TSTP Solution File: MGT020+1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : MGT020+1 : TPTP v3.4.2. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 14:00:36 EDT 2009
% Result : Theorem 0.8s
% Output : Refutation 0.8s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 11 unt; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 126 ( 60 ~; 63 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_l2,plain,
( environment(e)
& subpopulations(first_movers,efficient_producers,e,t)
& ~ greater(disbanding_rate(first_movers,t),disbanding_rate(efficient_producers,t)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),
[] ).
cnf(146083472,plain,
environment(e),
inference(rewrite,[status(thm)],[prove_l2]),
[] ).
fof(mp_earliest_time_point,plain,
! [A,B] :
( ( ~ subpopulations(first_movers,efficient_producers,A,B)
| greater_or_equal(B,initial_fm_ep(A))
| ~ environment(A) )
& ( ~ in_environment(A,initial_fm_ep(A))
| subpopulations(first_movers,efficient_producers,A,initial_fm_ep(A))
| ~ environment(A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),
[] ).
cnf(145900576,plain,
( ~ subpopulations(first_movers,efficient_producers,A,B)
| greater_or_equal(B,initial_fm_ep(A))
| ~ environment(A) ),
inference(rewrite,[status(thm)],[mp_earliest_time_point]),
[] ).
cnf(146074368,plain,
subpopulations(first_movers,efficient_producers,e,t),
inference(rewrite,[status(thm)],[prove_l2]),
[] ).
cnf(159385632,plain,
greater_or_equal(t,initial_fm_ep(e)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[146083472,145900576,146074368]),
[] ).
fof(a8,plain,
! [A] :
( ~ environment(A)
| greater(disbanding_rate(first_movers,initial_fm_ep(A)),disbanding_rate(efficient_producers,initial_fm_ep(A))) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),
[] ).
cnf(145990376,plain,
( ~ environment(A)
| greater(disbanding_rate(first_movers,initial_fm_ep(A)),disbanding_rate(efficient_producers,initial_fm_ep(A))) ),
inference(rewrite,[status(thm)],[a8]),
[] ).
cnf(159269440,plain,
greater(disbanding_rate(first_movers,initial_fm_ep(e)),disbanding_rate(efficient_producers,initial_fm_ep(e))),
inference(resolution,[status(thm)],[145990376,146083472]),
[] ).
cnf(146065048,plain,
~ greater(disbanding_rate(first_movers,t),disbanding_rate(efficient_producers,t)),
inference(rewrite,[status(thm)],[prove_l2]),
[] ).
fof(mp_positive_function_difference,plain,
! [A,B,C,D] :
( ~ environment(A)
| ~ greater_or_equal(B,C)
| ~ greater_or_equal(D,B)
| ~ subpopulations(first_movers,efficient_producers,A,D)
| ~ greater(disbanding_rate(first_movers,C),disbanding_rate(efficient_producers,C))
| decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| greater(disbanding_rate(first_movers,D),disbanding_rate(efficient_producers,D)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),
[] ).
cnf(145921808,plain,
( ~ environment(A)
| ~ greater_or_equal(B,C)
| ~ greater_or_equal(D,B)
| ~ subpopulations(first_movers,efficient_producers,A,D)
| ~ greater(disbanding_rate(first_movers,C),disbanding_rate(efficient_producers,C))
| decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| greater(disbanding_rate(first_movers,D),disbanding_rate(efficient_producers,D)) ),
inference(rewrite,[status(thm)],[mp_positive_function_difference]),
[] ).
cnf(159461064,plain,
( ~ greater_or_equal(A,B)
| ~ greater_or_equal(t,A)
| ~ greater(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))
| decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A))) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[146083472,146065048,145921808,146074368]),
[] ).
fof(mp_greater_or_equal,plain,
! [A,B] :
( ~ greater_or_equal(A,B)
| greater(A,B)
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),
[] ).
cnf(145985216,plain,
( ~ greater_or_equal(A,B)
| greater(A,B)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[mp_greater_or_equal]),
[] ).
cnf(159495080,plain,
( greater(t,initial_fm_ep(e))
| $equal(initial_fm_ep(e),t) ),
inference(resolution,[status(thm)],[145985216,159385632]),
[] ).
cnf(159963240,plain,
( greater(t,initial_fm_ep(e))
| greater_or_equal(initial_fm_ep(e),initial_fm_ep(e)) ),
inference(paramodulation,[status(thm)],[159495080,159385632,theory(equality)]),
[] ).
