%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : MGT023+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 : Thu Sep 24 01:26:04 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 5 unt; 0 def)
% Number of atoms : 109 ( 12 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 134 ( 49 ~; 51 |; 24 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1,hypothesis,
! [X1,X2] :
( ( ! [X3] :
( ( greater(X3,X2)
& subpopulations(first_movers,efficient_producers,X1,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
& in_environment(X1,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& environment(X1) )
=> X2 = critical_point(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(l12,hypothesis,
! [X1] :
( ( stable(X1)
& environment(X1) )
=> ? [X2] :
( ! [X3] :
( ( greater(X3,X2)
& subpopulations(first_movers,efficient_producers,X1,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& in_environment(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12) ).
fof(prove_l5,conjecture,
! [X1] :
( ( stable(X1)
& environment(X1) )
=> in_environment(X1,critical_point(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l5) ).
fof(c_0_3,hypothesis,
! [X1,X2] :
( ( ! [X3] :
( ( greater(X3,X2)
& subpopulations(first_movers,efficient_producers,X1,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
& in_environment(X1,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& environment(X1) )
=> X2 = critical_point(X1) ),
inference(fof_simplification,[status(thm)],[d1]) ).
fof(c_0_4,hypothesis,
! [X1] :
( ( stable(X1)
& environment(X1) )
=> ? [X2] :
( ! [X3] :
( ( greater(X3,X2)
& subpopulations(first_movers,efficient_producers,X1,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& in_environment(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[l12]) ).
fof(c_0_5,hypothesis,
! [X4,X5] :
( ( X5 = critical_point(X4)
| ~ in_environment(X4,X5)
| greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5))
| ~ environment(X4)
| ~ greater(growth_rate(efficient_producers,esk1_2(X4,X5)),growth_rate(first_movers,esk1_2(X4,X5))) )
& ( X5 = critical_point(X4)
| ~ in_environment(X4,X5)
| greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5))
| ~ environment(X4)
| greater(esk1_2(X4,X5),X5) )
& ( X5 = critical_point(X4)
| ~ in_environment(X4,X5)
| greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5))
| ~ environment(X4)
| subpopulations(first_movers,efficient_producers,X4,esk1_2(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])]) ).
fof(c_0_6,hypothesis,
! [X7,X9] :
( ( ~ stable(X7)
| ~ environment(X7)
| greater(growth_rate(efficient_producers,X9),growth_rate(first_movers,X9))
| ~ greater(X9,esk2_1(X7))
| ~ subpopulations(first_movers,efficient_producers,X7,X9) )
& ( ~ stable(X7)
| ~ environment(X7)
| ~ greater(growth_rate(efficient_producers,esk2_1(X7)),growth_rate(first_movers,esk2_1(X7))) )
& ( ~ stable(X7)
| ~ environment(X7)
| in_environment(X7,esk2_1(X7)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( stable(X1)
& environment(X1) )
=> in_environment(X1,critical_point(X1)) ),
inference(assume_negation,[status(cth)],[prove_l5]) ).
cnf(c_0_8,hypothesis,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| X2 = critical_point(X1)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| subpopulations(first_movers,efficient_producers,X1,esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,hypothesis,
( ~ stable(X1)
| ~ environment(X1)
| in_environment(X1,esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,hypothesis,
( ~ stable(X1)
| ~ environment(X1)
| ~ greater(growth_rate(efficient_producers,esk2_1(X1)),growth_rate(first_movers,esk2_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,hypothesis,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| X2 = critical_point(X1)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| greater(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,hypothesis,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| ~ greater(growth_rate(efficient_producers,esk1_2(X1,X2)),growth_rate(first_movers,esk1_2(X1,X2)))
| X2 = critical_point(X1)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_13,negated_conjecture,
( ~ in_environment(esk3_0,critical_point(esk3_0))
& stable(esk3_0)
& environment(esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_14,hypothesis,
( ~ stable(X1)
| ~ environment(X1)
| ~ greater(X2,esk2_1(X1))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,hypothesis,
( ~ environment(X1)
| ~ stable(X1)
| subpopulations(first_movers,efficient_producers,X1,esk1_2(X1,esk2_1(X1)))
| critical_point(X1) = esk2_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_16,hypothesis,
( ~ environment(X1)
| ~ stable(X1)
| greater(esk1_2(X1,esk2_1(X1)),esk2_1(X1))
| critical_point(X1) = esk2_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_9]),c_0_10]) ).
cnf(c_0_17,hypothesis,
( ~ environment(X1)
| ~ greater(growth_rate(efficient_producers,esk1_2(X1,esk2_1(X1))),growth_rate(first_movers,esk1_2(X1,esk2_1(X1))))
| ~ stable(X1)
| critical_point(X1) = esk2_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_9]),c_0_10]) ).
cnf(c_0_18,negated_conjecture,
~ in_environment(esk3_0,critical_point(esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,hypothesis,
( ~ environment(X1)
| ~ stable(X1)
| critical_point(X1) = esk2_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]) ).
