TSTP Solution File: MGT020+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : MGT020+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 : n008.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 10:49:33 EDT 2023
% Result : Theorem 4.67s 2.26s
% Output : CNFRefutation 4.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 23
% Syntax : Number of formulae : 62 ( 11 unt; 14 typ; 0 def)
% Number of atoms : 143 ( 5 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 171 ( 76 ~; 72 |; 11 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 10 >; 8 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 59 (; 59 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulations > in_environment > greater_or_equal > greater > environment > decreases > disbanding_rate > difference > #nlpp > start_time > initial_FM_EP > 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(disbanding_rate,type,
disbanding_rate: ( $i * $i ) > $i ).
tff(initial_FM_EP,type,
initial_FM_EP: $i > $i ).
tff(decreases,type,
decreases: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(environment,type,
environment: $i > $o ).
tff(start_time,type,
start_time: $i > $i ).
tff(first_movers,type,
first_movers: $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff(greater_or_equal,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(f_142,negated_conjecture,
~ ! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l2) ).
tff(f_51,axiom,
! [E,T] :
( environment(E)
=> ( ( in_environment(E,initial_FM_EP(E))
=> subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E)) )
& ( subpopulations(first_movers,efficient_producers,E,T)
=> greater_or_equal(T,initial_FM_EP(E)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_point) ).
tff(f_112,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
=> ( greater(X,Y)
| ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
tff(f_85,axiom,
! [E] :
( environment(E)
=> greater_or_equal(initial_FM_EP(E),start_time(E)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_initial_time) ).
tff(f_79,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_occurs) ).
tff(f_98,axiom,
! [E,T1,T2] :
( ( environment(E)
& greater_or_equal(T1,start_time(E))
& greater(T2,T1)
& in_environment(E,T2) )
=> in_environment(E,T1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_times_in_order) ).
tff(f_118,hypothesis,
! [E] :
( environment(E)
=> greater(disbanding_rate(first_movers,initial_FM_EP(E)),disbanding_rate(efficient_producers,initial_FM_EP(E))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a8) ).
tff(f_70,axiom,
! [E,T,T1,T2] :
( ( environment(E)
& greater_or_equal(T,T1)
& greater_or_equal(T2,T)
& subpopulations(first_movers,efficient_producers,E,T2)
& greater(disbanding_rate(first_movers,T1),disbanding_rate(efficient_producers,T1)) )
=> ( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
=> greater(disbanding_rate(first_movers,T2),disbanding_rate(efficient_producers,T2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_function_difference) ).
tff(f_39,axiom,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3) ).
tff(c_28,plain,
environment('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_26,plain,
subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_4,plain,
! [T_4,E_3] :
( greater_or_equal(T_4,initial_FM_EP(E_3))
| ~ subpopulations(first_movers,efficient_producers,E_3,T_4)
| ~ environment(E_3) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_24,plain,
~ greater(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2')),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_43,plain,
! [T_33,E_34] :
( greater_or_equal(T_33,initial_FM_EP(E_34))
| ~ subpopulations(first_movers,efficient_producers,E_34,T_33)
| ~ environment(E_34) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_18,plain,
! [Y_19,X_18] :
( ( Y_19 = X_18 )
| greater(X_18,Y_19)
| ~ greater_or_equal(X_18,Y_19) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_47,plain,
! [E_34,T_33] :
( ( initial_FM_EP(E_34) = T_33 )
| greater(T_33,initial_FM_EP(E_34))
| ~ subpopulations(first_movers,efficient_producers,E_34,T_33)
| ~ environment(E_34) ),
inference(resolution,[status(thm)],[c_43,c_18]) ).
tff(c_12,plain,
! [E_11] :
( greater_or_equal(initial_FM_EP(E_11),start_time(E_11))
| ~ environment(E_11) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_36,plain,
! [E_31,T_32] :
( in_environment(E_31,T_32)
| ~ subpopulations(first_movers,efficient_producers,E_31,T_32)
| ~ environment(E_31) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_39,plain,
( in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_26,c_36]) ).
tff(c_42,plain,
in_environment('#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_39]) ).
tff(c_70,plain,
! [E_44,T1_45,T2_46] :
( in_environment(E_44,T1_45)
| ~ in_environment(E_44,T2_46)
| ~ greater(T2_46,T1_45)
| ~ greater_or_equal(T1_45,start_time(E_44))
| ~ environment(E_44) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_72,plain,
! [T1_45] :
( in_environment('#skF_1',T1_45)
| ~ greater('#skF_2',T1_45)
| ~ greater_or_equal(T1_45,start_time('#skF_1'))
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_42,c_70]) ).
