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 v2.4.0.
% 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 : n032.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 10:49:34 EDT 2023
% Result : Unsatisfiable 6.63s 2.56s
% Output : CNFRefutation 6.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 32
% Syntax : Number of formulae : 93 ( 9 unt; 15 typ; 0 def)
% Number of atoms : 432 ( 48 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 637 ( 283 ~; 354 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 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 : 152 (; 152 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulations > in_environment > greater_or_equal > greater > stable > environment > sk3 > sk1 > growth_rate > #nlpp > sk4 > sk2 > critical_point > sk5 > 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(sk2,type,
sk2: $i > $i ).
tff(in_environment,type,
in_environment: ( $i * $i ) > $o ).
tff(efficient_producers,type,
efficient_producers: $i ).
tff(critical_point,type,
critical_point: $i > $i ).
tff(growth_rate,type,
growth_rate: ( $i * $i ) > $i ).
tff(sk4,type,
sk4: $i > $i ).
tff(environment,type,
environment: $i > $o ).
tff(sk5,type,
sk5: $i ).
tff(first_movers,type,
first_movers: $i ).
tff(sk3,type,
sk3: ( $i * $i ) > $i ).
tff(greater_or_equal,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(sk1,type,
sk1: ( $i * $i ) > $i ).
tff(stable,type,
stable: $i > $o ).
tff(f_199,axiom,
~ in_environment(sk5,critical_point(sk5)),
file(unknown,unknown) ).
tff(f_196,axiom,
environment(sk5),
file(unknown,unknown) ).
tff(f_197,axiom,
stable(sk5),
file(unknown,unknown) ).
tff(f_181,axiom,
! [A] :
( ~ environment(A)
| ~ stable(A)
| in_environment(A,sk4(A)) ),
file(unknown,unknown) ).
tff(f_32,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| in_environment(A,sk2(A)) ),
file(unknown,unknown) ).
tff(f_42,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| greater_or_equal(sk1(B,A),B)
| in_environment(A,sk2(A)) ),
file(unknown,unknown) ).
tff(f_195,axiom,
! [A,B] :
( ~ environment(A)
| ~ stable(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ greater_or_equal(B,sk4(A))
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) ),
file(unknown,unknown) ).
tff(f_107,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| in_environment(A,sk2(A)) ),
file(unknown,unknown) ).
tff(f_148,axiom,
! [A,B] :
( ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ in_environment(A,B)
| subpopulations(first_movers,efficient_producers,A,sk3(B,A))
| ( B = critical_point(A) ) ),
file(unknown,unknown) ).
tff(f_160,axiom,
! [A,B] :
( ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ in_environment(A,B)
| greater(sk3(B,A),B)
| ( B = critical_point(A) ) ),
file(unknown,unknown) ).
tff(f_69,axiom,
! [A,B,C] :
( ~ environment(A)
| ~ in_environment(A,B)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(C,sk2(A))
| greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) ),
file(unknown,unknown) ).
tff(f_173,axiom,
! [A,B] :
( ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ in_environment(A,B)
| ~ greater(growth_rate(efficient_producers,sk3(B,A)),growth_rate(first_movers,sk3(B,A)))
| ( B = critical_point(A) ) ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A))) ),
file(unknown,unknown) ).
tff(f_96,axiom,
! [A,B,C] :
( ~ environment(A)
| ~ in_environment(A,B)
| greater_or_equal(sk1(B,A),B)
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(C,sk2(A))
| greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) ),
file(unknown,unknown) ).
tff(f_80,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| greater_or_equal(sk1(B,A),B)
| ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A))) ),
file(unknown,unknown) ).
tff(f_119,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A))) ),
file(unknown,unknown) ).
tff(f_136,axiom,
! [A,B,C] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(C,sk2(A))
| greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) ),
file(unknown,unknown) ).
tff(c_34,plain,
~ in_environment(sk5,critical_point(sk5)),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_30,plain,
environment(sk5),
inference(cnfTransformation,[status(thm)],[f_196]) ).
tff(c_32,plain,
stable(sk5),
inference(cnfTransformation,[status(thm)],[f_197]) ).
