%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU307+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 07:09:36 EST 2010
% Result : Theorem 14.47s
% Output : CNFRefutation 14.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 21 unt; 0 def)
% Number of atoms : 102 ( 38 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 91 ( 40 ~; 32 |; 11 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 59 ( 0 sgn 38 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(6,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3) ),
file('/tmp/tmp3vvcU6/sel_SEU307+2.p_1',redefinition_k5_subset_1) ).
fof(45,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/tmp/tmp3vvcU6/sel_SEU307+2.p_1',t3_boole) ).
fof(113,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/tmp/tmp3vvcU6/sel_SEU307+2.p_1',t37_xboole_1) ).
fof(205,conjecture,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_intersection2(the_carrier(X1),X2,cast_as_carrier_subset(X1)) = X2 ) ),
file('/tmp/tmp3vvcU6/sel_SEU307+2.p_1',t15_pre_topc) ).
fof(233,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('/tmp/tmp3vvcU6/sel_SEU307+2.p_1',dt_k2_subset_1) ).
fof(258,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('/tmp/tmp3vvcU6/sel_SEU307+2.p_1',d4_subset_1) ).
fof(288,axiom,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('/tmp/tmp3vvcU6/sel_SEU307+2.p_1',d3_pre_topc) ).
fof(315,axiom,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/tmp/tmp3vvcU6/sel_SEU307+2.p_1',t48_xboole_1) ).
fof(424,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/tmp/tmp3vvcU6/sel_SEU307+2.p_1',t3_subset) ).
fof(490,negated_conjecture,
~ ! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_intersection2(the_carrier(X1),X2,cast_as_carrier_subset(X1)) = X2 ) ),
inference(assume_negation,[status(cth)],[205]) ).
fof(595,plain,
! [X1,X2,X3] :
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(596,plain,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ element(X6,powerset(X4))
| subset_intersection2(X4,X5,X6) = set_intersection2(X5,X6) ),
inference(variable_rename,[status(thm)],[595]) ).
cnf(597,plain,
( subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[596]) ).
fof(802,plain,
! [X2] : set_difference(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[45]) ).
cnf(803,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[802]) ).
fof(1393,plain,
! [X1,X2] :
( ( set_difference(X1,X2) != empty_set
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| set_difference(X1,X2) = empty_set ) ),
inference(fof_nnf,[status(thm)],[113]) ).
fof(1394,plain,
! [X3,X4] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| set_difference(X3,X4) = empty_set ) ),
inference(variable_rename,[status(thm)],[1393]) ).
cnf(1395,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[1394]) ).
fof(1849,negated_conjecture,
? [X1] :
( one_sorted_str(X1)
& ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& subset_intersection2(the_carrier(X1),X2,cast_as_carrier_subset(X1)) != X2 ) ),
inference(fof_nnf,[status(thm)],[490]) ).
fof(1850,negated_conjecture,
? [X3] :
( one_sorted_str(X3)
& ? [X4] :
( element(X4,powerset(the_carrier(X3)))
& subset_intersection2(the_carrier(X3),X4,cast_as_carrier_subset(X3)) != X4 ) ),
inference(variable_rename,[status(thm)],[1849]) ).
fof(1851,negated_conjecture,
( one_sorted_str(esk129_0)
& element(esk130_0,powerset(the_carrier(esk129_0)))
& subset_intersection2(the_carrier(esk129_0),esk130_0,cast_as_carrier_subset(esk129_0)) != esk130_0 ),
inference(skolemize,[status(esa)],[1850]) ).
cnf(1852,negated_conjecture,
subset_intersection2(the_carrier(esk129_0),esk130_0,cast_as_carrier_subset(esk129_0)) != esk130_0,
inference(split_conjunct,[status(thm)],[1851]) ).
cnf(1853,negated_conjecture,
element(esk130_0,powerset(the_carrier(esk129_0))),
inference(split_conjunct,[status(thm)],[1851]) ).
cnf(1854,negated_conjecture,
one_sorted_str(esk129_0),
inference(split_conjunct,[status(thm)],[1851]) ).
fof(1998,plain,
! [X2] : element(cast_to_subset(X2),powerset(X2)),
inference(variable_rename,[status(thm)],[233]) ).
cnf(1999,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[1998]) ).
fof(2167,plain,
! [X2] : cast_to_subset(X2) = X2,
inference(variable_rename,[status(thm)],[258]) ).
cnf(2168,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[2167]) ).
