%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU321+2 : 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 07:15:28 EST 2010
% Result : Theorem 10.20s
% Output : CNFRefutation 10.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 11 unt; 0 def)
% Number of atoms : 138 ( 11 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 158 ( 63 ~; 50 |; 22 &)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 37 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(24,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,subset_complement(the_carrier(X1),X2))
<=> ~ in(X3,X2) ) ) ) ),
file('/tmp/tmp6Rw7MU/sel_SEU321+2.p_1',l40_tops_1) ).
fof(86,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/tmp/tmp6Rw7MU/sel_SEU321+2.p_1',fc4_relat_1) ).
fof(343,axiom,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
file('/tmp/tmp6Rw7MU/sel_SEU321+2.p_1',t54_subset_1) ).
fof(357,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/tmp/tmp6Rw7MU/sel_SEU321+2.p_1',fc1_struct_0) ).
fof(503,axiom,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
file('/tmp/tmp6Rw7MU/sel_SEU321+2.p_1',t50_subset_1) ).
fof(524,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,subset_complement(the_carrier(X1),X2))
<=> ~ in(X3,X2) ) ) ) ),
inference(assume_negation,[status(cth)],[24]) ).
fof(528,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,subset_complement(the_carrier(X1),X2))
<=> ~ in(X3,X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[524,theory(equality)]) ).
fof(576,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[357,theory(equality)]) ).
fof(597,plain,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[503,theory(equality)]) ).
fof(710,negated_conjecture,
? [X1] :
( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& ? [X3] :
( element(X3,the_carrier(X1))
& ( ~ in(X3,subset_complement(the_carrier(X1),X2))
| in(X3,X2) )
& ( in(X3,subset_complement(the_carrier(X1),X2))
| ~ in(X3,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[528]) ).
fof(711,negated_conjecture,
? [X4] :
( ~ empty_carrier(X4)
& one_sorted_str(X4)
& ? [X5] :
( element(X5,powerset(the_carrier(X4)))
& ? [X6] :
( element(X6,the_carrier(X4))
& ( ~ in(X6,subset_complement(the_carrier(X4),X5))
| in(X6,X5) )
& ( in(X6,subset_complement(the_carrier(X4),X5))
| ~ in(X6,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[710]) ).
fof(712,negated_conjecture,
( ~ empty_carrier(esk9_0)
& one_sorted_str(esk9_0)
& element(esk10_0,powerset(the_carrier(esk9_0)))
& element(esk11_0,the_carrier(esk9_0))
& ( ~ in(esk11_0,subset_complement(the_carrier(esk9_0),esk10_0))
| in(esk11_0,esk10_0) )
& ( in(esk11_0,subset_complement(the_carrier(esk9_0),esk10_0))
| ~ in(esk11_0,esk10_0) ) ),
inference(skolemize,[status(esa)],[711]) ).
cnf(713,negated_conjecture,
( in(esk11_0,subset_complement(the_carrier(esk9_0),esk10_0))
| ~ in(esk11_0,esk10_0) ),
inference(split_conjunct,[status(thm)],[712]) ).
cnf(714,negated_conjecture,
( in(esk11_0,esk10_0)
| ~ in(esk11_0,subset_complement(the_carrier(esk9_0),esk10_0)) ),
inference(split_conjunct,[status(thm)],[712]) ).
cnf(715,negated_conjecture,
element(esk11_0,the_carrier(esk9_0)),
inference(split_conjunct,[status(thm)],[712]) ).
cnf(716,negated_conjecture,
element(esk10_0,powerset(the_carrier(esk9_0))),
inference(split_conjunct,[status(thm)],[712]) ).
cnf(717,negated_conjecture,
one_sorted_str(esk9_0),
inference(split_conjunct,[status(thm)],[712]) ).
cnf(718,negated_conjecture,
~ empty_carrier(esk9_0),
inference(split_conjunct,[status(thm)],[712]) ).
cnf(1178,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[86]) ).
fof(2831,plain,
! [X1,X2,X3] :
( ~ element(X3,powerset(X1))
| ~ in(X2,subset_complement(X1,X3))
| ~ in(X2,X3) ),
inference(fof_nnf,[status(thm)],[343]) ).
fof(2832,plain,
! [X4,X5,X6] :
( ~ element(X6,powerset(X4))
| ~ in(X5,subset_complement(X4,X6))
| ~ in(X5,X6) ),
inference(variable_rename,[status(thm)],[2831]) ).
