TSTP Solution File: MGT028+1 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : MGT028+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n026.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 : 600s
% DateTime : Sun Jul 17 22:09:42 EDT 2022
% Result : Theorem 0.22s 1.41s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 4 unt; 0 def)
% Number of atoms : 183 ( 0 equ)
% Maximal formula atoms : 36 ( 5 avg)
% Number of connectives : 259 ( 110 ~; 113 |; 27 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 15 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_l10,conjecture,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( greater(X5,appear(efficient_producers,X1))
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X5) )
=> greater(zero,growth_rate(first_movers,X3)) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_l10) ).
fof(mp_first_movers_negative_growth,axiom,
! [X1] :
( ( environment(X1)
& stable(X1)
& ? [X2] :
( in_environment(X1,X2)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X2) )
=> greater(zero,growth_rate(first_movers,X3)) ) ) )
=> ? [X4] :
( greater(X4,appear(efficient_producers,X1))
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X4) )
=> greater(zero,growth_rate(first_movers,X3)) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_first_movers_negative_growth) ).
fof(l11,hypothesis,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( in_environment(X1,X5)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X5) )
=> ( greater(growth_rate(efficient_producers,X3),zero)
& greater(zero,growth_rate(first_movers,X3)) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l11) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( greater(X5,appear(efficient_producers,X1))
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X5) )
=> greater(zero,growth_rate(first_movers,X3)) ) ) ),
inference(assume_negation,[status(cth)],[prove_l10]) ).
fof(c_0_4,plain,
! [X5,X6,X9] :
( ( greater(esk5_1(X5),appear(efficient_producers,X5))
| subpopulations(first_movers,efficient_producers,X5,esk4_2(X5,X6))
| ~ in_environment(X5,X6)
| ~ environment(X5)
| ~ stable(X5) )
& ( ~ subpopulations(first_movers,efficient_producers,X5,X9)
| ~ greater_or_equal(X9,esk5_1(X5))
| greater(zero,growth_rate(first_movers,X9))
| subpopulations(first_movers,efficient_producers,X5,esk4_2(X5,X6))
| ~ in_environment(X5,X6)
| ~ environment(X5)
| ~ stable(X5) )
& ( greater(esk5_1(X5),appear(efficient_producers,X5))
| greater_or_equal(esk4_2(X5,X6),X6)
| ~ in_environment(X5,X6)
| ~ environment(X5)
| ~ stable(X5) )
& ( ~ subpopulations(first_movers,efficient_producers,X5,X9)
| ~ greater_or_equal(X9,esk5_1(X5))
| greater(zero,growth_rate(first_movers,X9))
| greater_or_equal(esk4_2(X5,X6),X6)
| ~ in_environment(X5,X6)
| ~ environment(X5)
| ~ stable(X5) )
& ( greater(esk5_1(X5),appear(efficient_producers,X5))
| ~ greater(zero,growth_rate(first_movers,esk4_2(X5,X6)))
| ~ in_environment(X5,X6)
| ~ environment(X5)
| ~ stable(X5) )
& ( ~ subpopulations(first_movers,efficient_producers,X5,X9)
| ~ greater_or_equal(X9,esk5_1(X5))
| greater(zero,growth_rate(first_movers,X9))
| ~ greater(zero,growth_rate(first_movers,esk4_2(X5,X6)))
| ~ in_environment(X5,X6)
| ~ environment(X5)
| ~ stable(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_first_movers_negative_growth])])])])])])]) ).
fof(c_0_5,negated_conjecture,
! [X7] :
( environment(esk2_0)
& stable(esk2_0)
& ( subpopulations(first_movers,efficient_producers,esk2_0,esk3_1(X7))
| ~ greater(X7,appear(efficient_producers,esk2_0)) )
& ( greater_or_equal(esk3_1(X7),X7)
| ~ greater(X7,appear(efficient_producers,esk2_0)) )
& ( ~ greater(zero,growth_rate(first_movers,esk3_1(X7)))
| ~ greater(X7,appear(efficient_producers,esk2_0)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])])])]) ).