cnf(c_0_20,negated_conjecture,
stable(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
environment(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
~ in_environment(esk3_0,esk2_1(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_23,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_9]),c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT023+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n001.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 21 01:27:13 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.42 % Version: 3.5.1
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.42 % Starting sh5l with 300s (1) cores
% 0.13/0.42 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1906641 completed with status 0
% 0.13/0.42 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.42 % No SInE strategy applied
% 0.13/0.42 % Search class: FGHSF-FFSF21-SFFFFFNN
% 0.13/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.42 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.42 % new_bool_1 with pid 1906651 completed with status 0
% 0.13/0.42 % Result found by new_bool_1
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.42 % No SInE strategy applied
% 0.13/0.42 % Search class: FGHSF-FFSF21-SFFFFFNN
% 0.13/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.42 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.42 % Preprocessing time : 0.001 s
% 0.13/0.42 % Presaturation interreduction done
% 0.13/0.42
% 0.13/0.42 % Proof found!
% 0.13/0.42 % SZS status Theorem
% 0.13/0.42 % SZS output start CNFRefutation
% See solution above
% 0.13/0.42 % Parsed axioms : 3
% 0.13/0.42 % Removed by relevancy pruning/SinE : 0
% 0.13/0.42 % Initial clauses : 9
% 0.13/0.42 % Removed in clause preprocessing : 0
% 0.13/0.42 % Initial clauses in saturation : 9
% 0.13/0.42 % Processed clauses : 23
% 0.13/0.42 % ...of these trivial : 0
% 0.13/0.42 % ...subsumed : 0
% 0.13/0.42 % ...remaining for further processing : 23
% 0.13/0.42 % Other redundant clauses eliminated : 0
% 0.13/0.42 % Clauses deleted for lack of memory : 0
% 0.13/0.42 % Backward-subsumed : 3
% 0.13/0.42 % Backward-rewritten : 0
% 0.13/0.42 % Generated clauses : 6
% 0.13/0.42 % ...of the previous two non-redundant : 5
% 0.13/0.42 % ...aggressively subsumed : 0
% 0.13/0.42 % Contextual simplify-reflections : 5
% 0.13/0.42 % Paramodulations : 6
% 0.13/0.42 % Factorizations : 0
% 0.13/0.42 % NegExts : 0
% 0.13/0.42 % Equation resolutions : 0
% 0.13/0.42 % Disequality decompositions : 0
% 0.13/0.42 % Total rewrite steps : 4
% 0.13/0.42 % ...of those cached : 2
% 0.13/0.42 % Propositional unsat checks : 0
% 0.13/0.42 % Propositional check models : 0
% 0.13/0.42 % Propositional check unsatisfiable : 0
% 0.13/0.42 % Propositional clauses : 0
% 0.13/0.42 % Propositional clauses after purity: 0
% 0.13/0.42 % Propositional unsat core size : 0
% 0.13/0.42 % Propositional preprocessing time : 0.000
% 0.13/0.42 % Propositional encoding time : 0.000
% 0.13/0.42 % Propositional solver time : 0.000
% 0.13/0.42 % Success case prop preproc time : 0.000
% 0.13/0.42 % Success case prop encoding time : 0.000
% 0.13/0.42 % Success case prop solver time : 0.000
% 0.13/0.42 % Current number of processed clauses : 11
% 0.13/0.42 % Positive orientable unit clauses : 2
% 0.13/0.42 % Positive unorientable unit clauses: 0
% 0.13/0.42 % Negative unit clauses : 2
% 0.13/0.42 % Non-unit-clauses : 7
% 0.13/0.42 % Current number of unprocessed clauses: 0
% 0.13/0.42 % ...number of literals in the above : 0
% 0.13/0.42 % Current number of archived formulas : 0
% 0.13/0.42 % Current number of archived clauses : 12
% 0.13/0.42 % Clause-clause subsumption calls (NU) : 78
% 0.13/0.42 % Rec. Clause-clause subsumption calls : 12
% 0.13/0.42 % Non-unit clause-clause subsumptions : 8
% 0.13/0.42 % Unit Clause-clause subsumption calls : 0
% 0.13/0.42 % Rewrite failures with RHS unbound : 0
% 0.13/0.42 % BW rewrite match attempts : 0
% 0.13/0.42 % BW rewrite match successes : 0
% 0.13/0.42 % Condensation attempts : 0
% 0.13/0.42 % Condensation successes : 0
% 0.13/0.42 % Termbank termtop insertions : 1171
% 0.13/0.42 % Search garbage collected termcells : 182
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.004 s
% 0.13/0.42 % System time : 0.001 s
% 0.13/0.42 % Total time : 0.005 s
% 0.13/0.42 % Maximum resident set size: 3632 pages
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.014 s
% 0.13/0.42 % System time : 0.010 s
% 0.13/0.42 % Total time : 0.024 s
% 0.13/0.42 % Maximum resident set size: 4864 pages
% 0.13/0.42 % E exiting
%------------------------------------------------------------------------------