TSTP Solution File: MGT023+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : MGT023+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 : n026.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 10:49:35 EDT 2023
% Result : Theorem 6.97s 2.65s
% Output : CNFRefutation 6.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 19
% Syntax : Number of formulae : 80 ( 7 unt; 15 typ; 0 def)
% Number of atoms : 382 ( 45 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 556 ( 239 ~; 295 |; 14 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 12 >; 9 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 131 (; 128 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulations > in_environment > greater_or_equal > greater > stable > environment > growth_rate > #nlpp > critical_point > first_movers > efficient_producers > #skF_2 > #skF_4 > #skF_3 > #skF_5 > #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('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(in_environment,type,
in_environment: ( $i * $i ) > $o ).
tff(efficient_producers,type,
efficient_producers: $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(critical_point,type,
critical_point: $i > $i ).
tff(growth_rate,type,
growth_rate: ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $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('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(stable,type,
stable: $i > $o ).
tff(f_98,negated_conjecture,
~ ! [E] :
( ( environment(E)
& stable(E) )
=> in_environment(E,critical_point(E)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5) ).
tff(f_90,hypothesis,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
tff(f_55,axiom,
! [E] :
( ( environment(E)
& ? [To] :
( in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) )
=> ? [To] :
( in_environment(E,To)
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater(T,To) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds) ).
tff(f_74,hypothesis,
! [E,To] :
( ( environment(E)
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater(T,To) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) )
=> ( To = critical_point(E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
tff(c_34,plain,
environment('#skF_5'),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_32,plain,
stable('#skF_5'),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_28,plain,
! [E_15] :
( in_environment(E_15,'#skF_4'(E_15))
| ~ stable(E_15)
| ~ environment(E_15) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_18,plain,
! [E_1,To_8] :
( subpopulations(first_movers,efficient_producers,E_1,'#skF_1'(E_1,To_8))
| in_environment(E_1,'#skF_2'(E_1))
| ~ in_environment(E_1,To_8)
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_16,plain,
! [E_1,To_8] :
( greater_or_equal('#skF_1'(E_1,To_8),To_8)
| in_environment(E_1,'#skF_2'(E_1))
| ~ in_environment(E_1,To_8)
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_49,plain,
! [T_32,E_33] :
( greater(growth_rate(efficient_producers,T_32),growth_rate(first_movers,T_32))
| ~ greater_or_equal(T_32,'#skF_4'(E_33))
| ~ subpopulations(first_movers,efficient_producers,E_33,T_32)
| ~ stable(E_33)
| ~ environment(E_33) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_144,plain,
! [E_72,E_73] :
( greater(growth_rate(efficient_producers,'#skF_1'(E_72,'#skF_4'(E_73))),growth_rate(first_movers,'#skF_1'(E_72,'#skF_4'(E_73))))
| ~ subpopulations(first_movers,efficient_producers,E_73,'#skF_1'(E_72,'#skF_4'(E_73)))
| ~ stable(E_73)
| ~ environment(E_73)
| in_environment(E_72,'#skF_2'(E_72))
| ~ in_environment(E_72,'#skF_4'(E_73))
| ~ environment(E_72) ),
inference(resolution,[status(thm)],[c_16,c_49]) ).
tff(c_14,plain,
! [E_1,To_8] :
( ~ greater(growth_rate(efficient_producers,'#skF_1'(E_1,To_8)),growth_rate(first_movers,'#skF_1'(E_1,To_8)))
| in_environment(E_1,'#skF_2'(E_1))
| ~ in_environment(E_1,To_8)
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_164,plain,
! [E_77,E_78] :
( ~ subpopulations(first_movers,efficient_producers,E_77,'#skF_1'(E_78,'#skF_4'(E_77)))
| ~ stable(E_77)
| ~ environment(E_77)
| in_environment(E_78,'#skF_2'(E_78))
| ~ in_environment(E_78,'#skF_4'(E_77))
| ~ environment(E_78) ),
inference(resolution,[status(thm)],[c_144,c_14]) ).
