TSTP Solution File: SEU382+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU382+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 : Sun Dec 26 08:05:21 EST 2010
% Result : Theorem 0.33s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 20 unt; 0 def)
% Number of atoms : 99 ( 41 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 96 ( 44 ~; 37 |; 9 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 69 ( 5 sgn 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( rel_str(X1)
=> relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
file('/tmp/tmp43v-Jc/sel_SEU382+1.p_1',dt_u1_orders_2) ).
fof(3,axiom,
! [X1] : incl_POSet(X1) = rel_str_of(X1,inclusion_order(X1)),
file('/tmp/tmp43v-Jc/sel_SEU382+1.p_1',d1_yellow_1) ).
fof(5,axiom,
! [X1] :
( strict_rel_str(incl_POSet(X1))
& rel_str(incl_POSet(X1)) ),
file('/tmp/tmp43v-Jc/sel_SEU382+1.p_1',dt_k2_yellow_1) ).
fof(27,axiom,
! [X1] :
( rel_str(X1)
=> ( strict_rel_str(X1)
=> X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1)) ) ),
file('/tmp/tmp43v-Jc/sel_SEU382+1.p_1',abstractness_v1_orders_2) ).
fof(30,conjecture,
! [X1] : the_carrier(boole_POSet(X1)) = powerset(X1),
file('/tmp/tmp43v-Jc/sel_SEU382+1.p_1',t4_waybel_7) ).
fof(32,axiom,
! [X1,X2] :
( relation_of2(X2,X1,X1)
=> ! [X3,X4] :
( rel_str_of(X1,X2) = rel_str_of(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ) ),
file('/tmp/tmp43v-Jc/sel_SEU382+1.p_1',free_g1_orders_2) ).
fof(48,axiom,
! [X1] : boole_POSet(X1) = incl_POSet(powerset(X1)),
file('/tmp/tmp43v-Jc/sel_SEU382+1.p_1',t4_yellow_1) ).
fof(80,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/tmp/tmp43v-Jc/sel_SEU382+1.p_1',redefinition_m2_relset_1) ).
fof(90,negated_conjecture,
~ ! [X1] : the_carrier(boole_POSet(X1)) = powerset(X1),
inference(assume_negation,[status(cth)],[30]) ).
fof(145,plain,
! [X1] :
( ~ rel_str(X1)
| relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(146,plain,
! [X2] :
( ~ rel_str(X2)
| relation_of2_as_subset(the_InternalRel(X2),the_carrier(X2),the_carrier(X2)) ),
inference(variable_rename,[status(thm)],[145]) ).
cnf(147,plain,
( relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[146]) ).
fof(148,plain,
! [X2] : incl_POSet(X2) = rel_str_of(X2,inclusion_order(X2)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(149,plain,
incl_POSet(X1) = rel_str_of(X1,inclusion_order(X1)),
inference(split_conjunct,[status(thm)],[148]) ).
fof(153,plain,
! [X2] :
( strict_rel_str(incl_POSet(X2))
& rel_str(incl_POSet(X2)) ),
inference(variable_rename,[status(thm)],[5]) ).
cnf(154,plain,
rel_str(incl_POSet(X1)),
inference(split_conjunct,[status(thm)],[153]) ).
cnf(155,plain,
strict_rel_str(incl_POSet(X1)),
inference(split_conjunct,[status(thm)],[153]) ).
fof(273,plain,
! [X1] :
( ~ rel_str(X1)
| ~ strict_rel_str(X1)
| X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1)) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(274,plain,
! [X2] :
( ~ rel_str(X2)
| ~ strict_rel_str(X2)
| X2 = rel_str_of(the_carrier(X2),the_InternalRel(X2)) ),
inference(variable_rename,[status(thm)],[273]) ).
cnf(275,plain,
( X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1))
| ~ strict_rel_str(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[274]) ).
fof(284,negated_conjecture,
? [X1] : the_carrier(boole_POSet(X1)) != powerset(X1),
inference(fof_nnf,[status(thm)],[90]) ).
fof(285,negated_conjecture,
? [X2] : the_carrier(boole_POSet(X2)) != powerset(X2),
inference(variable_rename,[status(thm)],[284]) ).
fof(286,negated_conjecture,
the_carrier(boole_POSet(esk11_0)) != powerset(esk11_0),
inference(skolemize,[status(esa)],[285]) ).
cnf(287,negated_conjecture,
the_carrier(boole_POSet(esk11_0)) != powerset(esk11_0),
inference(split_conjunct,[status(thm)],[286]) ).
fof(301,plain,
! [X1,X2] :
( ~ relation_of2(X2,X1,X1)
| ! [X3,X4] :
( rel_str_of(X1,X2) != rel_str_of(X3,X4)
| ( X1 = X3
& X2 = X4 ) ) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(302,plain,
! [X5,X6] :
( ~ relation_of2(X6,X5,X5)
| ! [X7,X8] :
( rel_str_of(X5,X6) != rel_str_of(X7,X8)
| ( X5 = X7
& X6 = X8 ) ) ),
inference(variable_rename,[status(thm)],[301]) ).
