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 v2.4.0.
% 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 : n029.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 : Unsatisfiable 7.89s 3.00s
% Output : CNFRefutation 7.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 44
% Syntax : Number of formulae : 178 ( 62 unt; 20 typ; 0 def)
% Number of atoms : 397 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 497 ( 258 ~; 239 |; 0 &)
% ( 0 <=>; 0 =>; 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 : 133 (; 133 !; 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 > 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(founding_rate,type,
founding_rate: ( $i * $i ) > $i ).
tff(sk2,type,
sk2: $i ).
tff(sk1,type,
sk1: $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(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_255,axiom,
environment(sk1),
file(unknown,unknown) ).
tff(f_258,axiom,
greater(critical_point(sk1),sk2),
file(unknown,unknown) ).
tff(f_256,axiom,
in_environment(sk1,critical_point(sk1)),
file(unknown,unknown) ).
tff(f_53,axiom,
! [A] :
( ~ environment(A)
| ~ in_environment(A,critical_point(A))
| subpopulations(first_movers,efficient_producers,A,critical_point(A)) ),
file(unknown,unknown) ).
tff(f_179,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| greater_or_equal(B,appear(efficient_producers,A)) ),
file(unknown,unknown) ).
tff(f_186,axiom,
! [A,B] :
( ~ greater_or_equal(A,B)
| greater(A,B)
| ( A = B ) ),
file(unknown,unknown) ).
tff(f_196,axiom,
! [A,B] :
( ( A != B )
| greater_or_equal(A,B) ),
file(unknown,unknown) ).
tff(f_149,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,critical_point(A))
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ greater(critical_point(A),B)
| in_environment(A,B) ),
file(unknown,unknown) ).
tff(f_257,axiom,
greater_or_equal(sk2,appear(efficient_producers,sk1)),
file(unknown,unknown) ).
tff(f_125,axiom,
! [A,B,C,D] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ in_environment(A,C)
| ~ greater_or_equal(C,D)
| ~ greater_or_equal(D,B)
| in_environment(A,D) ),
file(unknown,unknown) ).
tff(f_191,axiom,
! [A,B] :
( ~ greater(A,B)
| greater_or_equal(A,B) ),
file(unknown,unknown) ).
tff(f_61,axiom,
! [A] :
( ~ environment(A)
| ~ in_environment(A,appear(efficient_producers,A))
| subpopulations(first_movers,efficient_producers,A,appear(efficient_producers,A)) ),
file(unknown,unknown) ).
tff(f_246,axiom,
! [A,B,C,D] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater_or_equal(D,B)
| ~ greater_or_equal(C,D)
| subpopulations(first_movers,efficient_producers,A,D) ),
file(unknown,unknown) ).
tff(f_171,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| subpopulations(efficient_producers,first_movers,A,B) ),
file(unknown,unknown) ).
tff(f_260,axiom,
~ selection_favors(first_movers,efficient_producers,sk2),
file(unknown,unknown) ).
tff(f_254,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| decreases(difference(founding_rate(first_movers,B),founding_rate(efficient_producers,B))) ),
file(unknown,unknown) ).
tff(f_68,axiom,
! [A] :
( ~ decreases(difference(founding_rate(first_movers,A),founding_rate(efficient_producers,A)))
| decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| decreases(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A))) ),
file(unknown,unknown) ).
tff(f_206,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| greater(zero,difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)))
| greater_or_equal(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero) ),
file(unknown,unknown) ).
tff(f_88,axiom,
! [A,B,C] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater_or_equal(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero)
| ~ greater_or_equal(C,appear(efficient_producers,A))
| ~ greater(B,C)
| ~ decreases(difference(growth_rate(first_movers,C),growth_rate(efficient_producers,C)))
| greater(difference(growth_rate(first_movers,C),growth_rate(efficient_producers,C)),zero) ),
file(unknown,unknown) ).
tff(f_93,axiom,
! [A] :
( ~ greater(zero,difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)))
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) ),
file(unknown,unknown) ).
tff(f_215,axiom,
! [A,B] :
( ~ environment(A)
| ( B != critical_point(A) )
| ~ greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) ),
file(unknown,unknown) ).