tff(c_26,plain,
! [A_28] :
( in_environment(A_28,sk4(A_28))
| ~ stable(A_28)
| ~ environment(A_28) ),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_2,plain,
! [A_1,B_2] :
( in_environment(A_1,sk2(A_1))
| subpopulations(first_movers,efficient_producers,A_1,sk1(B_2,A_1))
| ~ in_environment(A_1,B_2)
| ~ environment(A_1) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_4,plain,
! [A_3,B_4] :
( in_environment(A_3,sk2(A_3))
| greater_or_equal(sk1(B_4,A_3),B_4)
| ~ in_environment(A_3,B_4)
| ~ environment(A_3) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_44,plain,
! [B_40,A_41] :
( greater(growth_rate(efficient_producers,B_40),growth_rate(first_movers,B_40))
| ~ greater_or_equal(B_40,sk4(A_41))
| ~ subpopulations(first_movers,efficient_producers,A_41,B_40)
| ~ stable(A_41)
| ~ environment(A_41) ),
inference(cnfTransformation,[status(thm)],[f_195]) ).
tff(c_146,plain,
! [A_82,A_83] :
( greater(growth_rate(efficient_producers,sk1(sk4(A_82),A_83)),growth_rate(first_movers,sk1(sk4(A_82),A_83)))
| ~ subpopulations(first_movers,efficient_producers,A_82,sk1(sk4(A_82),A_83))
| ~ stable(A_82)
| ~ environment(A_82)
| in_environment(A_83,sk2(A_83))
| ~ in_environment(A_83,sk4(A_82))
| ~ environment(A_83) ),
inference(resolution,[status(thm)],[c_4,c_44]) ).
tff(c_14,plain,
! [A_15,B_16] :
( in_environment(A_15,sk2(A_15))
| ~ greater(growth_rate(efficient_producers,sk1(B_16,A_15)),growth_rate(first_movers,sk1(B_16,A_15)))
| ~ in_environment(A_15,B_16)
| ~ environment(A_15) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_164,plain,
! [A_87,A_88] :
( ~ subpopulations(first_movers,efficient_producers,A_87,sk1(sk4(A_87),A_88))
| ~ stable(A_87)
| ~ environment(A_87)
| in_environment(A_88,sk2(A_88))
| ~ in_environment(A_88,sk4(A_87))
| ~ environment(A_88) ),
inference(resolution,[status(thm)],[c_146,c_14]) ).
tff(c_177,plain,
! [A_89] :
( ~ stable(A_89)
| in_environment(A_89,sk2(A_89))
| ~ in_environment(A_89,sk4(A_89))
| ~ environment(A_89) ),
inference(resolution,[status(thm)],[c_2,c_164]) ).
tff(c_181,plain,
! [A_28] :
( in_environment(A_28,sk2(A_28))
| ~ stable(A_28)
| ~ environment(A_28) ),
inference(resolution,[status(thm)],[c_26,c_177]) ).
tff(c_20,plain,
! [A_22,B_23] :
( ( critical_point(A_22) = B_23 )
| subpopulations(first_movers,efficient_producers,A_22,sk3(B_23,A_22))
| ~ in_environment(A_22,B_23)
| greater(growth_rate(efficient_producers,B_23),growth_rate(first_movers,B_23))
| ~ environment(A_22) ),
inference(cnfTransformation,[status(thm)],[f_148]) ).
tff(c_22,plain,
! [A_24,B_25] :
( ( critical_point(A_24) = B_25 )
| greater(sk3(B_25,A_24),B_25)
| ~ in_environment(A_24,B_25)
| greater(growth_rate(efficient_producers,B_25),growth_rate(first_movers,B_25))
| ~ environment(A_24) ),
inference(cnfTransformation,[status(thm)],[f_160]) ).