cnf(2833,plain,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X3,X2))
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[2832]) ).
fof(2897,plain,
! [X1] :
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(fof_nnf,[status(thm)],[576]) ).
fof(2898,plain,
! [X2] :
( empty_carrier(X2)
| ~ one_sorted_str(X2)
| ~ empty(the_carrier(X2)) ),
inference(variable_rename,[status(thm)],[2897]) ).
cnf(2899,plain,
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[2898]) ).
fof(3904,plain,
! [X1] :
( X1 = empty_set
| ! [X2] :
( ~ element(X2,powerset(X1))
| ! [X3] :
( ~ element(X3,X1)
| in(X3,X2)
| in(X3,subset_complement(X1,X2)) ) ) ),
inference(fof_nnf,[status(thm)],[597]) ).
fof(3905,plain,
! [X4] :
( X4 = empty_set
| ! [X5] :
( ~ element(X5,powerset(X4))
| ! [X6] :
( ~ element(X6,X4)
| in(X6,X5)
| in(X6,subset_complement(X4,X5)) ) ) ),
inference(variable_rename,[status(thm)],[3904]) ).
fof(3906,plain,
! [X4,X5,X6] :
( ~ element(X6,X4)
| in(X6,X5)
| in(X6,subset_complement(X4,X5))
| ~ element(X5,powerset(X4))
| X4 = empty_set ),
inference(shift_quantors,[status(thm)],[3905]) ).
cnf(3907,plain,
( X1 = empty_set
| in(X3,subset_complement(X1,X2))
| in(X3,X2)
| ~ element(X2,powerset(X1))
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[3906]) ).
cnf(4913,negated_conjecture,
( ~ one_sorted_str(esk9_0)
| ~ empty(the_carrier(esk9_0)) ),
inference(spm,[status(thm)],[718,2899,theory(equality)]) ).
cnf(4915,negated_conjecture,
( $false
| ~ empty(the_carrier(esk9_0)) ),
inference(rw,[status(thm)],[4913,717,theory(equality)]) ).
cnf(4916,negated_conjecture,
~ empty(the_carrier(esk9_0)),
inference(cn,[status(thm)],[4915,theory(equality)]) ).
cnf(6526,negated_conjecture,
( ~ in(esk11_0,esk10_0)
| ~ element(esk10_0,powerset(the_carrier(esk9_0))) ),
inference(spm,[status(thm)],[2833,713,theory(equality)]) ).
cnf(6543,negated_conjecture,
( ~ in(esk11_0,esk10_0)
| $false ),
inference(rw,[status(thm)],[6526,716,theory(equality)]) ).
cnf(6544,negated_conjecture,
~ in(esk11_0,esk10_0),
inference(cn,[status(thm)],[6543,theory(equality)]) ).
cnf(8878,plain,
( in(esk11_0,esk10_0)
| empty_set = the_carrier(esk9_0)
| ~ element(esk10_0,powerset(the_carrier(esk9_0)))
| ~ element(esk11_0,the_carrier(esk9_0)) ),
inference(spm,[status(thm)],[714,3907,theory(equality)]) ).
cnf(8895,plain,
( in(esk11_0,esk10_0)
| empty_set = the_carrier(esk9_0)
| $false
| ~ element(esk11_0,the_carrier(esk9_0)) ),
inference(rw,[status(thm)],[8878,716,theory(equality)]) ).
cnf(8896,plain,
( in(esk11_0,esk10_0)
| empty_set = the_carrier(esk9_0)
| $false
| $false ),
inference(rw,[status(thm)],[8895,715,theory(equality)]) ).
cnf(8897,plain,
( in(esk11_0,esk10_0)
| empty_set = the_carrier(esk9_0) ),
inference(cn,[status(thm)],[8896,theory(equality)]) ).
cnf(99789,plain,
the_carrier(esk9_0) = empty_set,
inference(sr,[status(thm)],[8897,6544,theory(equality)]) ).
cnf(100624,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[4916,99789,theory(equality)]),1178,theory(equality)]) ).
cnf(100625,negated_conjecture,
$false,
inference(cn,[status(thm)],[100624,theory(equality)]) ).
cnf(100626,negated_conjecture,
$false,
100625,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU321+2.p
% --creating new selector for []
% -running prover on /tmp/tmp6Rw7MU/sel_SEU321+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU321+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU321+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU321+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
%
%------------------------------------------------------------------------------