tff(f_45,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(f_103,axiom,
! [A] :
( ~ greater(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero)
| greater(growth_rate(first_movers,A),growth_rate(efficient_producers,A)) ),
file(unknown,unknown) ).
tff(f_36,axiom,
! [A,B,C,D] :
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| selection_favors(C,B,D) ),
file(unknown,unknown) ).
tff(c_52,plain,
environment(sk1),
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_58,plain,
greater(critical_point(sk1),sk2),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_54,plain,
in_environment(sk1,critical_point(sk1)),
inference(cnfTransformation,[status(thm)],[f_256]) ).
tff(c_6,plain,
! [A_7] :
( subpopulations(first_movers,efficient_producers,A_7,critical_point(A_7))
| ~ in_environment(A_7,critical_point(A_7))
| ~ environment(A_7) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_91,plain,
! [B_61,A_62] :
( greater_or_equal(B_61,appear(efficient_producers,A_62))
| ~ subpopulations(first_movers,efficient_producers,A_62,B_61)
| ~ environment(A_62) ),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_36,plain,
! [B_32,A_31] :
( ( B_32 = A_31 )
| greater(A_31,B_32)
| ~ greater_or_equal(A_31,B_32) ),
inference(cnfTransformation,[status(thm)],[f_186]) ).
tff(c_95,plain,
! [A_62,B_61] :
( ( appear(efficient_producers,A_62) = B_61 )
| greater(B_61,appear(efficient_producers,A_62))
| ~ subpopulations(first_movers,efficient_producers,A_62,B_61)
| ~ environment(A_62) ),
inference(resolution,[status(thm)],[c_91,c_36]) ).
tff(c_40,plain,
! [B_36] : greater_or_equal(B_36,B_36),
inference(cnfTransformation,[status(thm)],[f_196]) ).
tff(c_197,plain,
! [A_102,B_103] :
( in_environment(A_102,B_103)
| ~ greater(critical_point(A_102),B_103)
| ~ greater_or_equal(B_103,appear(efficient_producers,A_102))
| ~ in_environment(A_102,critical_point(A_102))
| ~ environment(A_102) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_414,plain,
! [A_133] :
( in_environment(A_133,appear(efficient_producers,A_133))
| ~ greater(critical_point(A_133),appear(efficient_producers,A_133))
| ~ in_environment(A_133,critical_point(A_133))
| ~ environment(A_133) ),
inference(resolution,[status(thm)],[c_40,c_197]) ).
tff(c_655,plain,
! [A_178] :
( in_environment(A_178,appear(efficient_producers,A_178))
| ~ in_environment(A_178,critical_point(A_178))
| ( appear(efficient_producers,A_178) = critical_point(A_178) )
| ~ subpopulations(first_movers,efficient_producers,A_178,critical_point(A_178))
| ~ environment(A_178) ),
inference(resolution,[status(thm)],[c_95,c_414]) ).
tff(c_660,plain,
! [A_179] :
( in_environment(A_179,appear(efficient_producers,A_179))
| ( appear(efficient_producers,A_179) = critical_point(A_179) )
| ~ in_environment(A_179,critical_point(A_179))
| ~ environment(A_179) ),
inference(resolution,[status(thm)],[c_6,c_655]) ).
tff(c_56,plain,
greater_or_equal(sk2,appear(efficient_producers,sk1)),
inference(cnfTransformation,[status(thm)],[f_257]) ).
tff(c_126,plain,
! [A_78,D_79,B_80,C_81] :
( in_environment(A_78,D_79)
| ~ greater_or_equal(D_79,B_80)
| ~ greater_or_equal(C_81,D_79)
| ~ in_environment(A_78,C_81)
| ~ in_environment(A_78,B_80)
| ~ environment(A_78) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_143,plain,
! [A_84,C_85] :
( in_environment(A_84,sk2)
| ~ greater_or_equal(C_85,sk2)
| ~ in_environment(A_84,C_85)
| ~ in_environment(A_84,appear(efficient_producers,sk1))
| ~ environment(A_84) ),
inference(resolution,[status(thm)],[c_56,c_126]) ).
tff(c_147,plain,
( in_environment(sk1,sk2)
| ~ greater_or_equal(critical_point(sk1),sk2)
| ~ in_environment(sk1,appear(efficient_producers,sk1))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_54,c_143]) ).