tff(c_176,plain,
! [E_1] :
( ~ stable(E_1)
| in_environment(E_1,'#skF_2'(E_1))
| ~ in_environment(E_1,'#skF_4'(E_1))
| ~ environment(E_1) ),
inference(resolution,[status(thm)],[c_18,c_164]) ).
tff(c_24,plain,
! [E_12,To_13] :
( subpopulations(first_movers,efficient_producers,E_12,'#skF_3'(E_12,To_13))
| ( critical_point(E_12) = To_13 )
| ~ in_environment(E_12,To_13)
| greater(growth_rate(efficient_producers,To_13),growth_rate(first_movers,To_13))
| ~ environment(E_12) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_22,plain,
! [E_12,To_13] :
( greater('#skF_3'(E_12,To_13),To_13)
| ( critical_point(E_12) = To_13 )
| ~ in_environment(E_12,To_13)
| greater(growth_rate(efficient_producers,To_13),growth_rate(first_movers,To_13))
| ~ environment(E_12) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_95,plain,
! [E_45,To_46,T_47] :
( subpopulations(first_movers,efficient_producers,E_45,'#skF_1'(E_45,To_46))
| greater(growth_rate(efficient_producers,T_47),growth_rate(first_movers,T_47))
| ~ greater(T_47,'#skF_2'(E_45))
| ~ subpopulations(first_movers,efficient_producers,E_45,T_47)
| ~ in_environment(E_45,To_46)
| ~ environment(E_45) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_468,plain,
! [E_154,To_155,E_156] :
( subpopulations(first_movers,efficient_producers,E_154,'#skF_1'(E_154,To_155))
| greater(growth_rate(efficient_producers,'#skF_3'(E_156,'#skF_2'(E_154))),growth_rate(first_movers,'#skF_3'(E_156,'#skF_2'(E_154))))
| ~ subpopulations(first_movers,efficient_producers,E_154,'#skF_3'(E_156,'#skF_2'(E_154)))
| ~ in_environment(E_154,To_155)
| ~ environment(E_154)
| ( critical_point(E_156) = '#skF_2'(E_154) )
| ~ in_environment(E_156,'#skF_2'(E_154))
| greater(growth_rate(efficient_producers,'#skF_2'(E_154)),growth_rate(first_movers,'#skF_2'(E_154)))
| ~ environment(E_156) ),
inference(resolution,[status(thm)],[c_22,c_95]) ).
tff(c_20,plain,
! [E_12,To_13] :
( ~ greater(growth_rate(efficient_producers,'#skF_3'(E_12,To_13)),growth_rate(first_movers,'#skF_3'(E_12,To_13)))
| ( critical_point(E_12) = To_13 )
| ~ in_environment(E_12,To_13)
| greater(growth_rate(efficient_producers,To_13),growth_rate(first_movers,To_13))
| ~ environment(E_12) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_516,plain,
! [E_164,To_165,E_166] :
( subpopulations(first_movers,efficient_producers,E_164,'#skF_1'(E_164,To_165))
| ~ subpopulations(first_movers,efficient_producers,E_164,'#skF_3'(E_166,'#skF_2'(E_164)))
| ~ in_environment(E_164,To_165)
| ~ environment(E_164)
| ( critical_point(E_166) = '#skF_2'(E_164) )
| ~ in_environment(E_166,'#skF_2'(E_164))
| greater(growth_rate(efficient_producers,'#skF_2'(E_164)),growth_rate(first_movers,'#skF_2'(E_164)))
| ~ environment(E_166) ),
inference(resolution,[status(thm)],[c_468,c_20]) ).
tff(c_537,plain,
! [E_167,To_168] :
( subpopulations(first_movers,efficient_producers,E_167,'#skF_1'(E_167,To_168))
| ~ in_environment(E_167,To_168)
| ( critical_point(E_167) = '#skF_2'(E_167) )
| ~ in_environment(E_167,'#skF_2'(E_167))
| greater(growth_rate(efficient_producers,'#skF_2'(E_167)),growth_rate(first_movers,'#skF_2'(E_167)))
| ~ environment(E_167) ),
inference(resolution,[status(thm)],[c_24,c_516]) ).