tff(c_95,plain,
! [C_55,A_56,B_57] :
( greater(growth_rate(efficient_producers,C_55),growth_rate(first_movers,C_55))
| ~ greater(C_55,sk2(A_56))
| ~ subpopulations(first_movers,efficient_producers,A_56,C_55)
| subpopulations(first_movers,efficient_producers,A_56,sk1(B_57,A_56))
| ~ in_environment(A_56,B_57)
| ~ environment(A_56) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_387,plain,
! [A_127,A_128,B_129] :
( greater(growth_rate(efficient_producers,sk3(sk2(A_127),A_128)),growth_rate(first_movers,sk3(sk2(A_127),A_128)))
| ~ subpopulations(first_movers,efficient_producers,A_127,sk3(sk2(A_127),A_128))
| subpopulations(first_movers,efficient_producers,A_127,sk1(B_129,A_127))
| ~ in_environment(A_127,B_129)
| ~ environment(A_127)
| ( sk2(A_127) = critical_point(A_128) )
| ~ in_environment(A_128,sk2(A_127))
| greater(growth_rate(efficient_producers,sk2(A_127)),growth_rate(first_movers,sk2(A_127)))
| ~ environment(A_128) ),
inference(resolution,[status(thm)],[c_22,c_95]) ).
tff(c_24,plain,
! [A_26,B_27] :
( ( critical_point(A_26) = B_27 )
| ~ greater(growth_rate(efficient_producers,sk3(B_27,A_26)),growth_rate(first_movers,sk3(B_27,A_26)))
| ~ in_environment(A_26,B_27)
| greater(growth_rate(efficient_producers,B_27),growth_rate(first_movers,B_27))
| ~ environment(A_26) ),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_439,plain,
! [A_139,A_140,B_141] :
( ~ subpopulations(first_movers,efficient_producers,A_139,sk3(sk2(A_139),A_140))
| subpopulations(first_movers,efficient_producers,A_139,sk1(B_141,A_139))
| ~ in_environment(A_139,B_141)
| ~ environment(A_139)
| ( sk2(A_139) = critical_point(A_140) )
| ~ in_environment(A_140,sk2(A_139))
| greater(growth_rate(efficient_producers,sk2(A_139)),growth_rate(first_movers,sk2(A_139)))
| ~ environment(A_140) ),
inference(resolution,[status(thm)],[c_387,c_24]) ).
tff(c_452,plain,
! [A_142,B_143] :
( subpopulations(first_movers,efficient_producers,A_142,sk1(B_143,A_142))
| ~ in_environment(A_142,B_143)
| ( sk2(A_142) = critical_point(A_142) )
| ~ in_environment(A_142,sk2(A_142))
| greater(growth_rate(efficient_producers,sk2(A_142)),growth_rate(first_movers,sk2(A_142)))
| ~ environment(A_142) ),
inference(resolution,[status(thm)],[c_20,c_439]) ).
tff(c_6,plain,
! [A_5,B_6] :
( ~ greater(growth_rate(efficient_producers,sk2(A_5)),growth_rate(first_movers,sk2(A_5)))
| subpopulations(first_movers,efficient_producers,A_5,sk1(B_6,A_5))
| ~ in_environment(A_5,B_6)
| ~ environment(A_5) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_470,plain,
! [A_142,B_6,B_143] :
( subpopulations(first_movers,efficient_producers,A_142,sk1(B_6,A_142))
| ~ in_environment(A_142,B_6)
| subpopulations(first_movers,efficient_producers,A_142,sk1(B_143,A_142))
| ~ in_environment(A_142,B_143)
| ( sk2(A_142) = critical_point(A_142) )
| ~ in_environment(A_142,sk2(A_142))
| ~ environment(A_142) ),
inference(resolution,[status(thm)],[c_452,c_6]) ).
tff(c_484,plain,
! [A_142,B_6] :
( ~ in_environment(A_142,B_6)
| ( sk2(A_142) = critical_point(A_142) )
| ~ in_environment(A_142,sk2(A_142))
| ~ environment(A_142)
| subpopulations(first_movers,efficient_producers,A_142,sk1(B_6,A_142)) ),
inference(factorization,[status(thm),theory(equality)],[c_470]) ).
tff(c_81,plain,
! [C_50,A_51,B_52] :
( greater(growth_rate(efficient_producers,C_50),growth_rate(first_movers,C_50))
| ~ greater(C_50,sk2(A_51))
| ~ subpopulations(first_movers,efficient_producers,A_51,C_50)
| greater_or_equal(sk1(B_52,A_51),B_52)
| ~ in_environment(A_51,B_52)
| ~ environment(A_51) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_223,plain,
! [A_101,A_102,B_103] :
( greater(growth_rate(efficient_producers,sk3(sk2(A_101),A_102)),growth_rate(first_movers,sk3(sk2(A_101),A_102)))
| ~ subpopulations(first_movers,efficient_producers,A_101,sk3(sk2(A_101),A_102))
| greater_or_equal(sk1(B_103,A_101),B_103)
| ~ in_environment(A_101,B_103)
| ~ environment(A_101)
| ( sk2(A_101) = critical_point(A_102) )
| ~ in_environment(A_102,sk2(A_101))
| greater(growth_rate(efficient_producers,sk2(A_101)),growth_rate(first_movers,sk2(A_101)))
| ~ environment(A_102) ),
inference(resolution,[status(thm)],[c_22,c_81]) ).