tff(c_151,plain,
( in_environment(sk1,sk2)
| ~ greater_or_equal(critical_point(sk1),sk2)
| ~ in_environment(sk1,appear(efficient_producers,sk1)) ),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_147]) ).
tff(c_152,plain,
~ in_environment(sk1,appear(efficient_producers,sk1)),
inference(splitLeft,[status(thm)],[c_151]) ).
tff(c_684,plain,
( ( appear(efficient_producers,sk1) = critical_point(sk1) )
| ~ in_environment(sk1,critical_point(sk1))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_660,c_152]) ).
tff(c_705,plain,
appear(efficient_producers,sk1) = critical_point(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_54,c_684]) ).
tff(c_64,plain,
! [B_54,A_55] :
( ( B_54 = A_55 )
| greater(A_55,B_54)
| ~ greater_or_equal(A_55,B_54) ),
inference(cnfTransformation,[status(thm)],[f_186]) ).
tff(c_75,plain,
( ( appear(efficient_producers,sk1) = sk2 )
| greater(sk2,appear(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[c_56,c_64]) ).
tff(c_83,plain,
greater(sk2,appear(efficient_producers,sk1)),
inference(splitLeft,[status(thm)],[c_75]) ).
tff(c_204,plain,
( in_environment(sk1,sk2)
| ~ greater(critical_point(sk1),sk2)
| ~ in_environment(sk1,critical_point(sk1))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_56,c_197]) ).
tff(c_212,plain,
in_environment(sk1,sk2),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_54,c_58,c_204]) ).
tff(c_38,plain,
! [A_33,B_34] :
( greater_or_equal(A_33,B_34)
| ~ greater(A_33,B_34) ),
inference(cnfTransformation,[status(thm)],[f_191]) ).
tff(c_154,plain,
! [A_87,A_88,C_89,B_90] :
( in_environment(A_87,A_88)
| ~ greater_or_equal(C_89,A_88)
| ~ in_environment(A_87,C_89)
| ~ in_environment(A_87,B_90)
| ~ environment(A_87)
| ~ greater(A_88,B_90) ),
inference(resolution,[status(thm)],[c_38,c_126]) ).
tff(c_167,plain,
! [A_87,B_34,A_33,B_90] :
( in_environment(A_87,B_34)
| ~ in_environment(A_87,A_33)
| ~ in_environment(A_87,B_90)
| ~ environment(A_87)
| ~ greater(B_34,B_90)
| ~ greater(A_33,B_34) ),
inference(resolution,[status(thm)],[c_38,c_154]) ).
tff(c_217,plain,
! [B_34,B_90] :
( in_environment(sk1,B_34)
| ~ in_environment(sk1,B_90)
| ~ environment(sk1)
| ~ greater(B_34,B_90)
| ~ greater(sk2,B_34) ),
inference(resolution,[status(thm)],[c_212,c_167]) ).
tff(c_239,plain,
! [B_106,B_107] :
( in_environment(sk1,B_106)
| ~ in_environment(sk1,B_107)
| ~ greater(B_106,B_107)
| ~ greater(sk2,B_106) ),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_217]) ).
tff(c_252,plain,
! [B_108] :
( in_environment(sk1,B_108)
| ~ greater(B_108,sk2)
| ~ greater(sk2,B_108) ),
inference(resolution,[status(thm)],[c_212,c_239]) ).
tff(c_265,plain,
( ~ greater(appear(efficient_producers,sk1),sk2)
| ~ greater(sk2,appear(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[c_252,c_152]) ).
tff(c_278,plain,
~ greater(appear(efficient_producers,sk1),sk2),
inference(demodulation,[status(thm),theory(equality)],[c_83,c_265]) ).
tff(c_712,plain,
~ greater(critical_point(sk1),sk2),
inference(demodulation,[status(thm),theory(equality)],[c_705,c_278]) ).
tff(c_720,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_58,c_712]) ).
tff(c_722,plain,
in_environment(sk1,appear(efficient_producers,sk1)),
inference(splitRight,[status(thm)],[c_151]) ).