tff(c_12,plain,
! [E_1,To_8] :
( subpopulations(first_movers,efficient_producers,E_1,'#skF_1'(E_1,To_8))
| ~ greater(growth_rate(efficient_producers,'#skF_2'(E_1)),growth_rate(first_movers,'#skF_2'(E_1)))
| ~ in_environment(E_1,To_8)
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_555,plain,
! [E_167,To_8,To_168] :
( subpopulations(first_movers,efficient_producers,E_167,'#skF_1'(E_167,To_8))
| ~ in_environment(E_167,To_8)
| subpopulations(first_movers,efficient_producers,E_167,'#skF_1'(E_167,To_168))
| ~ in_environment(E_167,To_168)
| ( critical_point(E_167) = '#skF_2'(E_167) )
| ~ in_environment(E_167,'#skF_2'(E_167))
| ~ environment(E_167) ),
inference(resolution,[status(thm)],[c_537,c_12]) ).
tff(c_569,plain,
! [E_167,To_8] :
( ~ in_environment(E_167,To_8)
| ( critical_point(E_167) = '#skF_2'(E_167) )
| ~ in_environment(E_167,'#skF_2'(E_167))
| ~ environment(E_167)
| subpopulations(first_movers,efficient_producers,E_167,'#skF_1'(E_167,To_8)) ),
inference(factorization,[status(thm),theory(equality)],[c_555]) ).
tff(c_54,plain,
! [E_34,To_35] :
( subpopulations(first_movers,efficient_producers,E_34,'#skF_1'(E_34,To_35))
| ~ greater(growth_rate(efficient_producers,'#skF_2'(E_34)),growth_rate(first_movers,'#skF_2'(E_34)))
| ~ in_environment(E_34,To_35)
| ~ environment(E_34) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_58,plain,
! [E_34,To_35,E_12] :
( subpopulations(first_movers,efficient_producers,E_34,'#skF_1'(E_34,To_35))
| ~ in_environment(E_34,To_35)
| ~ environment(E_34)
| greater('#skF_3'(E_12,'#skF_2'(E_34)),'#skF_2'(E_34))
| ( critical_point(E_12) = '#skF_2'(E_34) )
| ~ in_environment(E_12,'#skF_2'(E_34))
| ~ environment(E_12) ),
inference(resolution,[status(thm)],[c_22,c_54]) ).
tff(c_39,plain,
! [E_28,To_29] :
( greater('#skF_3'(E_28,To_29),To_29)
| ( critical_point(E_28) = To_29 )
| ~ in_environment(E_28,To_29)
| greater(growth_rate(efficient_producers,To_29),growth_rate(first_movers,To_29))
| ~ environment(E_28) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_10,plain,
! [E_1,To_8] :
( greater_or_equal('#skF_1'(E_1,To_8),To_8)
| ~ greater(growth_rate(efficient_producers,'#skF_2'(E_1)),growth_rate(first_movers,'#skF_2'(E_1)))
| ~ in_environment(E_1,To_8)
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_100,plain,
! [E_48,To_49,E_50] :
( greater_or_equal('#skF_1'(E_48,To_49),To_49)
| ~ in_environment(E_48,To_49)
| ~ environment(E_48)
| greater('#skF_3'(E_50,'#skF_2'(E_48)),'#skF_2'(E_48))
| ( critical_point(E_50) = '#skF_2'(E_48) )
| ~ in_environment(E_50,'#skF_2'(E_48))
| ~ environment(E_50) ),
inference(resolution,[status(thm)],[c_39,c_10]) ).
tff(c_26,plain,
! [T_20,E_15] :
( greater(growth_rate(efficient_producers,T_20),growth_rate(first_movers,T_20))
| ~ greater_or_equal(T_20,'#skF_4'(E_15))
| ~ subpopulations(first_movers,efficient_producers,E_15,T_20)
| ~ stable(E_15)
| ~ environment(E_15) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_272,plain,
! [E_118,E_119,E_120] :
( greater(growth_rate(efficient_producers,'#skF_1'(E_118,'#skF_4'(E_119))),growth_rate(first_movers,'#skF_1'(E_118,'#skF_4'(E_119))))
| ~ subpopulations(first_movers,efficient_producers,E_119,'#skF_1'(E_118,'#skF_4'(E_119)))
| ~ stable(E_119)
| ~ environment(E_119)
| ~ in_environment(E_118,'#skF_4'(E_119))
| ~ environment(E_118)
| greater('#skF_3'(E_120,'#skF_2'(E_118)),'#skF_2'(E_118))
| ( critical_point(E_120) = '#skF_2'(E_118) )
| ~ in_environment(E_120,'#skF_2'(E_118))
| ~ environment(E_120) ),
inference(resolution,[status(thm)],[c_100,c_26]) ).