tff(c_76,plain,
! [T1_47] :
( in_environment('#skF_1',T1_47)
| ~ greater('#skF_2',T1_47)
| ~ greater_or_equal(T1_47,start_time('#skF_1')) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_72]) ).
tff(c_80,plain,
( in_environment('#skF_1',initial_FM_EP('#skF_1'))
| ~ greater('#skF_2',initial_FM_EP('#skF_1'))
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_12,c_76]) ).
tff(c_83,plain,
( in_environment('#skF_1',initial_FM_EP('#skF_1'))
| ~ greater('#skF_2',initial_FM_EP('#skF_1')) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_80]) ).
tff(c_84,plain,
~ greater('#skF_2',initial_FM_EP('#skF_1')),
inference(splitLeft,[status(thm)],[c_83]) ).
tff(c_87,plain,
( ( initial_FM_EP('#skF_1') = '#skF_2' )
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_47,c_84]) ).
tff(c_90,plain,
initial_FM_EP('#skF_1') = '#skF_2',
inference(demodulation,[status(thm),theory(equality)],[c_28,c_26,c_87]) ).
tff(c_20,plain,
! [E_20] :
( greater(disbanding_rate(first_movers,initial_FM_EP(E_20)),disbanding_rate(efficient_producers,initial_FM_EP(E_20)))
| ~ environment(E_20) ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_107,plain,
( greater(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,initial_FM_EP('#skF_1')))
| ~ environment('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_90,c_20]) ).
tff(c_128,plain,
greater(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_90,c_107]) ).
tff(c_130,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24,c_128]) ).
tff(c_131,plain,
in_environment('#skF_1',initial_FM_EP('#skF_1')),
inference(splitRight,[status(thm)],[c_83]) ).
tff(c_6,plain,
! [E_3] :
( subpopulations(first_movers,efficient_producers,E_3,initial_FM_EP(E_3))
| ~ in_environment(E_3,initial_FM_EP(E_3))
| ~ environment(E_3) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_325,plain,
! [T2_81,T_82,T1_83,E_84] :
( greater(disbanding_rate(first_movers,T2_81),disbanding_rate(efficient_producers,T2_81))
| decreases(difference(disbanding_rate(first_movers,T_82),disbanding_rate(efficient_producers,T_82)))
| ~ greater(disbanding_rate(first_movers,T1_83),disbanding_rate(efficient_producers,T1_83))
| ~ subpopulations(first_movers,efficient_producers,E_84,T2_81)
| ~ greater_or_equal(T2_81,T_82)
| ~ greater_or_equal(T_82,T1_83)
| ~ environment(E_84) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_955,plain,
! [T2_191,T_192,E_193,E_194] :
( greater(disbanding_rate(first_movers,T2_191),disbanding_rate(efficient_producers,T2_191))
| decreases(difference(disbanding_rate(first_movers,T_192),disbanding_rate(efficient_producers,T_192)))
| ~ subpopulations(first_movers,efficient_producers,E_193,T2_191)
| ~ greater_or_equal(T2_191,T_192)
| ~ greater_or_equal(T_192,initial_FM_EP(E_194))
| ~ environment(E_193)
| ~ environment(E_194) ),
inference(resolution,[status(thm)],[c_20,c_325]) ).
tff(c_959,plain,
! [T_192,E_194] :
( greater(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2'))
| decreases(difference(disbanding_rate(first_movers,T_192),disbanding_rate(efficient_producers,T_192)))
| ~ greater_or_equal('#skF_2',T_192)
| ~ greater_or_equal(T_192,initial_FM_EP(E_194))
| ~ environment('#skF_1')
| ~ environment(E_194) ),
inference(resolution,[status(thm)],[c_26,c_955]) ).
tff(c_963,plain,
! [T_192,E_194] :
( greater(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2'))
| decreases(difference(disbanding_rate(first_movers,T_192),disbanding_rate(efficient_producers,T_192)))
| ~ greater_or_equal('#skF_2',T_192)
| ~ greater_or_equal(T_192,initial_FM_EP(E_194))
| ~ environment(E_194) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_959]) ).
tff(c_965,plain,
! [T_195,E_196] :
( decreases(difference(disbanding_rate(first_movers,T_195),disbanding_rate(efficient_producers,T_195)))
| ~ greater_or_equal('#skF_2',T_195)
| ~ greater_or_equal(T_195,initial_FM_EP(E_196))
| ~ environment(E_196) ),
inference(negUnitSimplification,[status(thm)],[c_24,c_963]) ).
