%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU113+1 : TPTP v5.0.0. Released v3.2.0.
% 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 04:41:31 EST 2010
% Result : Theorem 1.52s
% Output : CNFRefutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 15 unt; 0 def)
% Number of atoms : 204 ( 21 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 256 ( 98 ~; 104 |; 47 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 89 ( 2 sgn 56 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(13,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/tmp/tmpc4qkCC/sel_SEU113+1.p_1',fc1_subset_1) ).
fof(19,conjecture,
! [X1] : subset(finite_subsets(X1),powerset(X1)),
file('/tmp/tmpc4qkCC/sel_SEU113+1.p_1',t26_finsub_1) ).
fof(22,axiom,
! [X1,X2] :
( preboolean(X2)
=> ( X2 = finite_subsets(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( subset(X3,X1)
& finite(X3) ) ) ) ),
file('/tmp/tmpc4qkCC/sel_SEU113+1.p_1',d5_finsub_1) ).
fof(23,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/tmp/tmpc4qkCC/sel_SEU113+1.p_1',t2_subset) ).
fof(24,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/tmp/tmpc4qkCC/sel_SEU113+1.p_1',t3_subset) ).
fof(25,axiom,
! [X1] :
( ~ empty(finite_subsets(X1))
& cup_closed(finite_subsets(X1))
& diff_closed(finite_subsets(X1))
& preboolean(finite_subsets(X1)) ),
file('/tmp/tmpc4qkCC/sel_SEU113+1.p_1',fc2_finsub_1) ).
fof(26,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpc4qkCC/sel_SEU113+1.p_1',d3_tarski) ).
fof(34,negated_conjecture,
~ ! [X1] : subset(finite_subsets(X1),powerset(X1)),
inference(assume_negation,[status(cth)],[19]) ).
fof(39,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[13,theory(equality)]) ).
fof(43,plain,
! [X1] :
( ~ empty(finite_subsets(X1))
& cup_closed(finite_subsets(X1))
& diff_closed(finite_subsets(X1))
& preboolean(finite_subsets(X1)) ),
inference(fof_simplification,[status(thm)],[25,theory(equality)]) ).
fof(102,plain,
! [X2] : ~ empty(powerset(X2)),
inference(variable_rename,[status(thm)],[39]) ).
cnf(103,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[102]) ).
fof(118,negated_conjecture,
? [X1] : ~ subset(finite_subsets(X1),powerset(X1)),
inference(fof_nnf,[status(thm)],[34]) ).
fof(119,negated_conjecture,
? [X2] : ~ subset(finite_subsets(X2),powerset(X2)),
inference(variable_rename,[status(thm)],[118]) ).
fof(120,negated_conjecture,
~ subset(finite_subsets(esk7_0),powerset(esk7_0)),
inference(skolemize,[status(esa)],[119]) ).
cnf(121,negated_conjecture,
~ subset(finite_subsets(esk7_0),powerset(esk7_0)),
inference(split_conjunct,[status(thm)],[120]) ).
fof(131,plain,
! [X1,X2] :
( ~ preboolean(X2)
| ( ( X2 != finite_subsets(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| ( subset(X3,X1)
& finite(X3) ) )
& ( ~ subset(X3,X1)
| ~ finite(X3)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ~ subset(X3,X1)
| ~ finite(X3) )
& ( in(X3,X2)
| ( subset(X3,X1)
& finite(X3) ) ) )
| X2 = finite_subsets(X1) ) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(132,plain,
! [X4,X5] :
( ~ preboolean(X5)
| ( ( X5 != finite_subsets(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| ( subset(X6,X4)
& finite(X6) ) )
& ( ~ subset(X6,X4)
| ~ finite(X6)
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| ~ subset(X7,X4)
| ~ finite(X7) )
& ( in(X7,X5)
| ( subset(X7,X4)
& finite(X7) ) ) )
| X5 = finite_subsets(X4) ) ) ),
inference(variable_rename,[status(thm)],[131]) ).
fof(133,plain,
! [X4,X5] :
( ~ preboolean(X5)
| ( ( X5 != finite_subsets(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| ( subset(X6,X4)
& finite(X6) ) )
& ( ~ subset(X6,X4)
| ~ finite(X6)
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk8_2(X4,X5),X5)
| ~ subset(esk8_2(X4,X5),X4)
| ~ finite(esk8_2(X4,X5)) )
& ( in(esk8_2(X4,X5),X5)
| ( subset(esk8_2(X4,X5),X4)
& finite(esk8_2(X4,X5)) ) ) )
| X5 = finite_subsets(X4) ) ) ),
inference(skolemize,[status(esa)],[132]) ).
fof(134,plain,
! [X4,X5,X6] :
( ( ( ( ( ~ in(X6,X5)
| ( subset(X6,X4)
& finite(X6) ) )
& ( ~ subset(X6,X4)
| ~ finite(X6)
| in(X6,X5) ) )
| X5 != finite_subsets(X4) )
& ( ( ( ~ in(esk8_2(X4,X5),X5)
| ~ subset(esk8_2(X4,X5),X4)
| ~ finite(esk8_2(X4,X5)) )
& ( in(esk8_2(X4,X5),X5)
| ( subset(esk8_2(X4,X5),X4)
& finite(esk8_2(X4,X5)) ) ) )
| X5 = finite_subsets(X4) ) )
| ~ preboolean(X5) ),
inference(shift_quantors,[status(thm)],[133]) ).
