(thm)],[c_10,c_1881]) ).
tff(c_1963,plain,
decreases(difference(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2'))),
inference(demodulation,[status(thm),theory(equality)],[c_1923,c_1885]) ).
tff(c_4,plain,
! [T_6,E_5] :
( ~ decreases(difference(disbanding_rate(first_movers,T_6),disbanding_rate(efficient_producers,T_6)))
| ~ subpopulations(first_movers,efficient_producers,E_5,T_6)
| ~ environment(E_5) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_1967,plain,
! [E_321] :
( ~ subpopulations(first_movers,efficient_producers,E_321,'#skF_2')
| ~ environment(E_321) ),
inference(resolution,[status(thm)],[c_1963,c_4]) ).
tff(c_1970,plain,
~ environment('#skF_1'),
inference(resolution,[status(thm)],[c_1900,c_1967]) ).
tff(c_1974,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_60,c_1970]) ).
tff(c_1975,plain,
! [E_279] :
( ~ greater_or_equal('#skF_2',appear(efficient_producers,E_279))
| ~ in_environment(E_279,critical_point('#skF_1'))
| ~ environment(E_279)
| greater(difference(growth_rate(first_movers,'#skF_2'),growth_rate(efficient_producers,'#skF_2')),zero) ),
inference(splitRight,[status(thm)],[c_1866]) ).
tff(c_2020,plain,
! [E_323] :
( ~ greater_or_equal('#skF_2',appear(efficient_producers,E_323))
| ~ in_environment(E_323,critical_point('#skF_1'))
| ~ environment(E_323) ),
inference(splitLeft,[status(thm)],[c_1975]) ).
tff(c_2027,plain,
( ~ greater_or_equal('#skF_2',appear(efficient_producers,'#skF_1'))
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_58,c_2020]) ).
tff(c_2034,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_60,c_56,c_2027]) ).
tff(c_2035,plain,
greater(difference(growth_rate(first_movers,'#skF_2'),growth_rate(efficient_producers,'#skF_2')),zero),
inference(splitRight,[status(thm)],[c_1975]) ).
tff(c_18,plain,
! [T_14] :
( greater(growth_rate(first_movers,T_14),growth_rate(efficient_producers,T_14))
| ~ greater(difference(growth_rate(first_movers,T_14),growth_rate(efficient_producers,T_14)),zero) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_2083,plain,
greater(growth_rate(first_movers,'#skF_2'),growth_rate(efficient_producers,'#skF_2')),
inference(resolution,[status(thm)],[c_2035,c_18]) ).
tff(c_2,plain,
! [S2_3,S1_2,T_4,E_1] :
( selection_favors(S2_3,S1_2,T_4)
| ~ greater(growth_rate(S2_3,T_4),growth_rate(S1_2,T_4))
| ~ subpopulations(S1_2,S2_3,E_1,T_4)
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_2119,plain,
! [E_1] :
( selection_favors(first_movers,efficient_producers,'#skF_2')
| ~ subpopulations(efficient_producers,first_movers,E_1,'#skF_2')
| ~ environment(E_1) ),
inference(resolution,[status(thm)],[c_2083,c_2]) ).
tff(c_2129,plain,
! [E_328] :
( ~ subpopulations(efficient_producers,first_movers,E_328,'#skF_2')
| ~ environment(E_328) ),
inference(negUnitSimplification,[status(thm)],[c_52,c_2119]) ).
tff(c_2132,plain,
~ environment('#skF_1'),
inference(resolution,[status(thm)],[c_2061,c_2129]) ).
tff(c_2136,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_60,c_2132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : MGT034+2 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14 % 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
% 0.17/0.36 % Computer : n019.cluster.edu
% 0.17/0.36 % Model : x86_64 x86_64
% 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36 % Memory : 8042.1875MB
% 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36 % CPULimit : 300
% 0.17/0.36 % WCLimit : 300
% 0.17/0.36 % DateTime : Thu Aug 3 20:34:01 EDT 2023
% 0.17/0.36 % CPUTime :
% 6.35/2.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.35/2.57
% 6.35/2.57 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.87/2.61
% 6.87/2.61 Inference rules
% 6.87/2.61 ----------------------
% 6.87/2.61 #Ref : 0
% 6.87/2.61 #Sup : 459
% 6.87/2.61 #Fact : 0
% 6.87/2.61 #Define : 0
% 6.87/2.61 #Split : 24
% 6.87/2.61 #Chain : 0
% 6.87/2.61 #Close : 0
% 6.87/2.61
% 6.87/2.61 Ordering : KBO
% 6.87/2.61
% 6.87/2.61 Simplification rules
% 6.87/2.61 ----------------------
% 6.87/2.61 #Subsume : 26
% 6.87/2.61 #Demod : 312
% 6.87/2.61 #Tautology : 88
% 6.87/2.61 #SimpNegUnit : 6
% 6.87/2.61 #BackRed : 13
% 6.87/2.61
% 6.87/2.61 #Partial instantiations: 0
% 6.87/2.61 #Strategies tried : 1
% 6.87/2.61
% 6.87/2.61 Timing (in seconds)
% 6.87/2.61 ----------------------
% 6.89/2.61 Preprocessing : 0.58
% 6.89/2.61 Parsing : 0.32
% 6.89/2.61 CNF conversion : 0.04
% 6.89/2.61 Main loop : 0.95
% 6.89/2.61 Inferencing : 0.34
% 6.89/2.61 Reduction : 0.26
% 6.89/2.62 Demodulation : 0.18
% 6.89/2.62 BG Simplification : 0.04
% 6.89/2.62 Subsumption : 0.24
% 6.89/2.62 Abstraction : 0.03
% 6.89/2.62 MUC search : 0.00
% 6.89/2.62 Cooper : 0.00
% 6.89/2.62 Total : 1.60
% 6.89/2.62 Index Insertion : 0.00
% 6.89/2.62 Index Deletion : 0.00
% 6.89/2.62 Index Matching : 0.00
% 6.89/2.62 BG Taut test : 0.00
%------------------------------------------------------------------------------