%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : MGT026+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:07:34 AM UTC 2026
% Result : Theorem 10.81s 3.49s
% Output : CNFRefutation 10.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of clauses : 55 ( 15 unt; 12 nHn; 55 RR)
% Number of literals : 149 ( 17 equ; 84 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_11,plain,
( X1 = X2
| greater(X1,X2)
| ~ greater_or_equal(X1,X2) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ml58ntnr/lgb.p',i_0_11) ).
cnf(i_0_7,plain,
( greater_or_equal(critical_point(X1),appear(efficient_producers,X1))
| ~ environment(X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ml58ntnr/lgb.p',i_0_7) ).
cnf(i_0_8,plain,
( greater(X1,X2)
| ~ greater(X3,X2)
| ~ greater(X1,X3) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ml58ntnr/lgb.p',i_0_8) ).
cnf(i_0_16,negated_conjecture,
greater(esk2_0,critical_point(esk1_0)),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ml58ntnr/lgb.p',i_0_16) ).
cnf(i_0_18,negated_conjecture,
environment(esk1_0),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ml58ntnr/lgb.p',i_0_18) ).
cnf(i_0_10,plain,
( greater_or_equal(X1,X2)
| ~ greater(X1,X2) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ml58ntnr/lgb.p',i_0_10) ).
cnf(i_0_14,hypothesis,
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X2)
| ~ in_environment(X2,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X2)) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ml58ntnr/lgb.p',i_0_14) ).
cnf(i_0_17,negated_conjecture,
in_environment(esk1_0,esk2_0),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ml58ntnr/lgb.p',i_0_17) ).
cnf(i_0_4,plain,
( greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X2)
| ~ in_environment(X2,X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ml58ntnr/lgb.p',i_0_4) ).
cnf(i_0_3,plain,
( subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(cardinality_at_time(first_movers,X2),zero)
| ~ greater(cardinality_at_time(efficient_producers,X2),zero) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ml58ntnr/lgb.p',i_0_3) ).
cnf(i_0_12,hypothesis,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| X2 != critical_point(X3)
| ~ environment(X3)
| ~ greater(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,X3,X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ml58ntnr/lgb.p',i_0_12) ).
cnf(i_0_1,plain,
( selection_favors(X1,X2,X3)
| ~ environment(X4)
| ~ subpopulations(X2,X1,X4,X3)
| ~ greater(growth_rate(X1,X3),growth_rate(X2,X3)) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ml58ntnr/lgb.p',i_0_1) ).
cnf(i_0_15,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,esk2_0),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ml58ntnr/lgb.p',i_0_15) ).
cnf(i_0_2,plain,
( selection_favors(X1,X2,X3)
| cardinality_at_time(X2,X3) != zero
| ~ environment(X4)
| ~ subpopulation(X2,X4,X3)
| ~ subpopulation(X1,X4,X3)
| ~ greater(cardinality_at_time(X1,X3),zero) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ml58ntnr/lgb.p',i_0_2) ).
cnf(i_0_6,plain,
( subpopulation(first_movers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ml58ntnr/lgb.p',i_0_6) ).
cnf(i_0_5,plain,
( subpopulation(efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ml58ntnr/lgb.p',i_0_5) ).
cnf(c_0_35,plain,
( X1 = X2
| greater(X1,X2)
| ~ greater_or_equal(X1,X2) ),
i_0_11 ).
cnf(c_0_36,plain,
( greater_or_equal(critical_point(X1),appear(efficient_producers,X1))
| ~ environment(X1) ),
i_0_7 ).
cnf(c_0_37,plain,
( greater(X1,X2)
| ~ greater(X3,X2)
| ~ greater(X1,X3) ),
i_0_8 ).
cnf(c_0_38,plain,
( appear(efficient_producers,X1) = critical_point(X1)
| greater(critical_point(X1),appear(efficient_producers,X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
( appear(efficient_producers,X1) = critical_point(X1)
| greater(X2,appear(efficient_producers,X1))
| ~ environment(X1)
| ~ greater(X2,critical_point(X1)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,negated_conjecture,
greater(esk2_0,critical_point(esk1_0)),
i_0_16 ).
cnf(c_0_41,negated_conjecture,
environment(esk1_0),
i_0_18 ).
cnf(c_0_42,plain,
( greater_or_equal(X1,X2)
| ~ greater(X1,X2) ),
i_0_10 ).
cnf(c_0_43,negated_conjecture,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| greater(esk2_0,appear(efficient_producers,esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
cnf(c_0_44,hypothesis,
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X2)
| ~ in_environment(X2,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X2)) ),
i_0_14 ).
cnf(c_0_45,plain,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| greater_or_equal(esk2_0,appear(efficient_producers,esk1_0)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,negated_conjecture,
in_environment(esk1_0,esk2_0),
i_0_17 ).
cnf(c_0_47,hypothesis,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| greater(cardinality_at_time(efficient_producers,esk2_0),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_41]),c_0_46])]) ).
cnf(c_0_48,hypothesis,
( greater(cardinality_at_time(efficient_producers,esk2_0),zero)
| greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater_or_equal(X1,critical_point(esk1_0))
| ~ in_environment(esk1_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_47]),c_0_41])]) ).
cnf(c_0_49,negated_conjecture,
greater_or_equal(esk2_0,critical_point(esk1_0)),
inference(spm,[status(thm)],[c_0_42,c_0_40]) ).