tff(c_8,plain,
! [A_8] :
( subpopulations(first_movers,efficient_producers,A_8,appear(efficient_producers,A_8))
| ~ in_environment(A_8,appear(efficient_producers,A_8))
| ~ environment(A_8) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_721,plain,
( ~ greater_or_equal(critical_point(sk1),sk2)
| in_environment(sk1,sk2) ),
inference(splitRight,[status(thm)],[c_151]) ).
tff(c_728,plain,
~ greater_or_equal(critical_point(sk1),sk2),
inference(splitLeft,[status(thm)],[c_721]) ).
tff(c_731,plain,
~ greater(critical_point(sk1),sk2),
inference(resolution,[status(thm)],[c_38,c_728]) ).
tff(c_735,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_58,c_731]) ).
tff(c_737,plain,
greater_or_equal(critical_point(sk1),sk2),
inference(splitRight,[status(thm)],[c_721]) ).
tff(c_873,plain,
! [A_207,D_208,C_209,B_210] :
( subpopulations(first_movers,efficient_producers,A_207,D_208)
| ~ greater_or_equal(C_209,D_208)
| ~ greater_or_equal(D_208,B_210)
| ~ subpopulations(first_movers,efficient_producers,A_207,C_209)
| ~ subpopulations(first_movers,efficient_producers,A_207,B_210)
| ~ environment(A_207) ),
inference(cnfTransformation,[status(thm)],[f_246]) ).
tff(c_1441,plain,
! [A_287,B_288] :
( subpopulations(first_movers,efficient_producers,A_287,sk2)
| ~ greater_or_equal(sk2,B_288)
| ~ subpopulations(first_movers,efficient_producers,A_287,critical_point(sk1))
| ~ subpopulations(first_movers,efficient_producers,A_287,B_288)
| ~ environment(A_287) ),
inference(resolution,[status(thm)],[c_737,c_873]) ).
tff(c_1444,plain,
! [B_288] :
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ greater_or_equal(sk2,B_288)
| ~ subpopulations(first_movers,efficient_producers,sk1,B_288)
| ~ in_environment(sk1,critical_point(sk1))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_6,c_1441]) ).
tff(c_1447,plain,
! [B_288] :
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ greater_or_equal(sk2,B_288)
| ~ subpopulations(first_movers,efficient_producers,sk1,B_288) ),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_54,c_1444]) ).
tff(c_1468,plain,
! [B_293] :
( ~ greater_or_equal(sk2,B_293)
| ~ subpopulations(first_movers,efficient_producers,sk1,B_293) ),
inference(splitLeft,[status(thm)],[c_1447]) ).
tff(c_1472,plain,
( ~ greater_or_equal(sk2,appear(efficient_producers,sk1))
| ~ in_environment(sk1,appear(efficient_producers,sk1))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_8,c_1468]) ).
tff(c_1480,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_52,c_722,c_56,c_1472]) ).
tff(c_1481,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(splitRight,[status(thm)],[c_1447]) ).
tff(c_32,plain,
! [A_27,B_28] :
( subpopulations(efficient_producers,first_movers,A_27,B_28)
| ~ subpopulations(first_movers,efficient_producers,A_27,B_28)
| ~ environment(A_27) ),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_1491,plain,
( subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_1481,c_32]) ).
tff(c_1502,plain,
subpopulations(efficient_producers,first_movers,sk1,sk2),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_1491]) ).
tff(c_60,plain,
~ selection_favors(first_movers,efficient_producers,sk2),
inference(cnfTransformation,[status(thm)],[f_260]) ).
tff(c_50,plain,
! [B_49,A_48] :
( decreases(difference(founding_rate(first_movers,B_49),founding_rate(efficient_producers,B_49)))
| ~ subpopulations(first_movers,efficient_producers,A_48,B_49)
| ~ environment(A_48) ),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_1488,plain,
( decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2)))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_1481,c_50]) ).
tff(c_1499,plain,
decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2))),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_1488]) ).
