TSTP Solution File: SEU319+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU319+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 07:14:28 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 6 unt; 0 def)
% Number of atoms : 138 ( 5 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 166 ( 69 ~; 72 |; 13 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 44 ( 0 sgn 25 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( closed_subset(X2,X1)
<=> open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1) ) ) ),
file('/tmp/tmprK9VJP/sel_SEU319+1.p_1',d6_pre_topc) ).
fof(9,axiom,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_complement(the_carrier(X1),X2) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2) ) ),
file('/tmp/tmprK9VJP/sel_SEU319+1.p_1',t17_pre_topc) ).
fof(13,axiom,
! [X1] :
( top_str(X1)
=> one_sorted_str(X1) ),
file('/tmp/tmprK9VJP/sel_SEU319+1.p_1',dt_l1_pre_topc) ).
fof(17,conjecture,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( closed_subset(X2,X1)
<=> open_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
file('/tmp/tmprK9VJP/sel_SEU319+1.p_1',t29_tops_1) ).
fof(20,negated_conjecture,
~ ! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( closed_subset(X2,X1)
<=> open_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[17]) ).
fof(21,plain,
! [X1] :
( ~ top_str(X1)
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X1)))
| ( ( ~ closed_subset(X2,X1)
| open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1) )
& ( ~ open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1)
| closed_subset(X2,X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(22,plain,
! [X3] :
( ~ top_str(X3)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X3)))
| ( ( ~ closed_subset(X4,X3)
| open_subset(subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4),X3) )
& ( ~ open_subset(subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4),X3)
| closed_subset(X4,X3) ) ) ) ),
inference(variable_rename,[status(thm)],[21]) ).
fof(23,plain,
! [X3,X4] :
( ~ element(X4,powerset(the_carrier(X3)))
| ( ( ~ closed_subset(X4,X3)
| open_subset(subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4),X3) )
& ( ~ open_subset(subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4),X3)
| closed_subset(X4,X3) ) )
| ~ top_str(X3) ),
inference(shift_quantors,[status(thm)],[22]) ).
fof(24,plain,
! [X3,X4] :
( ( ~ closed_subset(X4,X3)
| open_subset(subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4),X3)
| ~ element(X4,powerset(the_carrier(X3)))
| ~ top_str(X3) )
& ( ~ open_subset(subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4),X3)
| closed_subset(X4,X3)
| ~ element(X4,powerset(the_carrier(X3)))
| ~ top_str(X3) ) ),
inference(distribute,[status(thm)],[23]) ).
cnf(25,plain,
( closed_subset(X2,X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1) ),
inference(split_conjunct,[status(thm)],[24]) ).
cnf(26,plain,
( open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ closed_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(44,plain,
! [X1] :
( ~ one_sorted_str(X1)
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X1)))
| subset_complement(the_carrier(X1),X2) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(45,plain,
! [X3] :
( ~ one_sorted_str(X3)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X3)))
| subset_complement(the_carrier(X3),X4) = subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4) ) ),
inference(variable_rename,[status(thm)],[44]) ).
fof(46,plain,
! [X3,X4] :
( ~ element(X4,powerset(the_carrier(X3)))
| subset_complement(the_carrier(X3),X4) = subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4)
| ~ one_sorted_str(X3) ),
inference(shift_quantors,[status(thm)],[45]) ).
cnf(47,plain,
( subset_complement(the_carrier(X1),X2) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[46]) ).
fof(51,plain,
! [X1] :
( ~ top_str(X1)
| one_sorted_str(X1) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(52,plain,
! [X2] :
( ~ top_str(X2)
| one_sorted_str(X2) ),
inference(variable_rename,[status(thm)],[51]) ).