tff(c_232,plain,
! [A_104,A_105,B_106] :
( ~ subpopulations(first_movers,efficient_producers,A_104,sk3(sk2(A_104),A_105))
| greater_or_equal(sk1(B_106,A_104),B_106)
| ~ in_environment(A_104,B_106)
| ~ environment(A_104)
| ( sk2(A_104) = critical_point(A_105) )
| ~ in_environment(A_105,sk2(A_104))
| greater(growth_rate(efficient_producers,sk2(A_104)),growth_rate(first_movers,sk2(A_104)))
| ~ environment(A_105) ),
inference(resolution,[status(thm)],[c_223,c_24]) ).
tff(c_245,plain,
! [B_107,A_108] :
( greater_or_equal(sk1(B_107,A_108),B_107)
| ~ in_environment(A_108,B_107)
| ( sk2(A_108) = critical_point(A_108) )
| ~ in_environment(A_108,sk2(A_108))
| greater(growth_rate(efficient_producers,sk2(A_108)),growth_rate(first_movers,sk2(A_108)))
| ~ environment(A_108) ),
inference(resolution,[status(thm)],[c_20,c_232]) ).
tff(c_10,plain,
! [A_10,B_11] :
( ~ greater(growth_rate(efficient_producers,sk2(A_10)),growth_rate(first_movers,sk2(A_10)))
| greater_or_equal(sk1(B_11,A_10),B_11)
| ~ in_environment(A_10,B_11)
| ~ environment(A_10) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_262,plain,
! [B_109,A_110,B_111] :
( greater_or_equal(sk1(B_109,A_110),B_109)
| ~ in_environment(A_110,B_109)
| greater_or_equal(sk1(B_111,A_110),B_111)
| ~ in_environment(A_110,B_111)
| ( sk2(A_110) = critical_point(A_110) )
| ~ in_environment(A_110,sk2(A_110))
| ~ environment(A_110) ),
inference(resolution,[status(thm)],[c_245,c_10]) ).
tff(c_271,plain,
! [B_109,A_3,B_111,B_4] :
( greater_or_equal(sk1(B_109,A_3),B_109)
| ~ in_environment(A_3,B_109)
| greater_or_equal(sk1(B_111,A_3),B_111)
| ~ in_environment(A_3,B_111)
| ( sk2(A_3) = critical_point(A_3) )
| greater_or_equal(sk1(B_4,A_3),B_4)
| ~ in_environment(A_3,B_4)
| ~ environment(A_3) ),
inference(resolution,[status(thm)],[c_4,c_262]) ).
tff(c_345,plain,
! [B_109,A_3,B_111] :
( greater_or_equal(sk1(B_109,A_3),B_109)
| ~ in_environment(A_3,B_109)
| ( sk2(A_3) = critical_point(A_3) )
| ~ in_environment(A_3,B_111)
| ~ environment(A_3)
| greater_or_equal(sk1(B_111,A_3),B_111) ),
inference(factorization,[status(thm),theory(equality)],[c_271]) ).
tff(c_396,plain,
! [A_130,B_131] :
( ( sk2(A_130) = critical_point(A_130) )
| ~ in_environment(A_130,B_131)
| ~ environment(A_130)
| greater_or_equal(sk1(B_131,A_130),B_131) ),
inference(factorization,[status(thm),theory(equality)],[c_345]) ).
tff(c_28,plain,
! [B_30,A_29] :
( greater(growth_rate(efficient_producers,B_30),growth_rate(first_movers,B_30))
| ~ greater_or_equal(B_30,sk4(A_29))
| ~ subpopulations(first_movers,efficient_producers,A_29,B_30)
| ~ stable(A_29)
| ~ environment(A_29) ),
inference(cnfTransformation,[status(thm)],[f_195]) ).
