TSTP Solution File: MGT023+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : MGT023+1 : TPTP v5.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sat Dec 25 21:04:44 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 45 ( 6 unt; 0 def)
% Number of atoms : 204 ( 20 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 259 ( 100 ~; 107 |; 42 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 : 57 ( 0 sgn 30 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> in_environment(X1,critical_point(X1)) ),
file('/tmp/tmp3-2XYO/sel_MGT023+1.p_1',prove_l5) ).
fof(2,axiom,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X2] :
( in_environment(X1,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) ) ),
file('/tmp/tmp3-2XYO/sel_MGT023+1.p_1',l12) ).
fof(3,axiom,
! [X1,X2] :
( ( environment(X1)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& in_environment(X1,X2)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) )
=> X2 = critical_point(X1) ),
file('/tmp/tmp3-2XYO/sel_MGT023+1.p_1',d1) ).
fof(4,negated_conjecture,
~ ! [X1] :
( ( environment(X1)
& stable(X1) )
=> in_environment(X1,critical_point(X1)) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(5,plain,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X2] :
( in_environment(X1,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).
fof(6,plain,
! [X1,X2] :
( ( environment(X1)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& in_environment(X1,X2)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) )
=> X2 = critical_point(X1) ),
inference(fof_simplification,[status(thm)],[3,theory(equality)]) ).
fof(7,negated_conjecture,
? [X1] :
( environment(X1)
& stable(X1)
& ~ in_environment(X1,critical_point(X1)) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(8,negated_conjecture,
? [X2] :
( environment(X2)
& stable(X2)
& ~ in_environment(X2,critical_point(X2)) ),
inference(variable_rename,[status(thm)],[7]) ).
fof(9,negated_conjecture,
( environment(esk1_0)
& stable(esk1_0)
& ~ in_environment(esk1_0,critical_point(esk1_0)) ),
inference(skolemize,[status(esa)],[8]) ).
cnf(10,negated_conjecture,
~ in_environment(esk1_0,critical_point(esk1_0)),
inference(split_conjunct,[status(thm)],[9]) ).
cnf(11,negated_conjecture,
stable(esk1_0),
inference(split_conjunct,[status(thm)],[9]) ).
cnf(12,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[9]) ).
fof(13,plain,
! [X1] :
( ~ environment(X1)
| ~ stable(X1)
| ? [X2] :
( in_environment(X1,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& ! [X3] :
( ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ~ greater(X3,X2)
| greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(14,plain,
! [X4] :
( ~ environment(X4)
| ~ stable(X4)
| ? [X5] :
( in_environment(X4,X5)
& ~ greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5))
& ! [X6] :
( ~ subpopulations(first_movers,efficient_producers,X4,X6)
| ~ greater(X6,X5)
| greater(growth_rate(efficient_producers,X6),growth_rate(first_movers,X6)) ) ) ),
inference(variable_rename,[status(thm)],[13]) ).
fof(15,plain,
! [X4] :
( ~ environment(X4)
| ~ stable(X4)
| ( in_environment(X4,esk2_1(X4))
& ~ greater(growth_rate(efficient_producers,esk2_1(X4)),growth_rate(first_movers,esk2_1(X4)))
& ! [X6] :
( ~ subpopulations(first_movers,efficient_producers,X4,X6)
| ~ greater(X6,esk2_1(X4))
| greater(growth_rate(efficient_producers,X6),growth_rate(first_movers,X6)) ) ) ),
inference(skolemize,[status(esa)],[14]) ).
fof(16,plain,
! [X4,X6] :
( ( ( ~ subpopulations(first_movers,efficient_producers,X4,X6)
| ~ greater(X6,esk2_1(X4))
| greater(growth_rate(efficient_producers,X6),growth_rate(first_movers,X6)) )
& in_environment(X4,esk2_1(X4))
& ~ greater(growth_rate(efficient_producers,esk2_1(X4)),growth_rate(first_movers,esk2_1(X4))) )
| ~ environment(X4)
| ~ stable(X4) ),
inference(shift_quantors,[status(thm)],[15]) ).