tff(c_8,plain,
! [E_1,To_8] :
( ~ greater(growth_rate(efficient_producers,'#skF_1'(E_1,To_8)),growth_rate(first_movers,'#skF_1'(E_1,To_8)))
| ~ greater(growth_rate(efficient_producers,'#skF_2'(E_1)),growth_rate(first_movers,'#skF_2'(E_1)))
| ~ in_environment(E_1,To_8)
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_295,plain,
! [E_121,E_122,E_123] :
( ~ greater(growth_rate(efficient_producers,'#skF_2'(E_121)),growth_rate(first_movers,'#skF_2'(E_121)))
| ~ subpopulations(first_movers,efficient_producers,E_122,'#skF_1'(E_121,'#skF_4'(E_122)))
| ~ stable(E_122)
| ~ environment(E_122)
| ~ in_environment(E_121,'#skF_4'(E_122))
| ~ environment(E_121)
| greater('#skF_3'(E_123,'#skF_2'(E_121)),'#skF_2'(E_121))
| ( critical_point(E_123) = '#skF_2'(E_121) )
| ~ in_environment(E_123,'#skF_2'(E_121))
| ~ environment(E_123) ),
inference(resolution,[status(thm)],[c_272,c_8]) ).
tff(c_877,plain,
! [E_219,E_220,E_221,E_222] :
( ~ subpopulations(first_movers,efficient_producers,E_219,'#skF_1'(E_220,'#skF_4'(E_219)))
| ~ stable(E_219)
| ~ environment(E_219)
| ~ in_environment(E_220,'#skF_4'(E_219))
| ~ environment(E_220)
| greater('#skF_3'(E_221,'#skF_2'(E_220)),'#skF_2'(E_220))
| ( critical_point(E_221) = '#skF_2'(E_220) )
| ~ in_environment(E_221,'#skF_2'(E_220))
| ~ environment(E_221)
| greater('#skF_3'(E_222,'#skF_2'(E_220)),'#skF_2'(E_220))
| ( critical_point(E_222) = '#skF_2'(E_220) )
| ~ in_environment(E_222,'#skF_2'(E_220))
| ~ environment(E_222) ),
inference(resolution,[status(thm)],[c_22,c_295]) ).
tff(c_896,plain,
! [E_34,E_221,E_222,E_12] :
( ~ stable(E_34)
| greater('#skF_3'(E_221,'#skF_2'(E_34)),'#skF_2'(E_34))
| ( critical_point(E_221) = '#skF_2'(E_34) )
| ~ in_environment(E_221,'#skF_2'(E_34))
| ~ environment(E_221)
| greater('#skF_3'(E_222,'#skF_2'(E_34)),'#skF_2'(E_34))
| ( critical_point(E_222) = '#skF_2'(E_34) )
| ~ in_environment(E_222,'#skF_2'(E_34))
| ~ environment(E_222)
| ~ in_environment(E_34,'#skF_4'(E_34))
| ~ environment(E_34)
| greater('#skF_3'(E_12,'#skF_2'(E_34)),'#skF_2'(E_34))
| ( critical_point(E_12) = '#skF_2'(E_34) )
| ~ in_environment(E_12,'#skF_2'(E_34))
| ~ environment(E_12) ),
inference(resolution,[status(thm)],[c_58,c_877]) ).