tff(c_400,plain,
! [A_29,A_130] :
( greater(growth_rate(efficient_producers,sk1(sk4(A_29),A_130)),growth_rate(first_movers,sk1(sk4(A_29),A_130)))
| ~ subpopulations(first_movers,efficient_producers,A_29,sk1(sk4(A_29),A_130))
| ~ stable(A_29)
| ~ environment(A_29)
| ( sk2(A_130) = critical_point(A_130) )
| ~ in_environment(A_130,sk4(A_29))
| ~ environment(A_130) ),
inference(resolution,[status(thm)],[c_396,c_28]) ).
tff(c_54,plain,
! [A_44,B_45] :
( ~ greater(growth_rate(efficient_producers,sk2(A_44)),growth_rate(first_movers,sk2(A_44)))
| subpopulations(first_movers,efficient_producers,A_44,sk1(B_45,A_44))
| ~ in_environment(A_44,B_45)
| ~ environment(A_44) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_58,plain,
! [A_44,B_45,A_24] :
( subpopulations(first_movers,efficient_producers,A_44,sk1(B_45,A_44))
| ~ in_environment(A_44,B_45)
| ~ environment(A_44)
| ( sk2(A_44) = critical_point(A_24) )
| greater(sk3(sk2(A_44),A_24),sk2(A_44))
| ~ in_environment(A_24,sk2(A_44))
| ~ environment(A_24) ),
inference(resolution,[status(thm)],[c_22,c_54]) ).
tff(c_39,plain,
! [A_38,B_39] :
( ( critical_point(A_38) = B_39 )
| greater(sk3(B_39,A_38),B_39)
| ~ in_environment(A_38,B_39)
| greater(growth_rate(efficient_producers,B_39),growth_rate(first_movers,B_39))
| ~ environment(A_38) ),
inference(cnfTransformation,[status(thm)],[f_160]) ).
tff(c_100,plain,
! [B_58,A_59,A_60] :
( greater_or_equal(sk1(B_58,A_59),B_58)
| ~ in_environment(A_59,B_58)
| ~ environment(A_59)
| ( sk2(A_59) = critical_point(A_60) )
| greater(sk3(sk2(A_59),A_60),sk2(A_59))
| ~ in_environment(A_60,sk2(A_59))
| ~ environment(A_60) ),
inference(resolution,[status(thm)],[c_39,c_10]) ).
tff(c_613,plain,
! [A_183,A_184,A_185] :
( greater(growth_rate(efficient_producers,sk1(sk4(A_183),A_184)),growth_rate(first_movers,sk1(sk4(A_183),A_184)))
| ~ subpopulations(first_movers,efficient_producers,A_183,sk1(sk4(A_183),A_184))
| ~ stable(A_183)
| ~ environment(A_183)
| ~ in_environment(A_184,sk4(A_183))
| ~ environment(A_184)
| ( sk2(A_184) = critical_point(A_185) )
| greater(sk3(sk2(A_184),A_185),sk2(A_184))
| ~ in_environment(A_185,sk2(A_184))
| ~ environment(A_185) ),
inference(resolution,[status(thm)],[c_100,c_28]) ).
tff(c_16,plain,
! [A_17,B_18] :
( ~ greater(growth_rate(efficient_producers,sk2(A_17)),growth_rate(first_movers,sk2(A_17)))
| ~ greater(growth_rate(efficient_producers,sk1(B_18,A_17)),growth_rate(first_movers,sk1(B_18,A_17)))
| ~ in_environment(A_17,B_18)
| ~ environment(A_17) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_634,plain,
! [A_186,A_187,A_188] :
( ~ greater(growth_rate(efficient_producers,sk2(A_186)),growth_rate(first_movers,sk2(A_186)))
| ~ subpopulations(first_movers,efficient_producers,A_187,sk1(sk4(A_187),A_186))
| ~ stable(A_187)
| ~ environment(A_187)
| ~ in_environment(A_186,sk4(A_187))
| ~ environment(A_186)
| ( sk2(A_186) = critical_point(A_188) )
| greater(sk3(sk2(A_186),A_188),sk2(A_186))
| ~ in_environment(A_188,sk2(A_186))
| ~ environment(A_188) ),
inference(resolution,[status(thm)],[c_613,c_16]) ).
