%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU309+1 : 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 07:10:13 EST 2010
% Result : Theorem 0.56s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 14 unt; 0 def)
% Number of atoms : 131 ( 43 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 143 ( 68 ~; 56 |; 9 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 82 ( 0 sgn 50 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(6,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/tmp/tmpsFIlkH/sel_SEU309+1.p_1',redefinition_k6_subset_1) ).
fof(7,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_difference(X1,X2,X3),powerset(X1)) ),
file('/tmp/tmpsFIlkH/sel_SEU309+1.p_1',dt_k6_subset_1) ).
fof(35,conjecture,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)) = X2 ) ),
file('/tmp/tmpsFIlkH/sel_SEU309+1.p_1',t22_pre_topc) ).
fof(41,axiom,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/tmp/tmpsFIlkH/sel_SEU309+1.p_1',t48_xboole_1) ).
fof(43,axiom,
! [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/tmpsFIlkH/sel_SEU309+1.p_1',t15_pre_topc) ).
fof(51,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/tmp/tmpsFIlkH/sel_SEU309+1.p_1',commutativity_k3_xboole_0) ).
fof(66,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3) ),
file('/tmp/tmpsFIlkH/sel_SEU309+1.p_1',redefinition_k5_subset_1) ).
fof(70,axiom,
! [X1] :
( one_sorted_str(X1)
=> element(cast_as_carrier_subset(X1),powerset(the_carrier(X1))) ),
file('/tmp/tmpsFIlkH/sel_SEU309+1.p_1',dt_k2_pre_topc) ).
fof(71,negated_conjecture,
~ ! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)) = X2 ) ),
inference(assume_negation,[status(cth)],[35]) ).
fof(90,plain,
! [X1,X2,X3] :
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(91,plain,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ element(X6,powerset(X4))
| subset_difference(X4,X5,X6) = set_difference(X5,X6) ),
inference(variable_rename,[status(thm)],[90]) ).
cnf(92,plain,
( subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[91]) ).
fof(93,plain,
! [X1,X2,X3] :
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| element(subset_difference(X1,X2,X3),powerset(X1)) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(94,plain,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ element(X6,powerset(X4))
| element(subset_difference(X4,X5,X6),powerset(X4)) ),
inference(variable_rename,[status(thm)],[93]) ).
cnf(95,plain,
( element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[94]) ).
fof(206,negated_conjecture,
? [X1] :
( one_sorted_str(X1)
& ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)) != X2 ) ),
inference(fof_nnf,[status(thm)],[71]) ).
fof(207,negated_conjecture,
? [X3] :
( one_sorted_str(X3)
& ? [X4] :
( element(X4,powerset(the_carrier(X3)))
& subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4)) != X4 ) ),
inference(variable_rename,[status(thm)],[206]) ).
fof(208,negated_conjecture,
( one_sorted_str(esk3_0)
& element(esk4_0,powerset(the_carrier(esk3_0)))
& subset_difference(the_carrier(esk3_0),cast_as_carrier_subset(esk3_0),subset_difference(the_carrier(esk3_0),cast_as_carrier_subset(esk3_0),esk4_0)) != esk4_0 ),
inference(skolemize,[status(esa)],[207]) ).
cnf(209,negated_conjecture,
subset_difference(the_carrier(esk3_0),cast_as_carrier_subset(esk3_0),subset_difference(the_carrier(esk3_0),cast_as_carrier_subset(esk3_0),esk4_0)) != esk4_0,
inference(split_conjunct,[status(thm)],[208]) ).
cnf(210,negated_conjecture,
element(esk4_0,powerset(the_carrier(esk3_0))),
inference(split_conjunct,[status(thm)],[208]) ).
cnf(211,negated_conjecture,
one_sorted_str(esk3_0),
inference(split_conjunct,[status(thm)],[208]) ).
fof(240,plain,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[41]) ).
cnf(241,plain,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[240]) ).
fof(249,plain,
! [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)],[43]) ).
fof(250,plain,
! [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)],[249]) ).
fof(251,plain,
! [X3,X4] :
( ~ element(X4,powerset(the_carrier(X3)))
| subset_intersection2(the_carrier(X3),X4,cast_as_carrier_subset(X3)) = X4
| ~ one_sorted_str(X3) ),
inference(shift_quantors,[status(thm)],[250]) ).
cnf(252,plain,
( subset_intersection2(the_carrier(X1),X2,cast_as_carrier_subset(X1)) = X2
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[251]) ).
fof(282,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[51]) ).
cnf(283,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[282]) ).
fof(339,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)],[66]) ).
fof(340,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)],[339]) ).
cnf(341,plain,
( subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[340]) ).
fof(363,plain,
! [X1] :
( ~ one_sorted_str(X1)
| element(cast_as_carrier_subset(X1),powerset(the_carrier(X1))) ),
inference(fof_nnf,[status(thm)],[70]) ).
fof(364,plain,
! [X2] :
( ~ one_sorted_str(X2)
| element(cast_as_carrier_subset(X2),powerset(the_carrier(X2))) ),
inference(variable_rename,[status(thm)],[363]) ).
cnf(365,plain,
( element(cast_as_carrier_subset(X1),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[364]) ).
cnf(368,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[283,241,theory(equality)]),241,theory(equality)]),
[unfolding] ).
cnf(399,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)],[341,241,theory(equality)]),
[unfolding] ).
cnf(1035,negated_conjecture,
( subset_difference(the_carrier(esk3_0),cast_as_carrier_subset(esk3_0),set_difference(cast_as_carrier_subset(esk3_0),esk4_0)) != esk4_0
| ~ element(esk4_0,powerset(the_carrier(esk3_0)))
| ~ element(cast_as_carrier_subset(esk3_0),powerset(the_carrier(esk3_0))) ),
inference(spm,[status(thm)],[209,92,theory(equality)]) ).