tff(c_10,plain,
! [A_9] :
( decreases(difference(growth_rate(first_movers,A_9),growth_rate(efficient_producers,A_9)))
| decreases(difference(disbanding_rate(first_movers,A_9),disbanding_rate(efficient_producers,A_9)))
| ~ decreases(difference(founding_rate(first_movers,A_9),founding_rate(efficient_producers,A_9))) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_985,plain,
! [B_221,A_222] :
( greater_or_equal(difference(growth_rate(first_movers,B_221),growth_rate(efficient_producers,B_221)),zero)
| greater(zero,difference(growth_rate(first_movers,B_221),growth_rate(efficient_producers,B_221)))
| ~ subpopulations(first_movers,efficient_producers,A_222,B_221)
| ~ environment(A_222) ),
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_991,plain,
! [A_7] :
( greater_or_equal(difference(growth_rate(first_movers,critical_point(A_7)),growth_rate(efficient_producers,critical_point(A_7))),zero)
| greater(zero,difference(growth_rate(first_movers,critical_point(A_7)),growth_rate(efficient_producers,critical_point(A_7))))
| ~ in_environment(A_7,critical_point(A_7))
| ~ environment(A_7) ),
inference(resolution,[status(thm)],[c_6,c_985]) ).
tff(c_1037,plain,
! [C_229,B_230,A_231] :
( greater(difference(growth_rate(first_movers,C_229),growth_rate(efficient_producers,C_229)),zero)
| ~ decreases(difference(growth_rate(first_movers,C_229),growth_rate(efficient_producers,C_229)))
| ~ greater(B_230,C_229)
| ~ greater_or_equal(C_229,appear(efficient_producers,A_231))
| ~ greater_or_equal(difference(growth_rate(first_movers,B_230),growth_rate(efficient_producers,B_230)),zero)
| ~ in_environment(A_231,B_230)
| ~ environment(A_231) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_1055,plain,
! [A_231] :
( greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero)
| ~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))
| ~ greater_or_equal(sk2,appear(efficient_producers,A_231))
| ~ greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero)
| ~ in_environment(A_231,critical_point(sk1))
| ~ environment(A_231) ),
inference(resolution,[status(thm)],[c_58,c_1037]) ).
tff(c_2085,plain,
~ greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero),
inference(splitLeft,[status(thm)],[c_1055]) ).
tff(c_2088,plain,
( greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))))
| ~ in_environment(sk1,critical_point(sk1))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_991,c_2085]) ).
tff(c_2094,plain,
greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1)))),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_54,c_2088]) ).
tff(c_14,plain,
! [A_13] :
( greater(growth_rate(efficient_producers,A_13),growth_rate(first_movers,A_13))
| ~ greater(zero,difference(growth_rate(first_movers,A_13),growth_rate(efficient_producers,A_13))) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_2126,plain,
greater(growth_rate(efficient_producers,critical_point(sk1)),growth_rate(first_movers,critical_point(sk1))),
inference(resolution,[status(thm)],[c_2094,c_14]) ).
tff(c_44,plain,
! [A_39] :
( ~ greater(growth_rate(efficient_producers,critical_point(A_39)),growth_rate(first_movers,critical_point(A_39)))
| ~ environment(A_39) ),
inference(cnfTransformation,[status(thm)],[f_215]) ).
tff(c_2149,plain,
~ environment(sk1),
inference(resolution,[status(thm)],[c_2126,c_44]) ).
tff(c_2163,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_52,c_2149]) ).
tff(c_2164,plain,
! [A_231] :
( ~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))
| ~ greater_or_equal(sk2,appear(efficient_producers,A_231))
| ~ in_environment(A_231,critical_point(sk1))
| ~ environment(A_231)
| greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero) ),
inference(splitRight,[status(thm)],[c_1055]) ).
tff(c_2228,plain,
~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))),
inference(splitLeft,[status(thm)],[c_2164]) ).
tff(c_2231,plain,
( decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2))) ),
inference(resolution,[status(thm)],[c_10,c_2228]) ).
tff(c_2234,plain,
decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
inference(demodulation,[status(thm),theory(equality)],[c_1499,c_2231]) ).
tff(c_4,plain,
! [B_6,A_5] :
( ~ decreases(difference(disbanding_rate(first_movers,B_6),disbanding_rate(efficient_producers,B_6)))
| ~ subpopulations(first_movers,efficient_producers,A_5,B_6)
| ~ environment(A_5) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_2238,plain,
! [A_367] :
( ~ subpopulations(first_movers,efficient_producers,A_367,sk2)
| ~ environment(A_367) ),
inference(resolution,[status(thm)],[c_2234,c_4]) ).