tff(c_804,plain,
! [A_219,A_220,A_221,A_222] :
( ~ subpopulations(first_movers,efficient_producers,A_219,sk1(sk4(A_219),A_220))
| ~ stable(A_219)
| ~ environment(A_219)
| ~ in_environment(A_220,sk4(A_219))
| ~ environment(A_220)
| ( sk2(A_220) = critical_point(A_221) )
| greater(sk3(sk2(A_220),A_221),sk2(A_220))
| ~ in_environment(A_221,sk2(A_220))
| ~ environment(A_221)
| ( sk2(A_220) = critical_point(A_222) )
| greater(sk3(sk2(A_220),A_222),sk2(A_220))
| ~ in_environment(A_222,sk2(A_220))
| ~ environment(A_222) ),
inference(resolution,[status(thm)],[c_22,c_634]) ).
tff(c_823,plain,
! [A_44,A_221,A_222,A_24] :
( ~ stable(A_44)
| ( sk2(A_44) = critical_point(A_221) )
| greater(sk3(sk2(A_44),A_221),sk2(A_44))
| ~ in_environment(A_221,sk2(A_44))
| ~ environment(A_221)
| ( sk2(A_44) = critical_point(A_222) )
| greater(sk3(sk2(A_44),A_222),sk2(A_44))
| ~ in_environment(A_222,sk2(A_44))
| ~ environment(A_222)
| ~ in_environment(A_44,sk4(A_44))
| ~ environment(A_44)
| ( sk2(A_44) = critical_point(A_24) )
| greater(sk3(sk2(A_44),A_24),sk2(A_44))
| ~ in_environment(A_24,sk2(A_44))
| ~ environment(A_24) ),
inference(resolution,[status(thm)],[c_58,c_804]) ).
tff(c_1139,plain,
! [A_44,A_221,A_222] :
( ~ stable(A_44)
| ( sk2(A_44) = critical_point(A_221) )
| greater(sk3(sk2(A_44),A_221),sk2(A_44))
| ~ in_environment(A_221,sk2(A_44))
| ~ environment(A_221)
| ~ in_environment(A_44,sk4(A_44))
| ~ environment(A_44)
| ( sk2(A_44) = critical_point(A_222) )
| ~ in_environment(A_222,sk2(A_44))
| ~ environment(A_222)
| greater(sk3(sk2(A_44),A_222),sk2(A_44)) ),
inference(factorization,[status(thm),theory(equality)],[c_823]) ).
tff(c_1216,plain,
! [A_278,A_279] :
( ~ stable(A_278)
| ~ in_environment(A_278,sk4(A_278))
| ~ environment(A_278)
| ( sk2(A_278) = critical_point(A_279) )
| ~ in_environment(A_279,sk2(A_278))
| ~ environment(A_279)
| greater(sk3(sk2(A_278),A_279),sk2(A_278)) ),
inference(factorization,[status(thm),theory(equality)],[c_1139]) ).
tff(c_18,plain,
! [C_21,A_19,B_20] :
( greater(growth_rate(efficient_producers,C_21),growth_rate(first_movers,C_21))
| ~ greater(C_21,sk2(A_19))
| ~ subpopulations(first_movers,efficient_producers,A_19,C_21)
| ~ greater(growth_rate(efficient_producers,sk1(B_20,A_19)),growth_rate(first_movers,sk1(B_20,A_19)))
| ~ in_environment(A_19,B_20)
| ~ environment(A_19) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_1227,plain,
! [A_285,A_286,B_287] :
( greater(growth_rate(efficient_producers,sk3(sk2(A_285),A_286)),growth_rate(first_movers,sk3(sk2(A_285),A_286)))
| ~ subpopulations(first_movers,efficient_producers,A_285,sk3(sk2(A_285),A_286))
| ~ greater(growth_rate(efficient_producers,sk1(B_287,A_285)),growth_rate(first_movers,sk1(B_287,A_285)))
| ~ in_environment(A_285,B_287)
| ~ stable(A_285)
| ~ in_environment(A_285,sk4(A_285))
| ~ environment(A_285)
| ( sk2(A_285) = critical_point(A_286) )
| ~ in_environment(A_286,sk2(A_285))
| ~ environment(A_286) ),
inference(resolution,[status(thm)],[c_1216,c_18]) ).
