TSTP Solution File: MGT032+2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : MGT032+2 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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 : n005.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 10:49:37 EDT 2023
% Result : Theorem 3.18s 1.71s
% Output : CNFRefutation 3.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 37 ( 8 unt; 13 typ; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 90 ( 41 ~; 36 |; 8 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 10 >; 9 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 25 (; 23 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulations > selection_favors > in_environment > greater_or_equal > greater > stable > environment > growth_rate > #nlpp > first_movers > efficient_producers > #skF_1 > #skF_2 > #skF_3
%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('#skF_1',type,
'#skF_1': $i > $i ).
tff(efficient_producers,type,
efficient_producers: $i ).
tff(growth_rate,type,
growth_rate: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(environment,type,
environment: $i > $o ).
tff(first_movers,type,
first_movers: $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(greater_or_equal,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(selection_favors,type,
selection_favors: ( $i * $i * $i ) > $o ).
tff(stable,type,
stable: $i > $o ).
tff(f_71,negated_conjecture,
~ ! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> selection_favors(efficient_producers,first_movers,T) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t1) ).
tff(f_54,hypothesis,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
tff(f_38,axiom,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T)
& greater(growth_rate(S2,T),growth_rate(S1,T)) )
=> selection_favors(S2,S1,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
tff(c_10,plain,
environment('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_8,plain,
stable('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_6,plain,
! [E_5] :
( in_environment(E_5,'#skF_1'(E_5))
| ~ stable(E_5)
| ~ environment(E_5) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_16,plain,
! [To_14] :
( subpopulations(first_movers,efficient_producers,'#skF_2','#skF_3'(To_14))
| ~ in_environment('#skF_2',To_14) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_14,plain,
! [To_14] :
( greater_or_equal('#skF_3'(To_14),To_14)
| ~ in_environment('#skF_2',To_14) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_22,plain,
! [T_24,E_25] :
( greater(growth_rate(efficient_producers,T_24),growth_rate(first_movers,T_24))
| ~ greater_or_equal(T_24,'#skF_1'(E_25))
| ~ subpopulations(first_movers,efficient_producers,E_25,T_24)
| ~ stable(E_25)
| ~ environment(E_25) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_27,plain,
! [E_26] :
( greater(growth_rate(efficient_producers,'#skF_3'('#skF_1'(E_26))),growth_rate(first_movers,'#skF_3'('#skF_1'(E_26))))
| ~ subpopulations(first_movers,efficient_producers,E_26,'#skF_3'('#skF_1'(E_26)))
| ~ stable(E_26)
| ~ environment(E_26)
| ~ in_environment('#skF_2','#skF_1'(E_26)) ),
inference(resolution,[status(thm)],[c_14,c_22]) ).
tff(c_2,plain,
! [S2_3,S1_2,T_4,E_1] :
( selection_favors(S2_3,S1_2,T_4)
| ~ greater(growth_rate(S2_3,T_4),growth_rate(S1_2,T_4))
| ~ subpopulations(S1_2,S2_3,E_1,T_4)
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_31,plain,
! [E_27,E_28] :
( selection_favors(efficient_producers,first_movers,'#skF_3'('#skF_1'(E_27)))
| ~ subpopulations(first_movers,efficient_producers,E_28,'#skF_3'('#skF_1'(E_27)))
| ~ environment(E_28)
| ~ subpopulations(first_movers,efficient_producers,E_27,'#skF_3'('#skF_1'(E_27)))
| ~ stable(E_27)
| ~ environment(E_27)
| ~ in_environment('#skF_2','#skF_1'(E_27)) ),
inference(resolution,[status(thm)],[c_27,c_2]) ).
tff(c_34,plain,
! [E_27] :
( selection_favors(efficient_producers,first_movers,'#skF_3'('#skF_1'(E_27)))
| ~ environment('#skF_2')
| ~ subpopulations(first_movers,efficient_producers,E_27,'#skF_3'('#skF_1'(E_27)))
| ~ stable(E_27)
| ~ environment(E_27)
| ~ in_environment('#skF_2','#skF_1'(E_27)) ),
inference(resolution,[status(thm)],[c_16,c_31]) ).