fof(mp_initial_time,plain,
! [A] :
( ~ environment(A)
| greater_or_equal(initial_fm_ep(A),start_time(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),
[] ).
cnf(145935400,plain,
( ~ environment(A)
| greater_or_equal(initial_fm_ep(A),start_time(A)) ),
inference(rewrite,[status(thm)],[mp_initial_time]),
[] ).
fof(mp_times_in_order,plain,
! [A,B,C] :
( ~ environment(A)
| ~ greater_or_equal(B,start_time(A))
| ~ greater(C,B)
| ~ in_environment(A,C)
| in_environment(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),
[] ).
cnf(145961168,plain,
( ~ environment(A)
| ~ greater_or_equal(B,start_time(A))
| ~ greater(C,B)
| ~ in_environment(A,C)
| in_environment(A,B) ),
inference(rewrite,[status(thm)],[mp_times_in_order]),
[] ).
cnf(145879800,plain,
( ~ in_environment(A,initial_fm_ep(A))
| subpopulations(first_movers,efficient_producers,A,initial_fm_ep(A))
| ~ environment(A) ),
inference(rewrite,[status(thm)],[mp_earliest_time_point]),
[] ).
cnf(169498720,plain,
( ~ environment(A)
| ~ greater(B,initial_fm_ep(A))
| ~ in_environment(A,B)
| subpopulations(first_movers,efficient_producers,A,initial_fm_ep(A)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[145935400,145961168,145879800]),
[] ).
cnf(159283248,plain,
( ~ subpopulations(first_movers,efficient_producers,e,A)
| greater_or_equal(A,initial_fm_ep(e)) ),
inference(resolution,[status(thm)],[145900576,146083472]),
[] ).
cnf(169534832,plain,
( ~ greater(A,initial_fm_ep(e))
| ~ in_environment(e,A)
| greater_or_equal(initial_fm_ep(e),initial_fm_ep(e)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[146083472,169498720,159283248]),
[] ).
fof(mp_time_point_occurs,plain,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| in_environment(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),
[] ).
cnf(145930712,plain,
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| in_environment(A,B) ),
inference(rewrite,[status(thm)],[mp_time_point_occurs]),
[] ).
cnf(159369416,plain,
in_environment(e,t),
inference(forward_subsumption_resolution__resolution,[status(thm)],[146083472,145930712,146074368]),
[] ).
cnf(169547896,plain,
greater_or_equal(initial_fm_ep(e),initial_fm_ep(e)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[159963240,169534832,159369416]),
[] ).
cnf(169700928,plain,
decreases(difference(disbanding_rate(first_movers,initial_fm_ep(e)),disbanding_rate(efficient_producers,initial_fm_ep(e)))),
inference(forward_subsumption_resolution__resolution,[status(thm)],[159385632,159269440,159461064,169547896]),
[] ).
cnf(159944104,plain,
( greater(t,initial_fm_ep(e))
| in_environment(e,initial_fm_ep(e)) ),
inference(paramodulation,[status(thm)],[159495080,159369416,theory(equality)]),
[] ).
cnf(159331560,plain,
( ~ greater_or_equal(A,start_time(e))
| ~ greater(B,A)
| ~ in_environment(e,B)
| in_environment(e,A) ),
inference(resolution,[status(thm)],[145961168,146083472]),
[] ).
cnf(167916552,plain,
( ~ greater(A,initial_fm_ep(e))
| ~ in_environment(e,A)
| in_environment(e,initial_fm_ep(e)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[146083472,159331560,145935400]),
[] ).
cnf(168389160,plain,
( ~ greater(A,initial_fm_ep(e))
| in_environment(e,initial_fm_ep(e))
| ~ subpopulations(first_movers,efficient_producers,e,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[146083472,167916552,145930712]),
[] ).
cnf(168393944,plain,
in_environment(e,initial_fm_ep(e)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[159944104,168389160,146074368]),
[] ).
cnf(169488536,plain,
subpopulations(first_movers,efficient_producers,e,initial_fm_ep(e)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[146083472,168393944,145879800]),
[] ).
fof(l3,plain,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),
[] ).
cnf(145871024,plain,
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) ),
inference(rewrite,[status(thm)],[l3]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[169700928,146083472,169488536,145871024]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(prove_l2,plain,((environment(e)&subpopulations(first_movers,efficient_producers,e,t)&~greater(disbanding_rate(first_movers,t),disbanding_rate(efficient_producers,t)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),[]).