tff(c_1185,plain,
! [E_34,E_221,E_222] :
( ~ stable(E_34)
| greater('#skF_3'(E_221,'#skF_2'(E_34)),'#skF_2'(E_34))
| ( critical_point(E_221) = '#skF_2'(E_34) )
| ~ in_environment(E_221,'#skF_2'(E_34))
| ~ environment(E_221)
| ~ in_environment(E_34,'#skF_4'(E_34))
| ~ environment(E_34)
| ( critical_point(E_222) = '#skF_2'(E_34) )
| ~ in_environment(E_222,'#skF_2'(E_34))
| ~ environment(E_222)
| greater('#skF_3'(E_222,'#skF_2'(E_34)),'#skF_2'(E_34)) ),
inference(factorization,[status(thm),theory(equality)],[c_896]) ).
tff(c_1327,plain,
! [E_276,E_277] :
( ~ stable(E_276)
| ~ in_environment(E_276,'#skF_4'(E_276))
| ~ environment(E_276)
| ( critical_point(E_277) = '#skF_2'(E_276) )
| ~ in_environment(E_277,'#skF_2'(E_276))
| ~ environment(E_277)
| greater('#skF_3'(E_277,'#skF_2'(E_276)),'#skF_2'(E_276)) ),
inference(factorization,[status(thm),theory(equality)],[c_1185]) ).
tff(c_90,plain,
! [E_42,To_43,T_44] :
( greater_or_equal('#skF_1'(E_42,To_43),To_43)
| greater(growth_rate(efficient_producers,T_44),growth_rate(first_movers,T_44))
| ~ greater(T_44,'#skF_2'(E_42))
| ~ subpopulations(first_movers,efficient_producers,E_42,T_44)
| ~ in_environment(E_42,To_43)
| ~ environment(E_42) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_309,plain,
! [E_128,To_129,E_130] :
( greater_or_equal('#skF_1'(E_128,To_129),To_129)
| greater(growth_rate(efficient_producers,'#skF_3'(E_130,'#skF_2'(E_128))),growth_rate(first_movers,'#skF_3'(E_130,'#skF_2'(E_128))))
| ~ subpopulations(first_movers,efficient_producers,E_128,'#skF_3'(E_130,'#skF_2'(E_128)))
| ~ in_environment(E_128,To_129)
| ~ environment(E_128)
| ( critical_point(E_130) = '#skF_2'(E_128) )
| ~ in_environment(E_130,'#skF_2'(E_128))
| greater(growth_rate(efficient_producers,'#skF_2'(E_128)),growth_rate(first_movers,'#skF_2'(E_128)))
| ~ environment(E_130) ),
inference(resolution,[status(thm)],[c_22,c_90]) ).
tff(c_318,plain,
! [E_131,To_132,E_133] :
( greater_or_equal('#skF_1'(E_131,To_132),To_132)
| ~ subpopulations(first_movers,efficient_producers,E_131,'#skF_3'(E_133,'#skF_2'(E_131)))
| ~ in_environment(E_131,To_132)
| ~ environment(E_131)
| ( critical_point(E_133) = '#skF_2'(E_131) )
| ~ in_environment(E_133,'#skF_2'(E_131))
| greater(growth_rate(efficient_producers,'#skF_2'(E_131)),growth_rate(first_movers,'#skF_2'(E_131)))
| ~ environment(E_133) ),
inference(resolution,[status(thm)],[c_309,c_20]) ).
tff(c_339,plain,
! [E_134,To_135] :
( greater_or_equal('#skF_1'(E_134,To_135),To_135)
| ~ in_environment(E_134,To_135)
| ( critical_point(E_134) = '#skF_2'(E_134) )
| ~ in_environment(E_134,'#skF_2'(E_134))
| greater(growth_rate(efficient_producers,'#skF_2'(E_134)),growth_rate(first_movers,'#skF_2'(E_134)))
| ~ environment(E_134) ),
inference(resolution,[status(thm)],[c_24,c_318]) ).
tff(c_359,plain,
! [E_136,To_137,To_138] :
( greater_or_equal('#skF_1'(E_136,To_137),To_137)
| ~ in_environment(E_136,To_137)
| greater_or_equal('#skF_1'(E_136,To_138),To_138)
| ~ in_environment(E_136,To_138)
| ( critical_point(E_136) = '#skF_2'(E_136) )
| ~ in_environment(E_136,'#skF_2'(E_136))
| ~ environment(E_136) ),
inference(resolution,[status(thm)],[c_339,c_10]) ).