fof(17,plain,
! [X4,X6] :
( ( ~ subpopulations(first_movers,efficient_producers,X4,X6)
| ~ greater(X6,esk2_1(X4))
| greater(growth_rate(efficient_producers,X6),growth_rate(first_movers,X6))
| ~ environment(X4)
| ~ stable(X4) )
& ( in_environment(X4,esk2_1(X4))
| ~ environment(X4)
| ~ stable(X4) )
& ( ~ greater(growth_rate(efficient_producers,esk2_1(X4)),growth_rate(first_movers,esk2_1(X4)))
| ~ environment(X4)
| ~ stable(X4) ) ),
inference(distribute,[status(thm)],[16]) ).
cnf(18,plain,
( ~ stable(X1)
| ~ environment(X1)
| ~ greater(growth_rate(efficient_producers,esk2_1(X1)),growth_rate(first_movers,esk2_1(X1))) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(19,plain,
( in_environment(X1,esk2_1(X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(20,plain,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ stable(X1)
| ~ environment(X1)
| ~ greater(X2,esk2_1(X1))
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(21,plain,
! [X1,X2] :
( ~ environment(X1)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ in_environment(X1,X2)
| ? [X3] :
( subpopulations(first_movers,efficient_producers,X1,X3)
& greater(X3,X2)
& ~ greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
| X2 = critical_point(X1) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(22,plain,
! [X4,X5] :
( ~ environment(X4)
| greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5))
| ~ in_environment(X4,X5)
| ? [X6] :
( subpopulations(first_movers,efficient_producers,X4,X6)
& greater(X6,X5)
& ~ greater(growth_rate(efficient_producers,X6),growth_rate(first_movers,X6)) )
| X5 = critical_point(X4) ),
inference(variable_rename,[status(thm)],[21]) ).
fof(23,plain,
! [X4,X5] :
( ~ environment(X4)
| greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5))
| ~ in_environment(X4,X5)
| ( subpopulations(first_movers,efficient_producers,X4,esk3_2(X4,X5))
& greater(esk3_2(X4,X5),X5)
& ~ greater(growth_rate(efficient_producers,esk3_2(X4,X5)),growth_rate(first_movers,esk3_2(X4,X5))) )
| X5 = critical_point(X4) ),
inference(skolemize,[status(esa)],[22]) ).
fof(24,plain,
! [X4,X5] :
( ( subpopulations(first_movers,efficient_producers,X4,esk3_2(X4,X5))
| ~ environment(X4)
| greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5))
| ~ in_environment(X4,X5)
| X5 = critical_point(X4) )
& ( greater(esk3_2(X4,X5),X5)
| ~ environment(X4)
| greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5))
| ~ in_environment(X4,X5)
| X5 = critical_point(X4) )
& ( ~ greater(growth_rate(efficient_producers,esk3_2(X4,X5)),growth_rate(first_movers,esk3_2(X4,X5)))
| ~ environment(X4)
| greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5))
| ~ in_environment(X4,X5)
| X5 = critical_point(X4) ) ),
inference(distribute,[status(thm)],[23]) ).
cnf(25,plain,
( X1 = critical_point(X2)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X2,X1)
| ~ environment(X2)
| ~ greater(growth_rate(efficient_producers,esk3_2(X2,X1)),growth_rate(first_movers,esk3_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[24]) ).
cnf(26,plain,
( X1 = critical_point(X2)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| greater(esk3_2(X2,X1),X1)
| ~ in_environment(X2,X1)
| ~ environment(X2) ),
inference(split_conjunct,[status(thm)],[24]) ).
cnf(27,plain,
( X1 = critical_point(X2)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| subpopulations(first_movers,efficient_producers,X2,esk3_2(X2,X1))
| ~ in_environment(X2,X1)
| ~ environment(X2) ),
inference(split_conjunct,[status(thm)],[24]) ).