tff(c_969,plain,
! [T_197,E_198] :
( decreases(difference(disbanding_rate(first_movers,T_197),disbanding_rate(efficient_producers,T_197)))
| ~ greater_or_equal('#skF_2',T_197)
| ~ subpopulations(first_movers,efficient_producers,E_198,T_197)
| ~ environment(E_198) ),
inference(resolution,[status(thm)],[c_4,c_965]) ).
tff(c_979,plain,
! [E_199] :
( decreases(difference(disbanding_rate(first_movers,initial_FM_EP(E_199)),disbanding_rate(efficient_producers,initial_FM_EP(E_199))))
| ~ greater_or_equal('#skF_2',initial_FM_EP(E_199))
| ~ in_environment(E_199,initial_FM_EP(E_199))
| ~ environment(E_199) ),
inference(resolution,[status(thm)],[c_6,c_969]) ).
tff(c_2,plain,
! [T_2,E_1] :
( ~ decreases(difference(disbanding_rate(first_movers,T_2),disbanding_rate(efficient_producers,T_2)))
| ~ subpopulations(first_movers,efficient_producers,E_1,T_2)
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_983,plain,
! [E_200,E_201] :
( ~ subpopulations(first_movers,efficient_producers,E_200,initial_FM_EP(E_201))
| ~ environment(E_200)
| ~ greater_or_equal('#skF_2',initial_FM_EP(E_201))
| ~ in_environment(E_201,initial_FM_EP(E_201))
| ~ environment(E_201) ),
inference(resolution,[status(thm)],[c_979,c_2]) ).
tff(c_987,plain,
! [E_202] :
( ~ greater_or_equal('#skF_2',initial_FM_EP(E_202))
| ~ in_environment(E_202,initial_FM_EP(E_202))
| ~ environment(E_202) ),
inference(resolution,[status(thm)],[c_6,c_983]) ).
tff(c_990,plain,
( ~ greater_or_equal('#skF_2',initial_FM_EP('#skF_1'))
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_131,c_987]) ).
tff(c_993,plain,
~ greater_or_equal('#skF_2',initial_FM_EP('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_990]) ).
tff(c_996,plain,
( ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_4,c_993]) ).
tff(c_1000,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_26,c_996]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT020+1 : TPTP v8.1.2. Released v2.0.0.
% 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
% 0.17/0.34 % Computer : n008.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % 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 20:35:34 EDT 2023
% 0.17/0.35 % CPUTime :
% 4.67/2.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.67/2.27
% 4.67/2.27 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.67/2.30
% 4.67/2.30 Inference rules
% 4.67/2.30 ----------------------
% 4.67/2.30 #Ref : 0
% 4.67/2.30 #Sup : 199
% 4.67/2.30 #Fact : 0
% 4.67/2.30 #Define : 0
% 4.67/2.30 #Split : 6
% 4.67/2.30 #Chain : 0
% 4.67/2.30 #Close : 0
% 4.67/2.30
% 4.67/2.30 Ordering : KBO
% 4.67/2.30
% 4.67/2.30 Simplification rules
% 4.67/2.30 ----------------------
% 4.67/2.30 #Subsume : 51
% 4.67/2.30 #Demod : 176
% 4.67/2.30 #Tautology : 33
% 4.67/2.30 #SimpNegUnit : 14
% 4.67/2.30 #BackRed : 4
% 4.67/2.30
% 4.67/2.30 #Partial instantiations: 0
% 4.67/2.30 #Strategies tried : 1
% 4.67/2.30
% 4.67/2.30 Timing (in seconds)
% 4.67/2.30 ----------------------
% 4.67/2.30 Preprocessing : 0.51
% 4.67/2.30 Parsing : 0.29
% 4.67/2.30 CNF conversion : 0.03
% 4.67/2.30 Main loop : 0.69
% 4.67/2.30 Inferencing : 0.29
% 4.67/2.30 Reduction : 0.17
% 4.67/2.30 Demodulation : 0.11
% 4.67/2.30 BG Simplification : 0.03
% 4.67/2.30 Subsumption : 0.16
% 4.67/2.30 Abstraction : 0.03
% 4.67/2.30 MUC search : 0.00
% 4.67/2.30 Cooper : 0.00
% 4.67/2.30 Total : 1.26
% 4.67/2.30 Index Insertion : 0.00
% 4.67/2.30 Index Deletion : 0.00
% 4.67/2.30 Index Matching : 0.00
% 4.67/2.30 BG Taut test : 0.00
%------------------------------------------------------------------------------