%
% cnf(146083472,plain,(environment(e)),inference(rewrite,[status(thm)],[prove_l2]),[]).
%
% fof(mp_earliest_time_point,plain,(((~subpopulations(first_movers,efficient_producers,A,B)|greater_or_equal(B,initial_fm_ep(A))|~environment(A))&(~in_environment(A,initial_fm_ep(A))|subpopulations(first_movers,efficient_producers,A,initial_fm_ep(A))|~environment(A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),[]).
%
% cnf(145900576,plain,(~subpopulations(first_movers,efficient_producers,A,B)|greater_or_equal(B,initial_fm_ep(A))|~environment(A)),inference(rewrite,[status(thm)],[mp_earliest_time_point]),[]).
%
% cnf(146074368,plain,(subpopulations(first_movers,efficient_producers,e,t)),inference(rewrite,[status(thm)],[prove_l2]),[]).
%
% cnf(159385632,plain,(greater_or_equal(t,initial_fm_ep(e))),inference(forward_subsumption_resolution__resolution,[status(thm)],[146083472,145900576,146074368]),[]).
%
% fof(a8,plain,(~environment(A)|greater(disbanding_rate(first_movers,initial_fm_ep(A)),disbanding_rate(efficient_producers,initial_fm_ep(A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),[]).
%
% cnf(145990376,plain,(~environment(A)|greater(disbanding_rate(first_movers,initial_fm_ep(A)),disbanding_rate(efficient_producers,initial_fm_ep(A)))),inference(rewrite,[status(thm)],[a8]),[]).
%
% cnf(159269440,plain,(greater(disbanding_rate(first_movers,initial_fm_ep(e)),disbanding_rate(efficient_producers,initial_fm_ep(e)))),inference(resolution,[status(thm)],[145990376,146083472]),[]).
%
% cnf(146065048,plain,(~greater(disbanding_rate(first_movers,t),disbanding_rate(efficient_producers,t))),inference(rewrite,[status(thm)],[prove_l2]),[]).
%
% fof(mp_positive_function_difference,plain,(~environment(A)|~greater_or_equal(B,C)|~greater_or_equal(D,B)|~subpopulations(first_movers,efficient_producers,A,D)|~greater(disbanding_rate(first_movers,C),disbanding_rate(efficient_producers,C))|decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))|greater(disbanding_rate(first_movers,D),disbanding_rate(efficient_producers,D))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),[]).
%
% cnf(145921808,plain,(~environment(A)|~greater_or_equal(B,C)|~greater_or_equal(D,B)|~subpopulations(first_movers,efficient_producers,A,D)|~greater(disbanding_rate(first_movers,C),disbanding_rate(efficient_producers,C))|decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))|greater(disbanding_rate(first_movers,D),disbanding_rate(efficient_producers,D))),inference(rewrite,[status(thm)],[mp_positive_function_difference]),[]).
%
% cnf(159461064,plain,(~greater_or_equal(A,B)|~greater_or_equal(t,A)|~greater(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))|decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[146083472,146065048,145921808,146074368]),[]).
%
% fof(mp_greater_or_equal,plain,(~greater_or_equal(A,B)|greater(A,B)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),[]).
%
% cnf(145985216,plain,(~greater_or_equal(A,B)|greater(A,B)|$equal(B,A)),inference(rewrite,[status(thm)],[mp_greater_or_equal]),[]).
%
% cnf(159495080,plain,(greater(t,initial_fm_ep(e))|$equal(initial_fm_ep(e),t)),inference(resolution,[status(thm)],[145985216,159385632]),[]).
%
% cnf(159963240,plain,(greater(t,initial_fm_ep(e))|greater_or_equal(initial_fm_ep(e),initial_fm_ep(e))),inference(paramodulation,[status(thm)],[159495080,159385632,theory(equality)]),[]).
%
% fof(mp_initial_time,plain,(~environment(A)|greater_or_equal(initial_fm_ep(A),start_time(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),[]).
%
% cnf(145935400,plain,(~environment(A)|greater_or_equal(initial_fm_ep(A),start_time(A))),inference(rewrite,[status(thm)],[mp_initial_time]),[]).