tff(c_371,plain,
! [E_1,To_137,To_138,To_8] :
( greater_or_equal('#skF_1'(E_1,To_137),To_137)
| ~ in_environment(E_1,To_137)
| greater_or_equal('#skF_1'(E_1,To_138),To_138)
| ~ in_environment(E_1,To_138)
| ( critical_point(E_1) = '#skF_2'(E_1) )
| greater_or_equal('#skF_1'(E_1,To_8),To_8)
| ~ in_environment(E_1,To_8)
| ~ environment(E_1) ),
inference(resolution,[status(thm)],[c_16,c_359]) ).
tff(c_449,plain,
! [E_1,To_137,To_138] :
( greater_or_equal('#skF_1'(E_1,To_137),To_137)
| ~ in_environment(E_1,To_137)
| ( critical_point(E_1) = '#skF_2'(E_1) )
| ~ in_environment(E_1,To_138)
| ~ environment(E_1)
| greater_or_equal('#skF_1'(E_1,To_138),To_138) ),
inference(factorization,[status(thm),theory(equality)],[c_371]) ).
tff(c_500,plain,
! [E_160,To_161] :
( ( critical_point(E_160) = '#skF_2'(E_160) )
| ~ in_environment(E_160,To_161)
| ~ environment(E_160)
| greater_or_equal('#skF_1'(E_160,To_161),To_161) ),
inference(factorization,[status(thm),theory(equality)],[c_449]) ).
tff(c_505,plain,
! [E_162,E_163] :
( greater(growth_rate(efficient_producers,'#skF_1'(E_162,'#skF_4'(E_163))),growth_rate(first_movers,'#skF_1'(E_162,'#skF_4'(E_163))))
| ~ subpopulations(first_movers,efficient_producers,E_163,'#skF_1'(E_162,'#skF_4'(E_163)))
| ~ stable(E_163)
| ~ environment(E_163)
| ( critical_point(E_162) = '#skF_2'(E_162) )
| ~ in_environment(E_162,'#skF_4'(E_163))
| ~ environment(E_162) ),
inference(resolution,[status(thm)],[c_500,c_26]) ).
tff(c_2,plain,
! [E_1,To_8,T_11] :
( ~ greater(growth_rate(efficient_producers,'#skF_1'(E_1,To_8)),growth_rate(first_movers,'#skF_1'(E_1,To_8)))
| greater(growth_rate(efficient_producers,T_11),growth_rate(first_movers,T_11))
| ~ greater(T_11,'#skF_2'(E_1))
| ~ subpopulations(first_movers,efficient_producers,E_1,T_11)
| ~ in_environment(E_1,To_8)
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_513,plain,
! [T_11,E_162,E_163] :
( greater(growth_rate(efficient_producers,T_11),growth_rate(first_movers,T_11))
| ~ greater(T_11,'#skF_2'(E_162))
| ~ subpopulations(first_movers,efficient_producers,E_162,T_11)
| ~ subpopulations(first_movers,efficient_producers,E_163,'#skF_1'(E_162,'#skF_4'(E_163)))
| ~ stable(E_163)
| ~ environment(E_163)
| ( critical_point(E_162) = '#skF_2'(E_162) )
| ~ in_environment(E_162,'#skF_4'(E_163))
| ~ environment(E_162) ),
inference(resolution,[status(thm)],[c_505,c_2]) ).
tff(c_1378,plain,
! [E_288,E_289,E_290] :
( greater(growth_rate(efficient_producers,'#skF_3'(E_288,'#skF_2'(E_289))),growth_rate(first_movers,'#skF_3'(E_288,'#skF_2'(E_289))))
| ~ subpopulations(first_movers,efficient_producers,E_289,'#skF_3'(E_288,'#skF_2'(E_289)))
| ~ subpopulations(first_movers,efficient_producers,E_290,'#skF_1'(E_289,'#skF_4'(E_290)))
| ~ stable(E_290)
| ~ environment(E_290)
| ( critical_point(E_289) = '#skF_2'(E_289) )
| ~ in_environment(E_289,'#skF_4'(E_290))
| ~ stable(E_289)
| ~ in_environment(E_289,'#skF_4'(E_289))
| ~ environment(E_289)
| ( critical_point(E_288) = '#skF_2'(E_289) )
| ~ in_environment(E_288,'#skF_2'(E_289))
| ~ environment(E_288) ),
inference(resolution,[status(thm)],[c_1327,c_513]) ).