tff(c_1253,plain,
! [A_288,A_289,A_290] :
( greater(growth_rate(efficient_producers,sk3(sk2(A_288),A_289)),growth_rate(first_movers,sk3(sk2(A_288),A_289)))
| ~ subpopulations(first_movers,efficient_producers,A_288,sk3(sk2(A_288),A_289))
| ~ stable(A_288)
| ~ in_environment(A_288,sk4(A_288))
| ( sk2(A_288) = critical_point(A_289) )
| ~ in_environment(A_289,sk2(A_288))
| ~ environment(A_289)
| ~ subpopulations(first_movers,efficient_producers,A_290,sk1(sk4(A_290),A_288))
| ~ stable(A_290)
| ~ environment(A_290)
| ( sk2(A_288) = critical_point(A_288) )
| ~ in_environment(A_288,sk4(A_290))
| ~ environment(A_288) ),
inference(resolution,[status(thm)],[c_400,c_1227]) ).
tff(c_1278,plain,
! [A_291,A_292] :
( greater(growth_rate(efficient_producers,sk3(sk2(A_291),A_292)),growth_rate(first_movers,sk3(sk2(A_291),A_292)))
| ~ subpopulations(first_movers,efficient_producers,A_291,sk3(sk2(A_291),A_292))
| ( sk2(A_291) = critical_point(A_292) )
| ~ in_environment(A_292,sk2(A_291))
| ~ environment(A_292)
| ~ stable(A_291)
| ~ in_environment(A_291,sk4(A_291))
| ( sk2(A_291) = critical_point(A_291) )
| ~ in_environment(A_291,sk2(A_291))
| ~ environment(A_291) ),
inference(resolution,[status(thm)],[c_484,c_1253]) ).
tff(c_1283,plain,
! [A_293,A_294] :
( greater(growth_rate(efficient_producers,sk2(A_293)),growth_rate(first_movers,sk2(A_293)))
| ~ subpopulations(first_movers,efficient_producers,A_293,sk3(sk2(A_293),A_294))
| ( sk2(A_293) = critical_point(A_294) )
| ~ in_environment(A_294,sk2(A_293))
| ~ environment(A_294)
| ~ stable(A_293)
| ~ in_environment(A_293,sk4(A_293))
| ( sk2(A_293) = critical_point(A_293) )
| ~ in_environment(A_293,sk2(A_293))
| ~ environment(A_293) ),
inference(resolution,[status(thm)],[c_1278,c_24]) ).
tff(c_1312,plain,
! [A_295] :
( ~ stable(A_295)
| ~ in_environment(A_295,sk4(A_295))
| ( sk2(A_295) = critical_point(A_295) )
| ~ in_environment(A_295,sk2(A_295))
| greater(growth_rate(efficient_producers,sk2(A_295)),growth_rate(first_movers,sk2(A_295)))
| ~ environment(A_295) ),
inference(resolution,[status(thm)],[c_20,c_1283]) ).
tff(c_401,plain,
! [A_132,A_133] :
( greater(growth_rate(efficient_producers,sk1(sk4(A_132),A_133)),growth_rate(first_movers,sk1(sk4(A_132),A_133)))
| ~ subpopulations(first_movers,efficient_producers,A_132,sk1(sk4(A_132),A_133))
| ~ stable(A_132)
| ~ environment(A_132)
| ( sk2(A_133) = critical_point(A_133) )
| ~ in_environment(A_133,sk4(A_132))
| ~ environment(A_133) ),
inference(resolution,[status(thm)],[c_396,c_28]) ).
tff(c_408,plain,
! [A_133,A_132] :
( ~ greater(growth_rate(efficient_producers,sk2(A_133)),growth_rate(first_movers,sk2(A_133)))
| ~ subpopulations(first_movers,efficient_producers,A_132,sk1(sk4(A_132),A_133))
| ~ stable(A_132)
| ~ environment(A_132)
| ( sk2(A_133) = critical_point(A_133) )
| ~ in_environment(A_133,sk4(A_132))
| ~ environment(A_133) ),
inference(resolution,[status(thm)],[c_401,c_16]) ).