cnf(28,plain,
( critical_point(X1) = esk2_1(X1)
| greater(growth_rate(efficient_producers,esk2_1(X1)),growth_rate(first_movers,esk2_1(X1)))
| greater(esk3_2(X1,esk2_1(X1)),esk2_1(X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(spm,[status(thm)],[26,19,theory(equality)]) ).
cnf(29,plain,
( critical_point(X1) = esk2_1(X1)
| subpopulations(first_movers,efficient_producers,X1,esk3_2(X1,esk2_1(X1)))
| greater(growth_rate(efficient_producers,esk2_1(X1)),growth_rate(first_movers,esk2_1(X1)))
| ~ environment(X1)
| ~ stable(X1) ),
inference(spm,[status(thm)],[27,19,theory(equality)]) ).
cnf(30,plain,
( critical_point(X1) = esk2_1(X1)
| greater(esk3_2(X1,esk2_1(X1)),esk2_1(X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[28,18]) ).
cnf(31,plain,
( greater(growth_rate(efficient_producers,esk3_2(X1,esk2_1(X1))),growth_rate(first_movers,esk3_2(X1,esk2_1(X1))))
| critical_point(X1) = esk2_1(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,esk3_2(X1,esk2_1(X1)))
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[20,30,theory(equality)]) ).
cnf(32,plain,
( critical_point(X1) = esk2_1(X1)
| subpopulations(first_movers,efficient_producers,X1,esk3_2(X1,esk2_1(X1)))
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[29,18]) ).
cnf(33,plain,
( critical_point(X1) = esk2_1(X1)
| greater(growth_rate(efficient_producers,esk3_2(X1,esk2_1(X1))),growth_rate(first_movers,esk3_2(X1,esk2_1(X1))))
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[31,32,theory(equality)]) ).
cnf(34,plain,
( critical_point(X1) = esk2_1(X1)
| greater(growth_rate(efficient_producers,esk2_1(X1)),growth_rate(first_movers,esk2_1(X1)))
| ~ in_environment(X1,esk2_1(X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(spm,[status(thm)],[25,33,theory(equality)]) ).
cnf(35,plain,
( critical_point(X1) = esk2_1(X1)
| greater(growth_rate(efficient_producers,esk2_1(X1)),growth_rate(first_movers,esk2_1(X1)))
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[34,19]) ).
cnf(36,plain,
( critical_point(X1) = esk2_1(X1)
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[35,18]) ).
cnf(37,plain,
( ~ in_environment(esk1_0,esk2_1(esk1_0))
| ~ stable(esk1_0)
| ~ environment(esk1_0) ),
inference(spm,[status(thm)],[10,36,theory(equality)]) ).
cnf(38,plain,
( ~ in_environment(esk1_0,esk2_1(esk1_0))
| $false
| ~ environment(esk1_0) ),
inference(rw,[status(thm)],[37,11,theory(equality)]) ).
cnf(39,plain,
( ~ in_environment(esk1_0,esk2_1(esk1_0))
| $false
| $false ),
inference(rw,[status(thm)],[38,12,theory(equality)]) ).
cnf(40,plain,
~ in_environment(esk1_0,esk2_1(esk1_0)),
inference(cn,[status(thm)],[39,theory(equality)]) ).
cnf(41,plain,
( ~ stable(esk1_0)
| ~ environment(esk1_0) ),
inference(spm,[status(thm)],[40,19,theory(equality)]) ).
cnf(42,plain,
( $false
| ~ environment(esk1_0) ),
inference(rw,[status(thm)],[41,11,theory(equality)]) ).
cnf(43,plain,
( $false
| $false ),
inference(rw,[status(thm)],[42,12,theory(equality)]) ).
cnf(44,plain,
$false,
inference(cn,[status(thm)],[43,theory(equality)]) ).
cnf(45,plain,
$false,
44,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/MGT/MGT023+1.p
% --creating new selector for []
% -running prover on /tmp/tmp3-2XYO/sel_MGT023+1.p_1 with time limit 29
% -prover status Theorem
% Problem MGT023+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/MGT/MGT023+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/MGT/MGT023+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------