fof(2333,plain,
! [X1] :
( ~ one_sorted_str(X1)
| cast_as_carrier_subset(X1) = the_carrier(X1) ),
inference(fof_nnf,[status(thm)],[288]) ).
fof(2334,plain,
! [X2] :
( ~ one_sorted_str(X2)
| cast_as_carrier_subset(X2) = the_carrier(X2) ),
inference(variable_rename,[status(thm)],[2333]) ).
cnf(2335,plain,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[2334]) ).
fof(2504,plain,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[315]) ).
cnf(2505,plain,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[2504]) ).
fof(3330,plain,
! [X1,X2] :
( ( ~ element(X1,powerset(X2))
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| element(X1,powerset(X2)) ) ),
inference(fof_nnf,[status(thm)],[424]) ).
fof(3331,plain,
! [X3,X4] :
( ( ~ element(X3,powerset(X4))
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| element(X3,powerset(X4)) ) ),
inference(variable_rename,[status(thm)],[3330]) ).
cnf(3333,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[3331]) ).
cnf(3738,plain,
element(X1,powerset(X1)),
inference(rw,[status(thm)],[1999,2168,theory(equality)]),
[unfolding] ).
cnf(4038,plain,
( subset_intersection2(X1,X2,X3) = set_difference(X2,set_difference(X2,X3))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(rw,[status(thm)],[597,2505,theory(equality)]),
[unfolding] ).
cnf(4560,negated_conjecture,
( subset_intersection2(the_carrier(esk129_0),esk130_0,the_carrier(esk129_0)) != esk130_0
| ~ one_sorted_str(esk129_0) ),
inference(spm,[status(thm)],[1852,2335,theory(equality)]) ).
cnf(4561,negated_conjecture,
( subset_intersection2(the_carrier(esk129_0),esk130_0,the_carrier(esk129_0)) != esk130_0
| $false ),
inference(rw,[status(thm)],[4560,1854,theory(equality)]) ).
cnf(4562,negated_conjecture,
subset_intersection2(the_carrier(esk129_0),esk130_0,the_carrier(esk129_0)) != esk130_0,
inference(cn,[status(thm)],[4561,theory(equality)]) ).
cnf(4570,negated_conjecture,
subset(esk130_0,the_carrier(esk129_0)),
inference(spm,[status(thm)],[3333,1853,theory(equality)]) ).
cnf(93534,negated_conjecture,
( set_difference(esk130_0,set_difference(esk130_0,the_carrier(esk129_0))) != esk130_0
| ~ element(the_carrier(esk129_0),powerset(the_carrier(esk129_0)))
| ~ element(esk130_0,powerset(the_carrier(esk129_0))) ),
inference(spm,[status(thm)],[4562,4038,theory(equality)]) ).
cnf(93539,negated_conjecture,
( set_difference(esk130_0,set_difference(esk130_0,the_carrier(esk129_0))) != esk130_0
| $false
| ~ element(esk130_0,powerset(the_carrier(esk129_0))) ),
inference(rw,[status(thm)],[93534,3738,theory(equality)]) ).
cnf(93540,negated_conjecture,
( set_difference(esk130_0,set_difference(esk130_0,the_carrier(esk129_0))) != esk130_0
| $false
| $false ),
inference(rw,[status(thm)],[93539,1853,theory(equality)]) ).
cnf(93541,negated_conjecture,
set_difference(esk130_0,set_difference(esk130_0,the_carrier(esk129_0))) != esk130_0,
inference(cn,[status(thm)],[93540,theory(equality)]) ).
cnf(136046,plain,
( set_difference(esk130_0,empty_set) != esk130_0
| ~ subset(esk130_0,the_carrier(esk129_0)) ),
inference(spm,[status(thm)],[93541,1395,theory(equality)]) ).
cnf(136067,plain,
( $false
| ~ subset(esk130_0,the_carrier(esk129_0)) ),
inference(rw,[status(thm)],[136046,803,theory(equality)]) ).
cnf(136068,plain,
( $false
| $false ),
inference(rw,[status(thm)],[136067,4570,theory(equality)]) ).
cnf(136069,plain,
$false,
inference(cn,[status(thm)],[136068,theory(equality)]) ).
cnf(136070,plain,
$false,
136069,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU307+2.p
% --creating new selector for []
% -running prover on /tmp/tmp3vvcU6/sel_SEU307+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU307+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU307+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU307+2.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
%
%------------------------------------------------------------------------------