tff(c_2245,plain,
~ environment(sk1),
inference(resolution,[status(thm)],[c_1481,c_2238]) ).
tff(c_2252,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_52,c_2245]) ).
tff(c_2253,plain,
! [A_231] :
( ~ greater_or_equal(sk2,appear(efficient_producers,A_231))
| ~ in_environment(A_231,critical_point(sk1))
| ~ environment(A_231)
| greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero) ),
inference(splitRight,[status(thm)],[c_2164]) ).
tff(c_2266,plain,
! [A_370] :
( ~ greater_or_equal(sk2,appear(efficient_producers,A_370))
| ~ in_environment(A_370,critical_point(sk1))
| ~ environment(A_370) ),
inference(splitLeft,[status(thm)],[c_2253]) ).
tff(c_2273,plain,
( ~ greater_or_equal(sk2,appear(efficient_producers,sk1))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_54,c_2266]) ).
tff(c_2280,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_52,c_56,c_2273]) ).
tff(c_2281,plain,
greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero),
inference(splitRight,[status(thm)],[c_2253]) ).
tff(c_18,plain,
! [A_15] :
( greater(growth_rate(first_movers,A_15),growth_rate(efficient_producers,A_15))
| ~ greater(difference(growth_rate(first_movers,A_15),growth_rate(efficient_producers,A_15)),zero) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_2312,plain,
greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),
inference(resolution,[status(thm)],[c_2281,c_18]) ).
tff(c_2,plain,
! [C_3,B_2,D_4,A_1] :
( selection_favors(C_3,B_2,D_4)
| ~ greater(growth_rate(C_3,D_4),growth_rate(B_2,D_4))
| ~ subpopulations(B_2,C_3,A_1,D_4)
| ~ environment(A_1) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_2332,plain,
! [A_1] :
( selection_favors(first_movers,efficient_producers,sk2)
| ~ subpopulations(efficient_producers,first_movers,A_1,sk2)
| ~ environment(A_1) ),
inference(resolution,[status(thm)],[c_2312,c_2]) ).
tff(c_2346,plain,
! [A_371] :
( ~ subpopulations(efficient_producers,first_movers,A_371,sk2)
| ~ environment(A_371) ),
inference(negUnitSimplification,[status(thm)],[c_60,c_2332]) ).
tff(c_2353,plain,
~ environment(sk1),
inference(resolution,[status(thm)],[c_1502,c_2346]) ).
tff(c_2360,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_52,c_2353]) ).
tff(c_2361,plain,
appear(efficient_producers,sk1) = sk2,
inference(splitRight,[status(thm)],[c_75]) ).
tff(c_2400,plain,
! [A_379] :
( subpopulations(first_movers,efficient_producers,A_379,appear(efficient_producers,A_379))
| ~ in_environment(A_379,appear(efficient_producers,A_379))
| ~ environment(A_379) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_2410,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ in_environment(sk1,appear(efficient_producers,sk1))
| ~ environment(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_2361,c_2400]) ).
tff(c_2416,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ in_environment(sk1,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_2361,c_2410]) ).
tff(c_2417,plain,
~ in_environment(sk1,sk2),
inference(splitLeft,[status(thm)],[c_2416]) ).
tff(c_2540,plain,
! [A_413,B_414] :
( in_environment(A_413,B_414)
| ~ greater(critical_point(A_413),B_414)
| ~ greater_or_equal(B_414,appear(efficient_producers,A_413))
| ~ in_environment(A_413,critical_point(A_413))
| ~ environment(A_413) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_2544,plain,
! [B_414] :
( in_environment(sk1,B_414)
| ~ greater(critical_point(sk1),B_414)
| ~ greater_or_equal(B_414,sk2)
| ~ in_environment(sk1,critical_point(sk1))
| ~ environment(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_2361,c_2540]) ).
tff(c_2556,plain,
! [B_415] :
( in_environment(sk1,B_415)
| ~ greater(critical_point(sk1),B_415)
| ~ greater_or_equal(B_415,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_54,c_2544]) ).
tff(c_2563,plain,
( in_environment(sk1,sk2)
| ~ greater_or_equal(sk2,sk2) ),
inference(resolution,[status(thm)],[c_58,c_2556]) ).
