TSTP Solution File: MGT036+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : MGT036+1 : 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/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 : n006.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 10:49:39 EDT 2023
% Result : Theorem 3.17s 1.74s
% Output : CNFRefutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 65 ( 21 unt; 13 typ; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 115 ( 54 ~; 44 |; 9 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 8 >; 9 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 84 (; 84 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulations > outcompetes > in_environment > greater_or_equal > greater > environment > growth_rate > #nlpp > resilience > zero > first_movers > efficient_producers > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(subpopulations,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(greater,type,
greater: ( $i * $i ) > $o ).
tff(in_environment,type,
in_environment: ( $i * $i ) > $o ).
tff(efficient_producers,type,
efficient_producers: $i ).
tff(resilience,type,
resilience: $i > $i ).
tff(growth_rate,type,
growth_rate: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(environment,type,
environment: $i > $o ).
tff(first_movers,type,
first_movers: $i ).
tff(greater_or_equal,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(outcompetes,type,
outcompetes: ( $i * $i * $i ) > $o ).
tff(zero,type,
zero: $i ).
tff(f_90,negated_conjecture,
~ ! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ~ outcompetes(first_movers,efficient_producers,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5) ).
tff(f_34,axiom,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> subpopulations(efficient_producers,first_movers,E,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_FM_and_EP) ).
tff(f_52,axiom,
! [E,S1,S2,T] :
( ( ( environment(E)
& subpopulations(S1,S2,E,T) )
=> greater_or_equal(growth_rate(S1,T),zero) )
<=> ~ greater(zero,growth_rate(S1,T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships) ).
tff(f_65,hypothesis,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T) )
=> ( ( greater_or_equal(growth_rate(S2,T),zero)
& greater(zero,growth_rate(S1,T)) )
<=> outcompetes(S2,S1,T) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
tff(f_81,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
tff(f_79,hypothesis,
! [E,S1,S2,T] :
( ( environment(E)
& in_environment(E,T)
& ~ greater(zero,growth_rate(S1,T))
& greater(resilience(S2),resilience(S1)) )
=> ~ greater(zero,growth_rate(S2,T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a12) ).
tff(f_42,axiom,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur) ).
tff(c_24,plain,
outcompetes(first_movers,efficient_producers,'#skF_2'),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_26,plain,
subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_28,plain,
environment('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_38,plain,
! [E_21,T_22] :
( subpopulations(efficient_producers,first_movers,E_21,T_22)
| ~ subpopulations(first_movers,efficient_producers,E_21,T_22)
| ~ environment(E_21) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_41,plain,
( subpopulations(efficient_producers,first_movers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_26,c_38]) ).
tff(c_44,plain,
subpopulations(efficient_producers,first_movers,'#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_41]) ).
tff(c_12,plain,
! [E_5,S1_6,T_8] :
( environment(E_5)
| ~ greater(zero,growth_rate(S1_6,T_8)) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_29,plain,
! [S1_6,T_8] : ~ greater(zero,growth_rate(S1_6,T_8)),
inference(splitLeft,[status(thm)],[c_12]) ).
tff(c_16,plain,
! [S1_10,T_12,S2_11,E_9] :
( greater(zero,growth_rate(S1_10,T_12))
| ~ outcompetes(S2_11,S1_10,T_12)
| ~ subpopulations(S1_10,S2_11,E_9,T_12)
| ~ environment(E_9) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_46,plain,
! [S2_23,S1_24,T_25,E_26] :
( ~ outcompetes(S2_23,S1_24,T_25)
| ~ subpopulations(S1_24,S2_23,E_26,T_25)
| ~ environment(E_26) ),
inference(negUnitSimplification,[status(thm)],[c_29,c_16]) ).
tff(c_49,plain,
( ~ outcompetes(first_movers,efficient_producers,'#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_44,c_46]) ).
tff(c_56,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_24,c_49]) ).
tff(c_57,plain,
! [E_5] : environment(E_5),
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_6,plain,
! [S1_6,T_8,S2_7,E_5] :
( greater_or_equal(growth_rate(S1_6,T_8),zero)
| ~ subpopulations(S1_6,S2_7,E_5,T_8)
| ~ environment(E_5)
| greater(zero,growth_rate(S1_6,T_8)) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_118,plain,
! [S1_50,T_51,S2_52,E_53] :
( greater_or_equal(growth_rate(S1_50,T_51),zero)
| ~ subpopulations(S1_50,S2_52,E_53,T_51)
| greater(zero,growth_rate(S1_50,T_51)) ),
inference(demodulation,[status(thm),theory(equality)],[c_57,c_6]) ).