fof(135,plain,
! [X4,X5,X6] :
( ( subset(X6,X4)
| ~ in(X6,X5)
| X5 != finite_subsets(X4)
| ~ preboolean(X5) )
& ( finite(X6)
| ~ in(X6,X5)
| X5 != finite_subsets(X4)
| ~ preboolean(X5) )
& ( ~ subset(X6,X4)
| ~ finite(X6)
| in(X6,X5)
| X5 != finite_subsets(X4)
| ~ preboolean(X5) )
& ( ~ in(esk8_2(X4,X5),X5)
| ~ subset(esk8_2(X4,X5),X4)
| ~ finite(esk8_2(X4,X5))
| X5 = finite_subsets(X4)
| ~ preboolean(X5) )
& ( subset(esk8_2(X4,X5),X4)
| in(esk8_2(X4,X5),X5)
| X5 = finite_subsets(X4)
| ~ preboolean(X5) )
& ( finite(esk8_2(X4,X5))
| in(esk8_2(X4,X5),X5)
| X5 = finite_subsets(X4)
| ~ preboolean(X5) ) ),
inference(distribute,[status(thm)],[134]) ).
cnf(141,plain,
( subset(X3,X2)
| ~ preboolean(X1)
| X1 != finite_subsets(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[135]) ).
fof(142,plain,
! [X1,X2] :
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(143,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[142]) ).
cnf(144,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[143]) ).
fof(145,plain,
! [X1,X2] :
( ( ~ element(X1,powerset(X2))
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| element(X1,powerset(X2)) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(146,plain,
! [X3,X4] :
( ( ~ element(X3,powerset(X4))
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| element(X3,powerset(X4)) ) ),
inference(variable_rename,[status(thm)],[145]) ).
cnf(147,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[146]) ).
fof(149,plain,
! [X2] :
( ~ empty(finite_subsets(X2))
& cup_closed(finite_subsets(X2))
& diff_closed(finite_subsets(X2))
& preboolean(finite_subsets(X2)) ),
inference(variable_rename,[status(thm)],[43]) ).
cnf(150,plain,
preboolean(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[149]) ).
fof(154,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ in(X3,X1)
| in(X3,X2) ) )
& ( ? [X3] :
( in(X3,X1)
& ~ in(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(155,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ? [X7] :
( in(X7,X4)
& ~ in(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[154]) ).
fof(156,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk9_2(X4,X5),X4)
& ~ in(esk9_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[155]) ).
fof(157,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk9_2(X4,X5),X4)
& ~ in(esk9_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[156]) ).
fof(158,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk9_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk9_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[157]) ).
cnf(159,plain,
( subset(X1,X2)
| ~ in(esk9_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[158]) ).
cnf(160,plain,
( subset(X1,X2)
| in(esk9_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[158]) ).
cnf(239,plain,
( subset(esk9_2(X1,X2),X3)
| subset(X1,X2)
| finite_subsets(X3) != X1
| ~ preboolean(X1) ),
inference(spm,[status(thm)],[141,160,theory(equality)]) ).
cnf(478,plain,
( element(esk9_2(X1,X2),powerset(X3))
| subset(X1,X2)
| finite_subsets(X3) != X1
| ~ preboolean(X1) ),
inference(spm,[status(thm)],[147,239,theory(equality)]) ).
cnf(1458,plain,
( in(esk9_2(X1,X2),powerset(X3))
| empty(powerset(X3))
| subset(X1,X2)
| finite_subsets(X3) != X1
| ~ preboolean(X1) ),
inference(spm,[status(thm)],[144,478,theory(equality)]) ).
cnf(1463,plain,
( in(esk9_2(X1,X2),powerset(X3))
| subset(X1,X2)
| finite_subsets(X3) != X1
| ~ preboolean(X1) ),
inference(sr,[status(thm)],[1458,103,theory(equality)]) ).
cnf(21795,plain,
( subset(X1,powerset(X2))
| finite_subsets(X2) != X1
| ~ preboolean(X1) ),
inference(spm,[status(thm)],[159,1463,theory(equality)]) ).
cnf(21827,negated_conjecture,
~ preboolean(finite_subsets(esk7_0)),
inference(spm,[status(thm)],[121,21795,theory(equality)]) ).
cnf(21832,negated_conjecture,
$false,
inference(rw,[status(thm)],[21827,150,theory(equality)]) ).
cnf(21833,negated_conjecture,
$false,
inference(cn,[status(thm)],[21832,theory(equality)]) ).
cnf(21834,negated_conjecture,
$false,
21833,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU113+1.p
% --creating new selector for []
% -running prover on /tmp/tmpc4qkCC/sel_SEU113+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU113+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU113+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU113+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
%
%------------------------------------------------------------------------------