cnf(53,plain,
( one_sorted_str(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(62,negated_conjecture,
? [X1] :
( top_str(X1)
& ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& ( ~ closed_subset(X2,X1)
| ~ open_subset(subset_complement(the_carrier(X1),X2),X1) )
& ( closed_subset(X2,X1)
| open_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(63,negated_conjecture,
? [X3] :
( top_str(X3)
& ? [X4] :
( element(X4,powerset(the_carrier(X3)))
& ( ~ closed_subset(X4,X3)
| ~ open_subset(subset_complement(the_carrier(X3),X4),X3) )
& ( closed_subset(X4,X3)
| open_subset(subset_complement(the_carrier(X3),X4),X3) ) ) ),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,negated_conjecture,
( top_str(esk4_0)
& element(esk5_0,powerset(the_carrier(esk4_0)))
& ( ~ closed_subset(esk5_0,esk4_0)
| ~ open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0) )
& ( closed_subset(esk5_0,esk4_0)
| open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0) ) ),
inference(skolemize,[status(esa)],[63]) ).
cnf(65,negated_conjecture,
( open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0)
| closed_subset(esk5_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(66,negated_conjecture,
( ~ open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0)
| ~ closed_subset(esk5_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(67,negated_conjecture,
element(esk5_0,powerset(the_carrier(esk4_0))),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(68,negated_conjecture,
top_str(esk4_0),
inference(split_conjunct,[status(thm)],[64]) ).
cnf(85,plain,
( open_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ closed_subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[26,47,theory(equality)]) ).
cnf(87,plain,
( closed_subset(X1,X2)
| ~ open_subset(subset_complement(the_carrier(X2),X1),X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2)
| ~ one_sorted_str(X2) ),
inference(spm,[status(thm)],[25,47,theory(equality)]) ).
cnf(90,plain,
( open_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ closed_subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(csr,[status(thm)],[85,53]) ).
cnf(96,plain,
( closed_subset(X1,X2)
| ~ open_subset(subset_complement(the_carrier(X2),X1),X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(csr,[status(thm)],[87,53]) ).
cnf(97,negated_conjecture,
( closed_subset(esk5_0,esk4_0)
| ~ element(esk5_0,powerset(the_carrier(esk4_0)))
| ~ top_str(esk4_0) ),
inference(spm,[status(thm)],[96,65,theory(equality)]) ).
cnf(100,negated_conjecture,
( closed_subset(esk5_0,esk4_0)
| $false
| ~ top_str(esk4_0) ),
inference(rw,[status(thm)],[97,67,theory(equality)]) ).
cnf(101,negated_conjecture,
( closed_subset(esk5_0,esk4_0)
| $false
| $false ),
inference(rw,[status(thm)],[100,68,theory(equality)]) ).
cnf(102,negated_conjecture,
closed_subset(esk5_0,esk4_0),
inference(cn,[status(thm)],[101,theory(equality)]) ).
cnf(103,negated_conjecture,
( ~ open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0)
| $false ),
inference(rw,[status(thm)],[66,102,theory(equality)]) ).
cnf(104,negated_conjecture,
~ open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0),
inference(cn,[status(thm)],[103,theory(equality)]) ).
cnf(108,negated_conjecture,
( ~ closed_subset(esk5_0,esk4_0)
| ~ element(esk5_0,powerset(the_carrier(esk4_0)))
| ~ top_str(esk4_0) ),
inference(spm,[status(thm)],[104,90,theory(equality)]) ).
cnf(109,negated_conjecture,
( $false
| ~ element(esk5_0,powerset(the_carrier(esk4_0)))
| ~ top_str(esk4_0) ),
inference(rw,[status(thm)],[108,102,theory(equality)]) ).
cnf(110,negated_conjecture,
( $false
| $false
| ~ top_str(esk4_0) ),
inference(rw,[status(thm)],[109,67,theory(equality)]) ).
cnf(111,negated_conjecture,
( $false
| $false
| $false ),
inference(rw,[status(thm)],[110,68,theory(equality)]) ).
cnf(112,negated_conjecture,
$false,
inference(cn,[status(thm)],[111,theory(equality)]) ).
cnf(113,negated_conjecture,
$false,
112,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU319+1.p
% --creating new selector for []
% -running prover on /tmp/tmprK9VJP/sel_SEU319+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU319+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU319+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU319+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
%
%------------------------------------------------------------------------------