tff(c_1403,plain,
! [E_291,E_292] :
( greater(growth_rate(efficient_producers,'#skF_3'(E_291,'#skF_2'(E_292))),growth_rate(first_movers,'#skF_3'(E_291,'#skF_2'(E_292))))
| ~ subpopulations(first_movers,efficient_producers,E_292,'#skF_3'(E_291,'#skF_2'(E_292)))
| ~ stable(E_292)
| ( critical_point(E_291) = '#skF_2'(E_292) )
| ~ in_environment(E_291,'#skF_2'(E_292))
| ~ environment(E_291)
| ~ in_environment(E_292,'#skF_4'(E_292))
| ( critical_point(E_292) = '#skF_2'(E_292) )
| ~ in_environment(E_292,'#skF_2'(E_292))
| ~ environment(E_292) ),
inference(resolution,[status(thm)],[c_569,c_1378]) ).
tff(c_1408,plain,
! [E_293,E_294] :
( greater(growth_rate(efficient_producers,'#skF_2'(E_293)),growth_rate(first_movers,'#skF_2'(E_293)))
| ~ subpopulations(first_movers,efficient_producers,E_293,'#skF_3'(E_294,'#skF_2'(E_293)))
| ~ stable(E_293)
| ( critical_point(E_294) = '#skF_2'(E_293) )
| ~ in_environment(E_294,'#skF_2'(E_293))
| ~ environment(E_294)
| ~ in_environment(E_293,'#skF_4'(E_293))
| ( critical_point(E_293) = '#skF_2'(E_293) )
| ~ in_environment(E_293,'#skF_2'(E_293))
| ~ environment(E_293) ),
inference(resolution,[status(thm)],[c_1403,c_20]) ).
tff(c_1437,plain,
! [E_295] :
( ~ stable(E_295)
| ~ in_environment(E_295,'#skF_4'(E_295))
| ( critical_point(E_295) = '#skF_2'(E_295) )
| ~ in_environment(E_295,'#skF_2'(E_295))
| greater(growth_rate(efficient_producers,'#skF_2'(E_295)),growth_rate(first_movers,'#skF_2'(E_295)))
| ~ environment(E_295) ),
inference(resolution,[status(thm)],[c_24,c_1408]) ).
tff(c_514,plain,
! [E_162,E_163] :
( ~ greater(growth_rate(efficient_producers,'#skF_2'(E_162)),growth_rate(first_movers,'#skF_2'(E_162)))
| ~ subpopulations(first_movers,efficient_producers,E_163,'#skF_1'(E_162,'#skF_4'(E_163)))
| ~ stable(E_163)
| ~ environment(E_163)
| ( critical_point(E_162) = '#skF_2'(E_162) )
| ~ in_environment(E_162,'#skF_4'(E_163))
| ~ environment(E_162) ),
inference(resolution,[status(thm)],[c_505,c_8]) ).
tff(c_1471,plain,
! [E_301,E_302] :
( ~ subpopulations(first_movers,efficient_producers,E_301,'#skF_1'(E_302,'#skF_4'(E_301)))
| ~ stable(E_301)
| ~ environment(E_301)
| ~ in_environment(E_302,'#skF_4'(E_301))
| ~ stable(E_302)
| ~ in_environment(E_302,'#skF_4'(E_302))
| ( critical_point(E_302) = '#skF_2'(E_302) )
| ~ in_environment(E_302,'#skF_2'(E_302))
| ~ environment(E_302) ),
inference(resolution,[status(thm)],[c_1437,c_514]) ).