%
% fof(mp_times_in_order,plain,(~environment(A)|~greater_or_equal(B,start_time(A))|~greater(C,B)|~in_environment(A,C)|in_environment(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),[]).
%
% cnf(145961168,plain,(~environment(A)|~greater_or_equal(B,start_time(A))|~greater(C,B)|~in_environment(A,C)|in_environment(A,B)),inference(rewrite,[status(thm)],[mp_times_in_order]),[]).
%
% cnf(145879800,plain,(~in_environment(A,initial_fm_ep(A))|subpopulations(first_movers,efficient_producers,A,initial_fm_ep(A))|~environment(A)),inference(rewrite,[status(thm)],[mp_earliest_time_point]),[]).
%
% cnf(169498720,plain,(~environment(A)|~greater(B,initial_fm_ep(A))|~in_environment(A,B)|subpopulations(first_movers,efficient_producers,A,initial_fm_ep(A))),inference(forward_subsumption_resolution__resolution,[status(thm)],[145935400,145961168,145879800]),[]).
%
% cnf(159283248,plain,(~subpopulations(first_movers,efficient_producers,e,A)|greater_or_equal(A,initial_fm_ep(e))),inference(resolution,[status(thm)],[145900576,146083472]),[]).
%
% cnf(169534832,plain,(~greater(A,initial_fm_ep(e))|~in_environment(e,A)|greater_or_equal(initial_fm_ep(e),initial_fm_ep(e))),inference(forward_subsumption_resolution__resolution,[status(thm)],[146083472,169498720,159283248]),[]).
%
% fof(mp_time_point_occurs,plain,(~environment(A)|~subpopulations(first_movers,efficient_producers,A,B)|in_environment(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),[]).
%
% cnf(145930712,plain,(~environment(A)|~subpopulations(first_movers,efficient_producers,A,B)|in_environment(A,B)),inference(rewrite,[status(thm)],[mp_time_point_occurs]),[]).
%
% cnf(159369416,plain,(in_environment(e,t)),inference(forward_subsumption_resolution__resolution,[status(thm)],[146083472,145930712,146074368]),[]).
%
% cnf(169547896,plain,(greater_or_equal(initial_fm_ep(e),initial_fm_ep(e))),inference(forward_subsumption_resolution__resolution,[status(thm)],[159963240,169534832,159369416]),[]).
%
% cnf(169700928,plain,(decreases(difference(disbanding_rate(first_movers,initial_fm_ep(e)),disbanding_rate(efficient_producers,initial_fm_ep(e))))),inference(forward_subsumption_resolution__resolution,[status(thm)],[159385632,159269440,159461064,169547896]),[]).
%
% cnf(159944104,plain,(greater(t,initial_fm_ep(e))|in_environment(e,initial_fm_ep(e))),inference(paramodulation,[status(thm)],[159495080,159369416,theory(equality)]),[]).
%
% cnf(159331560,plain,(~greater_or_equal(A,start_time(e))|~greater(B,A)|~in_environment(e,B)|in_environment(e,A)),inference(resolution,[status(thm)],[145961168,146083472]),[]).
%
% cnf(167916552,plain,(~greater(A,initial_fm_ep(e))|~in_environment(e,A)|in_environment(e,initial_fm_ep(e))),inference(forward_subsumption_resolution__resolution,[status(thm)],[146083472,159331560,145935400]),[]).
%
% cnf(168389160,plain,(~greater(A,initial_fm_ep(e))|in_environment(e,initial_fm_ep(e))|~subpopulations(first_movers,efficient_producers,e,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[146083472,167916552,145930712]),[]).
%
% cnf(168393944,plain,(in_environment(e,initial_fm_ep(e))),inference(forward_subsumption_resolution__resolution,[status(thm)],[159944104,168389160,146074368]),[]).
%
% cnf(169488536,plain,(subpopulations(first_movers,efficient_producers,e,initial_fm_ep(e))),inference(forward_subsumption_resolution__resolution,[status(thm)],[146083472,168393944,145879800]),[]).
%
% fof(l3,plain,(~environment(A)|~subpopulations(first_movers,efficient_producers,A,B)|~decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/MGT/MGT020+1.tptp',unknown),[]).
%
% cnf(145871024,plain,(~environment(A)|~subpopulations(first_movers,efficient_producers,A,B)|~decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))),inference(rewrite,[status(thm)],[l3]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[169700928,146083472,169488536,145871024]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------