cnf(1037,plain,
( element(set_difference(X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(spm,[status(thm)],[95,92,theory(equality)]) ).
cnf(1038,negated_conjecture,
( subset_difference(the_carrier(esk3_0),cast_as_carrier_subset(esk3_0),set_difference(cast_as_carrier_subset(esk3_0),esk4_0)) != esk4_0
| $false
| ~ element(cast_as_carrier_subset(esk3_0),powerset(the_carrier(esk3_0))) ),
inference(rw,[status(thm)],[1035,210,theory(equality)]) ).
cnf(1039,negated_conjecture,
( subset_difference(the_carrier(esk3_0),cast_as_carrier_subset(esk3_0),set_difference(cast_as_carrier_subset(esk3_0),esk4_0)) != esk4_0
| ~ element(cast_as_carrier_subset(esk3_0),powerset(the_carrier(esk3_0))) ),
inference(cn,[status(thm)],[1038,theory(equality)]) ).
cnf(1067,plain,
( set_difference(X2,set_difference(X2,cast_as_carrier_subset(X1))) = X2
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(cast_as_carrier_subset(X1),powerset(the_carrier(X1))) ),
inference(spm,[status(thm)],[252,399,theory(equality)]) ).
cnf(2060,negated_conjecture,
( set_difference(cast_as_carrier_subset(esk3_0),set_difference(cast_as_carrier_subset(esk3_0),esk4_0)) != esk4_0
| ~ element(cast_as_carrier_subset(esk3_0),powerset(the_carrier(esk3_0)))
| ~ element(set_difference(cast_as_carrier_subset(esk3_0),esk4_0),powerset(the_carrier(esk3_0))) ),
inference(spm,[status(thm)],[1039,92,theory(equality)]) ).
cnf(2064,negated_conjecture,
( set_difference(esk4_0,set_difference(esk4_0,cast_as_carrier_subset(esk3_0))) != esk4_0
| ~ element(cast_as_carrier_subset(esk3_0),powerset(the_carrier(esk3_0)))
| ~ element(set_difference(cast_as_carrier_subset(esk3_0),esk4_0),powerset(the_carrier(esk3_0))) ),
inference(rw,[status(thm)],[2060,368,theory(equality)]) ).
cnf(2803,negated_conjecture,
( set_difference(esk4_0,set_difference(esk4_0,cast_as_carrier_subset(esk3_0))) != esk4_0
| ~ element(cast_as_carrier_subset(esk3_0),powerset(the_carrier(esk3_0)))
| ~ element(esk4_0,powerset(the_carrier(esk3_0))) ),
inference(spm,[status(thm)],[2064,1037,theory(equality)]) ).
cnf(2807,negated_conjecture,
( set_difference(esk4_0,set_difference(esk4_0,cast_as_carrier_subset(esk3_0))) != esk4_0
| ~ element(cast_as_carrier_subset(esk3_0),powerset(the_carrier(esk3_0)))
| $false ),
inference(rw,[status(thm)],[2803,210,theory(equality)]) ).
cnf(2808,negated_conjecture,
( set_difference(esk4_0,set_difference(esk4_0,cast_as_carrier_subset(esk3_0))) != esk4_0
| ~ element(cast_as_carrier_subset(esk3_0),powerset(the_carrier(esk3_0))) ),
inference(cn,[status(thm)],[2807,theory(equality)]) ).
cnf(2810,negated_conjecture,
( set_difference(esk4_0,set_difference(esk4_0,cast_as_carrier_subset(esk3_0))) != esk4_0
| ~ one_sorted_str(esk3_0) ),
inference(spm,[status(thm)],[2808,365,theory(equality)]) ).
cnf(2814,negated_conjecture,
( set_difference(esk4_0,set_difference(esk4_0,cast_as_carrier_subset(esk3_0))) != esk4_0
| $false ),
inference(rw,[status(thm)],[2810,211,theory(equality)]) ).
cnf(2815,negated_conjecture,
set_difference(esk4_0,set_difference(esk4_0,cast_as_carrier_subset(esk3_0))) != esk4_0,
inference(cn,[status(thm)],[2814,theory(equality)]) ).
cnf(7562,plain,
( set_difference(X2,set_difference(X2,cast_as_carrier_subset(X1))) = X2
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(csr,[status(thm)],[1067,365]) ).
cnf(7563,negated_conjecture,
( set_difference(esk4_0,set_difference(esk4_0,cast_as_carrier_subset(esk3_0))) = esk4_0
| ~ one_sorted_str(esk3_0) ),
inference(spm,[status(thm)],[7562,210,theory(equality)]) ).
cnf(7574,negated_conjecture,
( set_difference(esk4_0,set_difference(esk4_0,cast_as_carrier_subset(esk3_0))) = esk4_0
| $false ),
inference(rw,[status(thm)],[7563,211,theory(equality)]) ).
cnf(7575,negated_conjecture,
set_difference(esk4_0,set_difference(esk4_0,cast_as_carrier_subset(esk3_0))) = esk4_0,
inference(cn,[status(thm)],[7574,theory(equality)]) ).
cnf(7576,negated_conjecture,
$false,
inference(sr,[status(thm)],[7575,2815,theory(equality)]) ).
cnf(7577,negated_conjecture,
$false,
7576,
[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/SEU309+1.p
% --creating new selector for []
% -running prover on /tmp/tmpsFIlkH/sel_SEU309+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU309+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU309+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU309+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
%
%------------------------------------------------------------------------------