cnf(c_0_50,plain,
( greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X2)
| ~ in_environment(X2,X1) ),
i_0_4 ).
cnf(c_0_51,plain,
( subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(cardinality_at_time(first_movers,X2),zero)
| ~ greater(cardinality_at_time(efficient_producers,X2),zero) ),
i_0_3 ).
cnf(c_0_52,negated_conjecture,
greater(cardinality_at_time(efficient_producers,esk2_0),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_46]),c_0_49])]) ).
cnf(c_0_53,negated_conjecture,
greater_or_equal(cardinality_at_time(first_movers,esk2_0),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_46]),c_0_41])]) ).
cnf(c_0_54,hypothesis,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| X2 != critical_point(X3)
| ~ environment(X3)
| ~ greater(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,X3,X1) ),
i_0_12 ).
cnf(c_0_55,plain,
( subpopulations(first_movers,efficient_producers,X1,esk2_0)
| ~ environment(X1)
| ~ in_environment(X1,esk2_0)
| ~ greater(cardinality_at_time(first_movers,esk2_0),zero) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,plain,
( cardinality_at_time(first_movers,esk2_0) = zero
| greater(cardinality_at_time(first_movers,esk2_0),zero) ),
inference(spm,[status(thm)],[c_0_35,c_0_53]) ).
cnf(c_0_57,hypothesis,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2)
| ~ greater(X1,critical_point(X2)) ),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_58,plain,
( cardinality_at_time(first_movers,esk2_0) = zero
| subpopulations(first_movers,efficient_producers,X1,esk2_0)
| ~ environment(X1)
| ~ in_environment(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_59,negated_conjecture,
( greater(growth_rate(efficient_producers,esk2_0),growth_rate(first_movers,esk2_0))
| ~ subpopulations(first_movers,efficient_producers,esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_40]),c_0_41])]) ).
cnf(c_0_60,negated_conjecture,
( cardinality_at_time(first_movers,esk2_0) = zero
| subpopulations(first_movers,efficient_producers,esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_46]),c_0_41])]) ).
cnf(c_0_61,plain,
( selection_favors(X1,X2,X3)
| ~ environment(X4)
| ~ subpopulations(X2,X1,X4,X3)
| ~ greater(growth_rate(X1,X3),growth_rate(X2,X3)) ),
i_0_1 ).
cnf(c_0_62,negated_conjecture,
( cardinality_at_time(first_movers,esk2_0) = zero
| greater(growth_rate(efficient_producers,esk2_0),growth_rate(first_movers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_63,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,esk2_0),
i_0_15 ).
cnf(c_0_64,plain,
( cardinality_at_time(first_movers,esk2_0) = zero
| ~ subpopulations(first_movers,efficient_producers,X1,esk2_0)
| ~ environment(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_65,plain,
( selection_favors(X1,X2,X3)
| cardinality_at_time(X2,X3) != zero
| ~ environment(X4)
| ~ subpopulation(X2,X4,X3)
| ~ subpopulation(X1,X4,X3)
| ~ greater(cardinality_at_time(X1,X3),zero) ),
i_0_2 ).
cnf(c_0_66,negated_conjecture,
cardinality_at_time(first_movers,esk2_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_60]),c_0_41])]) ).
cnf(c_0_67,plain,
( subpopulation(first_movers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
i_0_6 ).
cnf(c_0_68,plain,
( selection_favors(X1,first_movers,esk2_0)
| ~ subpopulation(first_movers,X2,esk2_0)
| ~ subpopulation(X1,X2,esk2_0)
| ~ environment(X2)
| ~ greater(cardinality_at_time(X1,esk2_0),zero) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,negated_conjecture,
subpopulation(first_movers,esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_46]),c_0_41])]) ).
cnf(c_0_70,plain,
( subpopulation(efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
i_0_5 ).
cnf(c_0_71,negated_conjecture,
( selection_favors(X1,first_movers,esk2_0)
| ~ subpopulation(X1,esk1_0,esk2_0)
| ~ greater(cardinality_at_time(X1,esk2_0),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_41])]) ).
cnf(c_0_72,negated_conjecture,
subpopulation(efficient_producers,esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_46]),c_0_41])]) ).
cnf(c_0_73,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_52])]),c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT026+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.03 % Command : enigmatic-eprover.py %s %d 1
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 7 12:08:59 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.45 # ENIGMATIC: Selected complete mode:
% 10.81/3.49 # ENIGMATIC: Solved by autoschedule-lgb:
% 10.81/3.49 # No SInE strategy applied
% 10.81/3.49 # Trying AutoSched0 for 150 seconds
% 10.81/3.49 # AutoSched0-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S2S
% 10.81/3.49 # and selection function SelectNewComplexAHP.
% 10.81/3.49 #
% 10.81/3.49 # Preprocessing time : 0.024 s
% 10.81/3.49 # Presaturation interreduction done
% 10.81/3.49
% 10.81/3.49 # Proof found!
% 10.81/3.49 # SZS status Theorem
% 10.81/3.49 # SZS output start CNFRefutation
% See solution above
% 10.81/3.49 # Training examples: 0 positive, 0 negative
% 10.81/3.49
% 10.81/3.49 # -------------------------------------------------
% 10.81/3.49 # User time : 0.026 s
% 10.81/3.49 # System time : 0.006 s
% 10.81/3.49 # Total time : 0.032 s
% 10.81/3.49 # Maximum resident set size: 3328 pages
% 10.81/3.49
%------------------------------------------------------------------------------