tff(c_125,plain,
( greater_or_equal(growth_rate(first_movers,'#skF_2'),zero)
| greater(zero,growth_rate(first_movers,'#skF_2')) ),
inference(resolution,[status(thm)],[c_26,c_118]) ).
tff(c_126,plain,
greater(zero,growth_rate(first_movers,'#skF_2')),
inference(splitLeft,[status(thm)],[c_125]) ).
tff(c_2,plain,
! [E_1,T_2] :
( subpopulations(efficient_producers,first_movers,E_1,T_2)
| ~ subpopulations(first_movers,efficient_producers,E_1,T_2)
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_71,plain,
! [E_36,T_37] :
( subpopulations(efficient_producers,first_movers,E_36,T_37)
| ~ subpopulations(first_movers,efficient_producers,E_36,T_37) ),
inference(demodulation,[status(thm),theory(equality)],[c_57,c_2]) ).
tff(c_75,plain,
subpopulations(efficient_producers,first_movers,'#skF_1','#skF_2'),
inference(resolution,[status(thm)],[c_26,c_71]) ).
tff(c_78,plain,
! [S1_38,T_39,S2_40,E_41] :
( greater(zero,growth_rate(S1_38,T_39))
| ~ outcompetes(S2_40,S1_38,T_39)
| ~ subpopulations(S1_38,S2_40,E_41,T_39) ),
inference(demodulation,[status(thm),theory(equality)],[c_57,c_16]) ).
tff(c_80,plain,
( greater(zero,growth_rate(efficient_producers,'#skF_2'))
| ~ outcompetes(first_movers,efficient_producers,'#skF_2') ),
inference(resolution,[status(thm)],[c_75,c_78]) ).
tff(c_85,plain,
greater(zero,growth_rate(efficient_producers,'#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_80]) ).
tff(c_10,plain,
! [S1_6,S2_7,E_5,T_8] :
( subpopulations(S1_6,S2_7,E_5,T_8)
| ~ greater(zero,growth_rate(S1_6,T_8)) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_89,plain,
! [S2_7,E_5] : subpopulations(efficient_producers,S2_7,E_5,'#skF_2'),
inference(resolution,[status(thm)],[c_85,c_10]) ).
tff(c_18,plain,
! [S2_11,T_12,S1_10,E_9] :
( greater_or_equal(growth_rate(S2_11,T_12),zero)
| ~ outcompetes(S2_11,S1_10,T_12)
| ~ subpopulations(S1_10,S2_11,E_9,T_12)
| ~ environment(E_9) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_99,plain,
! [S2_44,T_45,S1_46,E_47] :
( greater_or_equal(growth_rate(S2_44,T_45),zero)
| ~ outcompetes(S2_44,S1_46,T_45)
| ~ subpopulations(S1_46,S2_44,E_47,T_45) ),
inference(demodulation,[status(thm),theory(equality)],[c_57,c_18]) ).
tff(c_106,plain,
! [S2_48] :
( greater_or_equal(growth_rate(S2_48,'#skF_2'),zero)
| ~ outcompetes(S2_48,efficient_producers,'#skF_2') ),
inference(resolution,[status(thm)],[c_89,c_99]) ).
tff(c_8,plain,
! [S1_6,T_8] :
( ~ greater_or_equal(growth_rate(S1_6,T_8),zero)
| ~ greater(zero,growth_rate(S1_6,T_8)) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_110,plain,
! [S2_48] :
( ~ greater(zero,growth_rate(S2_48,'#skF_2'))
| ~ outcompetes(S2_48,efficient_producers,'#skF_2') ),
inference(resolution,[status(thm)],[c_106,c_8]) ).
tff(c_129,plain,
~ outcompetes(first_movers,efficient_producers,'#skF_2'),
inference(resolution,[status(thm)],[c_126,c_110]) ).
tff(c_135,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_129]) ).
tff(c_137,plain,
~ greater(zero,growth_rate(first_movers,'#skF_2')),
inference(splitRight,[status(thm)],[c_125]) ).