cnf(c_0_6,plain,
( subpopulations(first_movers,efficient_producers,X1,esk4_2(X1,X2))
| greater(zero,growth_rate(first_movers,X3))
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater_or_equal(X3,esk5_1(X1))
| ~ subpopulations(first_movers,efficient_producers,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk2_0,esk3_1(X1))
| ~ greater(X1,appear(efficient_producers,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
stable(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
environment(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
( ~ greater(X1,appear(efficient_producers,esk2_0))
| ~ greater(zero,growth_rate(first_movers,esk3_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_11,hypothesis,
! [X6,X8] :
( ( in_environment(X6,esk1_1(X6))
| ~ environment(X6)
| ~ stable(X6) )
& ( greater(growth_rate(efficient_producers,X8),zero)
| ~ subpopulations(first_movers,efficient_producers,X6,X8)
| ~ greater_or_equal(X8,esk1_1(X6))
| ~ environment(X6)
| ~ stable(X6) )
& ( greater(zero,growth_rate(first_movers,X8))
| ~ subpopulations(first_movers,efficient_producers,X6,X8)
| ~ greater_or_equal(X8,esk1_1(X6))
| ~ environment(X6)
| ~ stable(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l11])])])])])])]) ).
cnf(c_0_12,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk2_0,esk4_2(esk2_0,X1))
| ~ greater(X2,appear(efficient_producers,esk2_0))
| ~ greater_or_equal(esk3_1(X2),esk5_1(esk2_0))
| ~ in_environment(esk2_0,X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]),c_0_9])]),c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( greater_or_equal(esk3_1(X1),X1)
| ~ greater(X1,appear(efficient_producers,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,plain,
( greater_or_equal(esk4_2(X1,X2),X2)
| greater(zero,growth_rate(first_movers,X3))
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater_or_equal(X3,esk5_1(X1))
| ~ subpopulations(first_movers,efficient_producers,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_15,hypothesis,
( greater(zero,growth_rate(first_movers,X2))
| ~ stable(X1)
| ~ environment(X1)
| ~ greater_or_equal(X2,esk1_1(X1))
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk2_0,esk4_2(esk2_0,X1))
| ~ greater(esk5_1(esk2_0),appear(efficient_producers,esk2_0))
| ~ in_environment(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( greater_or_equal(esk4_2(esk2_0,X1),X1)
| ~ greater(X2,appear(efficient_producers,esk2_0))
| ~ greater_or_equal(esk3_1(X2),esk5_1(esk2_0))
| ~ in_environment(esk2_0,X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_7]),c_0_8]),c_0_9])]),c_0_10]) ).
cnf(c_0_18,hypothesis,
( greater(zero,growth_rate(first_movers,esk4_2(esk2_0,X1)))
| ~ greater(esk5_1(esk2_0),appear(efficient_producers,esk2_0))
| ~ greater_or_equal(esk4_2(esk2_0,X1),esk1_1(esk2_0))
| ~ in_environment(esk2_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_8]),c_0_9])]) ).
cnf(c_0_19,negated_conjecture,
( greater_or_equal(esk4_2(esk2_0,X1),X1)
| ~ greater(esk5_1(esk2_0),appear(efficient_producers,esk2_0))
| ~ in_environment(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_20,plain,
( greater(zero,growth_rate(first_movers,X3))
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(zero,growth_rate(first_movers,esk4_2(X1,X2)))
| ~ greater_or_equal(X3,esk5_1(X1))
| ~ subpopulations(first_movers,efficient_producers,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_21,hypothesis,
( greater(zero,growth_rate(first_movers,esk4_2(esk2_0,esk1_1(esk2_0))))
| ~ greater(esk5_1(esk2_0),appear(efficient_producers,esk2_0))
| ~ in_environment(esk2_0,esk1_1(esk2_0)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( subpopulations(first_movers,efficient_producers,X1,esk4_2(X1,X2))
| greater(esk5_1(X1),appear(efficient_producers,X1))
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_23,plain,
( greater(esk5_1(X1),appear(efficient_producers,X1))
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(zero,growth_rate(first_movers,esk4_2(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_24,hypothesis,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater(esk5_1(esk2_0),appear(efficient_producers,esk2_0))
| ~ greater_or_equal(X1,esk5_1(esk2_0))
| ~ subpopulations(first_movers,efficient_producers,esk2_0,X1)
| ~ in_environment(esk2_0,esk1_1(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_8]),c_0_9])]) ).
cnf(c_0_25,hypothesis,
( in_environment(X1,esk1_1(X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_26,hypothesis,
( greater(esk5_1(X1),appear(efficient_producers,X1))
| ~ greater_or_equal(esk4_2(X1,X2),esk1_1(X1))
| ~ in_environment(X1,X2)
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_22]),c_0_23]) ).
cnf(c_0_27,plain,
( greater_or_equal(esk4_2(X1,X2),X2)
| greater(esk5_1(X1),appear(efficient_producers,X1))
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_28,hypothesis,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater(esk5_1(esk2_0),appear(efficient_producers,esk2_0))
| ~ greater_or_equal(X1,esk5_1(esk2_0))
| ~ subpopulations(first_movers,efficient_producers,esk2_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_8]),c_0_9])]) ).