tff(c_1496,plain,
! [E_303] :
( ~ stable(E_303)
| ~ in_environment(E_303,'#skF_4'(E_303))
| ( critical_point(E_303) = '#skF_2'(E_303) )
| ~ in_environment(E_303,'#skF_2'(E_303))
| ~ environment(E_303) ),
inference(resolution,[status(thm)],[c_569,c_1471]) ).
tff(c_1513,plain,
! [E_304] :
( ( critical_point(E_304) = '#skF_2'(E_304) )
| ~ stable(E_304)
| ~ in_environment(E_304,'#skF_4'(E_304))
| ~ environment(E_304) ),
inference(resolution,[status(thm)],[c_176,c_1496]) ).
tff(c_1518,plain,
! [E_305] :
( ( critical_point(E_305) = '#skF_2'(E_305) )
| ~ stable(E_305)
| ~ environment(E_305) ),
inference(resolution,[status(thm)],[c_28,c_1513]) ).
tff(c_1521,plain,
( ( critical_point('#skF_5') = '#skF_2'('#skF_5') )
| ~ environment('#skF_5') ),
inference(resolution,[status(thm)],[c_32,c_1518]) ).
tff(c_1524,plain,
critical_point('#skF_5') = '#skF_2'('#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_1521]) ).
tff(c_30,plain,
~ in_environment('#skF_5',critical_point('#skF_5')),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_1525,plain,
~ in_environment('#skF_5','#skF_2'('#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_1524,c_30]) ).
tff(c_1533,plain,
( ~ stable('#skF_5')
| ~ in_environment('#skF_5','#skF_4'('#skF_5'))
| ~ environment('#skF_5') ),
inference(resolution,[status(thm)],[c_176,c_1525]) ).
tff(c_1540,plain,
~ in_environment('#skF_5','#skF_4'('#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_32,c_1533]) ).
tff(c_1546,plain,
( ~ stable('#skF_5')
| ~ environment('#skF_5') ),
inference(resolution,[status(thm)],[c_28,c_1540]) ).
tff(c_1550,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_34,c_32,c_1546]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : MGT023+2 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % 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
% 0.17/0.35 % Computer : n026.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 3 20:49:16 EDT 2023
% 0.17/0.35 % CPUTime :
% 6.97/2.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.97/2.66
% 6.97/2.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.97/2.70
% 6.97/2.70 Inference rules
% 6.97/2.70 ----------------------
% 6.97/2.70 #Ref : 0
% 6.97/2.70 #Sup : 347
% 6.97/2.70 #Fact : 26
% 6.97/2.70 #Define : 0
% 6.97/2.70 #Split : 0
% 6.97/2.70 #Chain : 0
% 6.97/2.70 #Close : 0
% 6.97/2.70
% 6.97/2.70 Ordering : KBO
% 6.97/2.70
% 6.97/2.70 Simplification rules
% 6.97/2.70 ----------------------
% 6.97/2.70 #Subsume : 217
% 6.97/2.70 #Demod : 7
% 6.97/2.70 #Tautology : 2
% 6.97/2.70 #SimpNegUnit : 0
% 6.97/2.70 #BackRed : 1
% 6.97/2.70
% 6.97/2.70 #Partial instantiations: 0
% 6.97/2.70 #Strategies tried : 1
% 6.97/2.70
% 6.97/2.70 Timing (in seconds)
% 6.97/2.70 ----------------------
% 6.97/2.70 Preprocessing : 0.50
% 7.22/2.70 Parsing : 0.27
% 7.22/2.70 CNF conversion : 0.04
% 7.22/2.70 Main loop : 1.11
% 7.22/2.70 Inferencing : 0.43
% 7.22/2.70 Reduction : 0.20
% 7.22/2.70 Demodulation : 0.14
% 7.22/2.70 BG Simplification : 0.04
% 7.22/2.70 Subsumption : 0.37
% 7.22/2.70 Abstraction : 0.04
% 7.22/2.70 MUC search : 0.00
% 7.22/2.70 Cooper : 0.00
% 7.22/2.70 Total : 1.67
% 7.22/2.70 Index Insertion : 0.00
% 7.22/2.70 Index Deletion : 0.00
% 7.22/2.70 Index Matching : 0.00
% 7.22/2.70 BG Taut test : 0.00
%------------------------------------------------------------------------------