tff(c_38,plain,
! [E_29] :
( selection_favors(efficient_producers,first_movers,'#skF_3'('#skF_1'(E_29)))
| ~ subpopulations(first_movers,efficient_producers,E_29,'#skF_3'('#skF_1'(E_29)))
| ~ stable(E_29)
| ~ environment(E_29)
| ~ in_environment('#skF_2','#skF_1'(E_29)) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_34]) ).
tff(c_42,plain,
( selection_favors(efficient_producers,first_movers,'#skF_3'('#skF_1'('#skF_2')))
| ~ stable('#skF_2')
| ~ environment('#skF_2')
| ~ in_environment('#skF_2','#skF_1'('#skF_2')) ),
inference(resolution,[status(thm)],[c_16,c_38]) ).
tff(c_45,plain,
( selection_favors(efficient_producers,first_movers,'#skF_3'('#skF_1'('#skF_2')))
| ~ in_environment('#skF_2','#skF_1'('#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8,c_42]) ).
tff(c_46,plain,
~ in_environment('#skF_2','#skF_1'('#skF_2')),
inference(splitLeft,[status(thm)],[c_45]) ).
tff(c_49,plain,
( ~ stable('#skF_2')
| ~ environment('#skF_2') ),
inference(resolution,[status(thm)],[c_6,c_46]) ).
tff(c_53,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8,c_49]) ).
tff(c_55,plain,
in_environment('#skF_2','#skF_1'('#skF_2')),
inference(splitRight,[status(thm)],[c_45]) ).
tff(c_54,plain,
selection_favors(efficient_producers,first_movers,'#skF_3'('#skF_1'('#skF_2'))),
inference(splitRight,[status(thm)],[c_45]) ).
tff(c_12,plain,
! [To_14] :
( ~ selection_favors(efficient_producers,first_movers,'#skF_3'(To_14))
| ~ in_environment('#skF_2',To_14) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_58,plain,
~ in_environment('#skF_2','#skF_1'('#skF_2')),
inference(resolution,[status(thm)],[c_54,c_12]) ).
tff(c_62,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_55,c_58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : MGT032+2 : TPTP v8.1.2. Released v2.0.0.
% 0.13/0.14 % 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
% 0.15/0.35 % Computer : n005.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 20:30:42 EDT 2023
% 0.15/0.35 % CPUTime :
% 3.18/1.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.18/1.71
% 3.18/1.71 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.25/1.74
% 3.25/1.74 Inference rules
% 3.25/1.74 ----------------------
% 3.25/1.74 #Ref : 0
% 3.25/1.74 #Sup : 6
% 3.25/1.74 #Fact : 0
% 3.25/1.74 #Define : 0
% 3.25/1.74 #Split : 1
% 3.25/1.74 #Chain : 0
% 3.25/1.74 #Close : 0
% 3.25/1.74
% 3.28/1.74 Ordering : KBO
% 3.28/1.74
% 3.28/1.74 Simplification rules
% 3.28/1.74 ----------------------
% 3.28/1.74 #Subsume : 1
% 3.28/1.74 #Demod : 6
% 3.28/1.74 #Tautology : 0
% 3.28/1.74 #SimpNegUnit : 0
% 3.28/1.74 #BackRed : 0
% 3.28/1.74
% 3.28/1.74 #Partial instantiations: 0
% 3.28/1.74 #Strategies tried : 1
% 3.28/1.74
% 3.28/1.74 Timing (in seconds)
% 3.28/1.74 ----------------------
% 3.28/1.75 Preprocessing : 0.44
% 3.28/1.75 Parsing : 0.25
% 3.28/1.75 CNF conversion : 0.03
% 3.28/1.75 Main loop : 0.22
% 3.28/1.75 Inferencing : 0.11
% 3.28/1.75 Reduction : 0.04
% 3.28/1.75 Demodulation : 0.03
% 3.28/1.75 BG Simplification : 0.01
% 3.28/1.75 Subsumption : 0.05
% 3.28/1.75 Abstraction : 0.01
% 3.28/1.75 MUC search : 0.00
% 3.28/1.75 Cooper : 0.00
% 3.28/1.75 Total : 0.72
% 3.28/1.75 Index Insertion : 0.00
% 3.28/1.75 Index Deletion : 0.00
% 3.28/1.75 Index Matching : 0.00
% 3.28/1.75 BG Taut test : 0.00
%------------------------------------------------------------------------------