tff(c_2567,plain,
in_environment(sk1,sk2),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_2563]) ).
tff(c_2569,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2417,c_2567]) ).
tff(c_2570,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(splitRight,[status(thm)],[c_2416]) ).
tff(c_2574,plain,
( subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_2570,c_32]) ).
tff(c_2580,plain,
subpopulations(efficient_producers,first_movers,sk1,sk2),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_2574]) ).
tff(c_2583,plain,
! [B_416,A_417] :
( decreases(difference(founding_rate(first_movers,B_416),founding_rate(efficient_producers,B_416)))
| ~ subpopulations(first_movers,efficient_producers,A_417,B_416)
| ~ environment(A_417) ),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_2585,plain,
( decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2)))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_2570,c_2583]) ).
tff(c_2592,plain,
decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2))),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_2585]) ).
tff(c_2896,plain,
! [B_485,A_486] :
( greater_or_equal(difference(growth_rate(first_movers,B_485),growth_rate(efficient_producers,B_485)),zero)
| greater(zero,difference(growth_rate(first_movers,B_485),growth_rate(efficient_producers,B_485)))
| ~ subpopulations(first_movers,efficient_producers,A_486,B_485)
| ~ environment(A_486) ),
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_2907,plain,
! [A_7] :
( greater_or_equal(difference(growth_rate(first_movers,critical_point(A_7)),growth_rate(efficient_producers,critical_point(A_7))),zero)
| greater(zero,difference(growth_rate(first_movers,critical_point(A_7)),growth_rate(efficient_producers,critical_point(A_7))))
| ~ in_environment(A_7,critical_point(A_7))
| ~ environment(A_7) ),
inference(resolution,[status(thm)],[c_6,c_2896]) ).
tff(c_2973,plain,
! [C_496,B_497,A_498] :
( greater(difference(growth_rate(first_movers,C_496),growth_rate(efficient_producers,C_496)),zero)
| ~ decreases(difference(growth_rate(first_movers,C_496),growth_rate(efficient_producers,C_496)))
| ~ greater(B_497,C_496)
| ~ greater_or_equal(C_496,appear(efficient_producers,A_498))
| ~ greater_or_equal(difference(growth_rate(first_movers,B_497),growth_rate(efficient_producers,B_497)),zero)
| ~ in_environment(A_498,B_497)
| ~ environment(A_498) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_2988,plain,
! [A_498] :
( greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero)
| ~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))
| ~ greater_or_equal(sk2,appear(efficient_producers,A_498))
| ~ greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero)
| ~ in_environment(A_498,critical_point(sk1))
| ~ environment(A_498) ),
inference(resolution,[status(thm)],[c_58,c_2973]) ).
tff(c_3788,plain,
~ greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero),
inference(splitLeft,[status(thm)],[c_2988]) ).
tff(c_3791,plain,
( greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))))
| ~ in_environment(sk1,critical_point(sk1))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_2907,c_3788]) ).
tff(c_3797,plain,
greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1)))),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_54,c_3791]) ).
tff(c_3829,plain,
greater(growth_rate(efficient_producers,critical_point(sk1)),growth_rate(first_movers,critical_point(sk1))),
inference(resolution,[status(thm)],[c_3797,c_14]) ).
tff(c_3852,plain,
~ environment(sk1),
inference(resolution,[status(thm)],[c_3829,c_44]) ).
tff(c_3866,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_52,c_3852]) ).
tff(c_3867,plain,
! [A_498] :
( ~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))
| ~ greater_or_equal(sk2,appear(efficient_producers,A_498))
| ~ in_environment(A_498,critical_point(sk1))
| ~ environment(A_498)
| greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero) ),
inference(splitRight,[status(thm)],[c_2988]) ).
tff(c_4049,plain,
~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))),
inference(splitLeft,[status(thm)],[c_3867]) ).
tff(c_4052,plain,
( decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2))) ),
inference(resolution,[status(thm)],[c_10,c_4049]) ).
tff(c_4055,plain,
decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
inference(demodulation,[status(thm),theory(equality)],[c_2592,c_4052]) ).
tff(c_4059,plain,
! [A_625] :
( ~ subpopulations(first_movers,efficient_producers,A_625,sk2)
| ~ environment(A_625) ),
inference(resolution,[status(thm)],[c_4055,c_4]) ).