tff(c_1338,plain,
! [A_301,A_302] :
( ~ subpopulations(first_movers,efficient_producers,A_301,sk1(sk4(A_301),A_302))
| ~ stable(A_301)
| ~ environment(A_301)
| ~ in_environment(A_302,sk4(A_301))
| ~ stable(A_302)
| ~ in_environment(A_302,sk4(A_302))
| ( sk2(A_302) = critical_point(A_302) )
| ~ in_environment(A_302,sk2(A_302))
| ~ environment(A_302) ),
inference(resolution,[status(thm)],[c_1312,c_408]) ).
tff(c_1363,plain,
! [A_303] :
( ~ stable(A_303)
| ~ in_environment(A_303,sk4(A_303))
| ( sk2(A_303) = critical_point(A_303) )
| ~ in_environment(A_303,sk2(A_303))
| ~ environment(A_303) ),
inference(resolution,[status(thm)],[c_484,c_1338]) ).
tff(c_1368,plain,
! [A_304] :
( ( sk2(A_304) = critical_point(A_304) )
| ~ in_environment(A_304,sk2(A_304))
| ~ stable(A_304)
| ~ environment(A_304) ),
inference(resolution,[status(thm)],[c_26,c_1363]) ).
tff(c_1385,plain,
! [A_305] :
( ( sk2(A_305) = critical_point(A_305) )
| ~ stable(A_305)
| ~ environment(A_305) ),
inference(resolution,[status(thm)],[c_181,c_1368]) ).
tff(c_1388,plain,
( ( sk2(sk5) = critical_point(sk5) )
| ~ environment(sk5) ),
inference(resolution,[status(thm)],[c_32,c_1385]) ).
tff(c_1391,plain,
sk2(sk5) = critical_point(sk5),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_1388]) ).
tff(c_1479,plain,
( in_environment(sk5,critical_point(sk5))
| ~ stable(sk5)
| ~ environment(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_1391,c_181]) ).
tff(c_1589,plain,
in_environment(sk5,critical_point(sk5)),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_32,c_1479]) ).
tff(c_1591,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_1589]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT023-2 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.13/0.33 % Computer : n032.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Aug 3 20:34:06 EDT 2023
% 0.13/0.33 % CPUTime :
% 6.63/2.56 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.63/2.57
% 6.63/2.57 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.77/2.62
% 6.77/2.62 Inference rules
% 6.77/2.62 ----------------------
% 6.77/2.62 #Ref : 0
% 6.77/2.62 #Sup : 339
% 6.77/2.62 #Fact : 28
% 6.77/2.62 #Define : 0
% 6.77/2.62 #Split : 0
% 6.77/2.62 #Chain : 0
% 6.77/2.62 #Close : 0
% 6.77/2.62
% 6.77/2.62 Ordering : KBO
% 6.77/2.62
% 6.77/2.62 Simplification rules
% 6.77/2.62 ----------------------
% 6.77/2.62 #Subsume : 184
% 6.77/2.62 #Demod : 136
% 6.77/2.62 #Tautology : 3
% 6.77/2.62 #SimpNegUnit : 1
% 6.77/2.62 #BackRed : 0
% 6.77/2.62
% 6.77/2.62 #Partial instantiations: 0
% 6.77/2.62 #Strategies tried : 1
% 6.77/2.62
% 6.77/2.62 Timing (in seconds)
% 6.77/2.62 ----------------------
% 6.77/2.62 Preprocessing : 0.52
% 6.77/2.62 Parsing : 0.29
% 6.77/2.62 CNF conversion : 0.03
% 6.77/2.62 Main loop : 1.05
% 6.77/2.62 Inferencing : 0.42
% 6.77/2.62 Reduction : 0.20
% 6.77/2.62 Demodulation : 0.13
% 6.77/2.62 BG Simplification : 0.04
% 6.77/2.62 Subsumption : 0.34
% 6.77/2.62 Abstraction : 0.04
% 6.77/2.62 MUC search : 0.00
% 6.77/2.62 Cooper : 0.00
% 6.77/2.62 Total : 1.64
% 6.77/2.62 Index Insertion : 0.00
% 6.77/2.62 Index Deletion : 0.00
% 6.77/2.62 Index Matching : 0.00
% 6.77/2.62 BG Taut test : 0.00
%------------------------------------------------------------------------------