tff(c_22,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_20,plain,
! [S2_15,T_16,S1_14,E_13] :
( ~ greater(zero,growth_rate(S2_15,T_16))
| ~ greater(resilience(S2_15),resilience(S1_14))
| greater(zero,growth_rate(S1_14,T_16))
| ~ in_environment(E_13,T_16)
| ~ environment(E_13) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_144,plain,
! [S2_54,T_55,S1_56,E_57] :
( ~ greater(zero,growth_rate(S2_54,T_55))
| ~ greater(resilience(S2_54),resilience(S1_56))
| greater(zero,growth_rate(S1_56,T_55))
| ~ in_environment(E_57,T_55) ),
inference(demodulation,[status(thm),theory(equality)],[c_57,c_20]) ).
tff(c_147,plain,
! [S1_56,E_57] :
( ~ greater(resilience(efficient_producers),resilience(S1_56))
| greater(zero,growth_rate(S1_56,'#skF_2'))
| ~ in_environment(E_57,'#skF_2') ),
inference(resolution,[status(thm)],[c_85,c_144]) ).
tff(c_148,plain,
! [E_57] : ~ in_environment(E_57,'#skF_2'),
inference(splitLeft,[status(thm)],[c_147]) ).
tff(c_4,plain,
! [E_3,T_4] :
( in_environment(E_3,T_4)
| ~ subpopulations(first_movers,efficient_producers,E_3,T_4)
| ~ environment(E_3) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_64,plain,
! [E_34,T_35] :
( in_environment(E_34,T_35)
| ~ subpopulations(first_movers,efficient_producers,E_34,T_35) ),
inference(demodulation,[status(thm),theory(equality)],[c_57,c_4]) ).
tff(c_68,plain,
in_environment('#skF_1','#skF_2'),
inference(resolution,[status(thm)],[c_26,c_64]) ).
tff(c_150,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_148,c_68]) ).
tff(c_152,plain,
! [S1_58] :
( ~ greater(resilience(efficient_producers),resilience(S1_58))
| greater(zero,growth_rate(S1_58,'#skF_2')) ),
inference(splitRight,[status(thm)],[c_147]) ).
tff(c_155,plain,
greater(zero,growth_rate(first_movers,'#skF_2')),
inference(resolution,[status(thm)],[c_22,c_152]) ).
tff(c_159,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_137,c_155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : MGT036+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14 % 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
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 20:27:58 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.17/1.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.17/1.75
% 3.17/1.75 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.40/1.79
% 3.40/1.79 Inference rules
% 3.40/1.79 ----------------------
% 3.40/1.79 #Ref : 0
% 3.40/1.79 #Sup : 21
% 3.40/1.79 #Fact : 0
% 3.40/1.79 #Define : 0
% 3.40/1.79 #Split : 4
% 3.40/1.79 #Chain : 0
% 3.40/1.79 #Close : 0
% 3.40/1.79
% 3.40/1.79 Ordering : KBO
% 3.40/1.79
% 3.40/1.79 Simplification rules
% 3.40/1.79 ----------------------
% 3.40/1.79 #Subsume : 4
% 3.40/1.79 #Demod : 16
% 3.40/1.79 #Tautology : 4
% 3.40/1.79 #SimpNegUnit : 3
% 3.40/1.79 #BackRed : 1
% 3.40/1.79
% 3.40/1.79 #Partial instantiations: 0
% 3.40/1.79 #Strategies tried : 1
% 3.40/1.79
% 3.40/1.79 Timing (in seconds)
% 3.40/1.79 ----------------------
% 3.40/1.79 Preprocessing : 0.44
% 3.40/1.79 Parsing : 0.25
% 3.40/1.79 CNF conversion : 0.03
% 3.40/1.79 Main loop : 0.28
% 3.40/1.79 Inferencing : 0.12
% 3.40/1.79 Reduction : 0.07
% 3.40/1.79 Demodulation : 0.05
% 3.40/1.79 BG Simplification : 0.01
% 3.40/1.79 Subsumption : 0.05
% 3.40/1.79 Abstraction : 0.01
% 3.40/1.79 MUC search : 0.00
% 3.40/1.79 Cooper : 0.00
% 3.40/1.79 Total : 0.78
% 3.40/1.79 Index Insertion : 0.00
% 3.40/1.79 Index Deletion : 0.00
% 3.40/1.80 Index Matching : 0.00
% 3.40/1.80 BG Taut test : 0.00
%------------------------------------------------------------------------------