cnf(c_0_29,hypothesis,
( greater(esk5_1(X1),appear(efficient_producers,X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_25]) ).
cnf(c_0_30,hypothesis,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,esk5_1(esk2_0))
| ~ subpopulations(first_movers,efficient_producers,esk2_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_8]),c_0_9])]) ).
cnf(c_0_31,negated_conjecture,
( ~ greater(X1,appear(efficient_producers,esk2_0))
| ~ greater_or_equal(esk3_1(X1),esk5_1(esk2_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_7]),c_0_10]) ).
cnf(c_0_32,negated_conjecture,
~ greater(esk5_1(esk2_0),appear(efficient_producers,esk2_0)),
inference(spm,[status(thm)],[c_0_31,c_0_13]) ).
cnf(c_0_33,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_29]),c_0_8]),c_0_9])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : MGT028+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 09:46:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.22/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.41 # Preprocessing time : 0.014 s
% 0.22/1.41
% 0.22/1.41 # Proof found!
% 0.22/1.41 # SZS status Theorem
% 0.22/1.41 # SZS output start CNFRefutation
% See solution above
% 0.22/1.41 # Proof object total steps : 34
% 0.22/1.41 # Proof object clause steps : 27
% 0.22/1.41 # Proof object formula steps : 7
% 0.22/1.41 # Proof object conjectures : 14
% 0.22/1.41 # Proof object clause conjectures : 11
% 0.22/1.41 # Proof object formula conjectures : 3
% 0.22/1.41 # Proof object initial clauses used : 13
% 0.22/1.41 # Proof object initial formulas used : 3
% 0.22/1.41 # Proof object generating inferences : 14
% 0.22/1.41 # Proof object simplifying inferences : 26
% 0.22/1.41 # Training examples: 0 positive, 0 negative
% 0.22/1.41 # Parsed axioms : 3
% 0.22/1.41 # Removed by relevancy pruning/SinE : 0
% 0.22/1.41 # Initial clauses : 14
% 0.22/1.41 # Removed in clause preprocessing : 0
% 0.22/1.41 # Initial clauses in saturation : 14
% 0.22/1.41 # Processed clauses : 33
% 0.22/1.41 # ...of these trivial : 0
% 0.22/1.41 # ...subsumed : 2
% 0.22/1.41 # ...remaining for further processing : 31
% 0.22/1.41 # Other redundant clauses eliminated : 0
% 0.22/1.41 # Clauses deleted for lack of memory : 0
% 0.22/1.41 # Backward-subsumed : 8
% 0.22/1.41 # Backward-rewritten : 0
% 0.22/1.41 # Generated clauses : 29
% 0.22/1.41 # ...of the previous two non-trivial : 24
% 0.22/1.41 # Contextual simplify-reflections : 8
% 0.22/1.41 # Paramodulations : 29
% 0.22/1.41 # Factorizations : 0
% 0.22/1.41 # Equation resolutions : 0
% 0.22/1.41 # Current number of processed clauses : 23
% 0.22/1.41 # Positive orientable unit clauses : 2
% 0.22/1.41 # Positive unorientable unit clauses: 0
% 0.22/1.41 # Negative unit clauses : 2
% 0.22/1.41 # Non-unit-clauses : 19
% 0.22/1.41 # Current number of unprocessed clauses: 3
% 0.22/1.41 # ...number of literals in the above : 16
% 0.22/1.41 # Current number of archived formulas : 0
% 0.22/1.41 # Current number of archived clauses : 8
% 0.22/1.41 # Clause-clause subsumption calls (NU) : 217
% 0.22/1.41 # Rec. Clause-clause subsumption calls : 49
% 0.22/1.41 # Non-unit clause-clause subsumptions : 18
% 0.22/1.41 # Unit Clause-clause subsumption calls : 18
% 0.22/1.41 # Rewrite failures with RHS unbound : 0
% 0.22/1.41 # BW rewrite match attempts : 0
% 0.22/1.41 # BW rewrite match successes : 0
% 0.22/1.41 # Condensation attempts : 0
% 0.22/1.41 # Condensation successes : 0
% 0.22/1.41 # Termbank termtop insertions : 2217
% 0.22/1.41
% 0.22/1.41 # -------------------------------------------------
% 0.22/1.41 # User time : 0.015 s
% 0.22/1.41 # System time : 0.003 s
% 0.22/1.41 # Total time : 0.018 s
% 0.22/1.41 # Maximum resident set size: 2772 pages
%------------------------------------------------------------------------------