tff(c_4066,plain,
~ environment(sk1),
inference(resolution,[status(thm)],[c_2570,c_4059]) ).
tff(c_4073,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_52,c_4066]) ).
tff(c_4074,plain,
! [A_498] :
( ~ greater_or_equal(sk2,appear(efficient_producers,A_498))
| ~ in_environment(A_498,critical_point(sk1))
| ~ environment(A_498)
| greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero) ),
inference(splitRight,[status(thm)],[c_3867]) ).
tff(c_4104,plain,
! [A_630] :
( ~ greater_or_equal(sk2,appear(efficient_producers,A_630))
| ~ in_environment(A_630,critical_point(sk1))
| ~ environment(A_630) ),
inference(splitLeft,[status(thm)],[c_4074]) ).
tff(c_4111,plain,
( ~ greater_or_equal(sk2,appear(efficient_producers,sk1))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_54,c_4104]) ).
tff(c_4118,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_52,c_40,c_2361,c_4111]) ).
tff(c_4119,plain,
greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero),
inference(splitRight,[status(thm)],[c_4074]) ).
tff(c_4150,plain,
greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),
inference(resolution,[status(thm)],[c_4119,c_18]) ).
tff(c_4170,plain,
! [A_1] :
( selection_favors(first_movers,efficient_producers,sk2)
| ~ subpopulations(efficient_producers,first_movers,A_1,sk2)
| ~ environment(A_1) ),
inference(resolution,[status(thm)],[c_4150,c_2]) ).
tff(c_4184,plain,
! [A_631] :
( ~ subpopulations(efficient_producers,first_movers,A_631,sk2)
| ~ environment(A_631) ),
inference(negUnitSimplification,[status(thm)],[c_60,c_4170]) ).
tff(c_4191,plain,
~ environment(sk1),
inference(resolution,[status(thm)],[c_2580,c_4184]) ).
tff(c_4198,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_52,c_4191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT034-2 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % 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
% 0.15/0.34 % Computer : n029.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Thu Aug 3 20:47:23 EDT 2023
% 0.15/0.34 % CPUTime :
% 7.89/3.00 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.89/3.01
% 7.89/3.01 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.89/3.06
% 7.89/3.06 Inference rules
% 7.89/3.06 ----------------------
% 7.89/3.06 #Ref : 0
% 7.89/3.06 #Sup : 923
% 7.89/3.06 #Fact : 0
% 7.89/3.06 #Define : 0
% 7.89/3.06 #Split : 38
% 7.89/3.06 #Chain : 0
% 7.89/3.06 #Close : 0
% 7.89/3.06
% 7.89/3.06 Ordering : KBO
% 7.89/3.06
% 7.89/3.06 Simplification rules
% 7.89/3.06 ----------------------
% 7.89/3.06 #Subsume : 116
% 7.89/3.06 #Demod : 657
% 7.89/3.06 #Tautology : 144
% 7.89/3.06 #SimpNegUnit : 12
% 7.89/3.06 #BackRed : 12
% 7.89/3.06
% 7.89/3.06 #Partial instantiations: 0
% 7.89/3.06 #Strategies tried : 1
% 7.89/3.06
% 7.89/3.06 Timing (in seconds)
% 7.89/3.06 ----------------------
% 7.89/3.06 Preprocessing : 0.58
% 7.89/3.06 Parsing : 0.31
% 7.89/3.06 CNF conversion : 0.03
% 7.89/3.06 Main loop : 1.36
% 7.89/3.06 Inferencing : 0.52
% 7.89/3.06 Reduction : 0.39
% 7.89/3.06 Demodulation : 0.26
% 7.89/3.06 BG Simplification : 0.05
% 7.89/3.06 Subsumption : 0.31
% 7.89/3.06 Abstraction : 0.04
% 7.89/3.06 MUC search : 0.00
% 7.89/3.06 Cooper : 0.00
% 7.89/3.06 Total : 2.02
% 7.89/3.06 Index Insertion : 0.00
% 7.89/3.06 Index Deletion : 0.00
% 7.89/3.06 Index Matching : 0.00
% 7.89/3.06 BG Taut test : 0.00
%------------------------------------------------------------------------------