fof(303,plain,
! [X5,X6,X7,X8] :
( rel_str_of(X5,X6) != rel_str_of(X7,X8)
| ( X5 = X7
& X6 = X8 )
| ~ relation_of2(X6,X5,X5) ),
inference(shift_quantors,[status(thm)],[302]) ).
fof(304,plain,
! [X5,X6,X7,X8] :
( ( X5 = X7
| rel_str_of(X5,X6) != rel_str_of(X7,X8)
| ~ relation_of2(X6,X5,X5) )
& ( X6 = X8
| rel_str_of(X5,X6) != rel_str_of(X7,X8)
| ~ relation_of2(X6,X5,X5) ) ),
inference(distribute,[status(thm)],[303]) ).
cnf(306,plain,
( X2 = X3
| ~ relation_of2(X1,X2,X2)
| rel_str_of(X2,X1) != rel_str_of(X3,X4) ),
inference(split_conjunct,[status(thm)],[304]) ).
fof(375,plain,
! [X2] : boole_POSet(X2) = incl_POSet(powerset(X2)),
inference(variable_rename,[status(thm)],[48]) ).
cnf(376,plain,
boole_POSet(X1) = incl_POSet(powerset(X1)),
inference(split_conjunct,[status(thm)],[375]) ).
fof(559,plain,
! [X1,X2,X3] :
( ( ~ relation_of2_as_subset(X3,X1,X2)
| relation_of2(X3,X1,X2) )
& ( ~ relation_of2(X3,X1,X2)
| relation_of2_as_subset(X3,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[80]) ).
fof(560,plain,
! [X4,X5,X6] :
( ( ~ relation_of2_as_subset(X6,X4,X5)
| relation_of2(X6,X4,X5) )
& ( ~ relation_of2(X6,X4,X5)
| relation_of2_as_subset(X6,X4,X5) ) ),
inference(variable_rename,[status(thm)],[559]) ).
cnf(562,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[560]) ).
cnf(662,negated_conjecture,
the_carrier(incl_POSet(powerset(esk11_0))) != powerset(esk11_0),
inference(rw,[status(thm)],[287,376,theory(equality)]),
[unfolding] ).
cnf(663,plain,
rel_str(rel_str_of(X1,inclusion_order(X1))),
inference(rw,[status(thm)],[154,149,theory(equality)]),
[unfolding] ).
cnf(665,plain,
strict_rel_str(rel_str_of(X1,inclusion_order(X1))),
inference(rw,[status(thm)],[155,149,theory(equality)]),
[unfolding] ).
cnf(721,negated_conjecture,
the_carrier(rel_str_of(powerset(esk11_0),inclusion_order(powerset(esk11_0)))) != powerset(esk11_0),
inference(rw,[status(thm)],[662,149,theory(equality)]),
[unfolding] ).
cnf(857,plain,
( relation_of2(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[562,147,theory(equality)]) ).
cnf(1404,plain,
( the_carrier(X1) = X2
| rel_str_of(the_carrier(X1),the_InternalRel(X1)) != rel_str_of(X2,X3)
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[306,857,theory(equality)]) ).
cnf(1439,plain,
( the_carrier(X1) = X2
| X1 != rel_str_of(X2,X3)
| ~ rel_str(X1)
| ~ strict_rel_str(X1) ),
inference(spm,[status(thm)],[1404,275,theory(equality)]) ).
cnf(1441,plain,
( the_carrier(rel_str_of(X1,X2)) = X1
| ~ strict_rel_str(rel_str_of(X1,X2))
| ~ rel_str(rel_str_of(X1,X2)) ),
inference(er,[status(thm)],[1439,theory(equality)]) ).
cnf(1444,negated_conjecture,
( ~ strict_rel_str(rel_str_of(powerset(esk11_0),inclusion_order(powerset(esk11_0))))
| ~ rel_str(rel_str_of(powerset(esk11_0),inclusion_order(powerset(esk11_0)))) ),
inference(spm,[status(thm)],[721,1441,theory(equality)]) ).
cnf(1453,negated_conjecture,
( $false
| ~ rel_str(rel_str_of(powerset(esk11_0),inclusion_order(powerset(esk11_0)))) ),
inference(rw,[status(thm)],[1444,665,theory(equality)]) ).
cnf(1454,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[1453,663,theory(equality)]) ).
cnf(1455,negated_conjecture,
$false,
inference(cn,[status(thm)],[1454,theory(equality)]) ).
cnf(1456,negated_conjecture,
$false,
1455,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU382+1.p
% --creating new selector for []
% -running prover on /tmp/tmp43v-Jc/sel_SEU382+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU382+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU382+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU382+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
%
%------------------------------------------------------------------------------