%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU146+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 04:52:07 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 9 unt; 0 def)
% Number of atoms : 146 ( 54 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 149 ( 53 ~; 70 |; 19 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 3 sgn 42 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpVaKAwa/sel_SEU146+1.p_1',d10_xboole_0) ).
fof(3,axiom,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
file('/tmp/tmpVaKAwa/sel_SEU146+1.p_1',l3_zfmisc_1) ).
fof(7,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/tmp/tmpVaKAwa/sel_SEU146+1.p_1',t37_xboole_1) ).
fof(8,axiom,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/tmp/tmpVaKAwa/sel_SEU146+1.p_1',l2_zfmisc_1) ).
fof(9,conjecture,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/tmp/tmpVaKAwa/sel_SEU146+1.p_1',l4_zfmisc_1) ).
fof(10,axiom,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/tmp/tmpVaKAwa/sel_SEU146+1.p_1',t3_xboole_1) ).
fof(13,axiom,
! [X1] : subset(empty_set,X1),
file('/tmp/tmpVaKAwa/sel_SEU146+1.p_1',t2_xboole_1) ).
fof(15,axiom,
! [X1,X2] : subset(X1,X1),
file('/tmp/tmpVaKAwa/sel_SEU146+1.p_1',reflexivity_r1_tarski) ).
fof(16,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
inference(assume_negation,[status(cth)],[9]) ).
fof(19,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(20,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[19]) ).
fof(21,plain,
! [X3,X4] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(distribute,[status(thm)],[20]) ).
cnf(22,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[21]) ).
fof(26,plain,
! [X1,X2,X3] :
( ~ subset(X1,X2)
| in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(27,plain,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| in(X6,X4)
| subset(X4,set_difference(X5,singleton(X6))) ),
inference(variable_rename,[status(thm)],[26]) ).
cnf(28,plain,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(34,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)],[7]) ).
fof(35,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)],[34]) ).
cnf(36,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[35]) ).
fof(38,plain,
! [X1,X2] :
( ( ~ subset(singleton(X1),X2)
| in(X1,X2) )
& ( ~ in(X1,X2)
| subset(singleton(X1),X2) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(39,plain,
! [X3,X4] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X3,X4)
| subset(singleton(X3),X4) ) ),
inference(variable_rename,[status(thm)],[38]) ).
cnf(40,plain,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[39]) ).
fof(42,negated_conjecture,
? [X1,X2] :
( ( ~ subset(X1,singleton(X2))
| ( X1 != empty_set
& X1 != singleton(X2) ) )
& ( subset(X1,singleton(X2))
| X1 = empty_set
| X1 = singleton(X2) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(43,negated_conjecture,
? [X3,X4] :
( ( ~ subset(X3,singleton(X4))
| ( X3 != empty_set
& X3 != singleton(X4) ) )
& ( subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,negated_conjecture,
( ( ~ subset(esk2_0,singleton(esk3_0))
| ( esk2_0 != empty_set
& esk2_0 != singleton(esk3_0) ) )
& ( subset(esk2_0,singleton(esk3_0))
| esk2_0 = empty_set
| esk2_0 = singleton(esk3_0) ) ),
inference(skolemize,[status(esa)],[43]) ).
fof(45,negated_conjecture,
( ( esk2_0 != empty_set
| ~ subset(esk2_0,singleton(esk3_0)) )
& ( esk2_0 != singleton(esk3_0)
| ~ subset(esk2_0,singleton(esk3_0)) )
& ( subset(esk2_0,singleton(esk3_0))
| esk2_0 = empty_set
| esk2_0 = singleton(esk3_0) ) ),
inference(distribute,[status(thm)],[44]) ).
cnf(46,negated_conjecture,
( esk2_0 = singleton(esk3_0)
| esk2_0 = empty_set
| subset(esk2_0,singleton(esk3_0)) ),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(47,negated_conjecture,
( ~ subset(esk2_0,singleton(esk3_0))
| esk2_0 != singleton(esk3_0) ),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(48,negated_conjecture,
( ~ subset(esk2_0,singleton(esk3_0))
| esk2_0 != empty_set ),
inference(split_conjunct,[status(thm)],[45]) ).
fof(49,plain,
! [X1] :
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(50,plain,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[49]) ).
cnf(51,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[50]) ).
fof(58,plain,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[13]) ).
cnf(59,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[58]) ).
fof(61,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[15]) ).
cnf(62,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[61]) ).
cnf(70,negated_conjecture,
( singleton(esk3_0) = esk2_0
| esk2_0 = empty_set
| ~ subset(singleton(esk3_0),esk2_0) ),
inference(spm,[status(thm)],[22,46,theory(equality)]) ).
cnf(75,plain,
( in(X1,X2)
| subset(X2,empty_set)
| ~ subset(X2,X3)
| ~ subset(X3,singleton(X1)) ),
inference(spm,[status(thm)],[28,36,theory(equality)]) ).
cnf(84,plain,
( in(X1,X2)
| subset(X2,empty_set)
| ~ subset(X2,singleton(X1)) ),
inference(spm,[status(thm)],[75,62,theory(equality)]) ).
cnf(86,plain,
( subset(singleton(X1),X2)
| subset(X2,empty_set)
| ~ subset(X2,singleton(X1)) ),
inference(spm,[status(thm)],[40,84,theory(equality)]) ).
cnf(101,negated_conjecture,
( subset(singleton(esk3_0),esk2_0)
| subset(esk2_0,empty_set)
| singleton(esk3_0) = esk2_0
| esk2_0 = empty_set ),
inference(spm,[status(thm)],[86,46,theory(equality)]) ).
cnf(104,negated_conjecture,
( singleton(esk3_0) = esk2_0
| esk2_0 = empty_set
| subset(singleton(esk3_0),esk2_0) ),
inference(csr,[status(thm)],[101,51]) ).
cnf(105,negated_conjecture,
( singleton(esk3_0) = esk2_0
| esk2_0 = empty_set ),
inference(csr,[status(thm)],[104,70]) ).
cnf(108,negated_conjecture,
( esk2_0 = empty_set
| ~ subset(esk2_0,esk2_0) ),
inference(spm,[status(thm)],[47,105,theory(equality)]) ).
cnf(119,negated_conjecture,
( esk2_0 = empty_set
| $false ),
inference(rw,[status(thm)],[108,62,theory(equality)]) ).
cnf(120,negated_conjecture,
esk2_0 = empty_set,
inference(cn,[status(thm)],[119,theory(equality)]) ).
cnf(126,negated_conjecture,
( $false
| ~ subset(esk2_0,singleton(esk3_0)) ),
inference(rw,[status(thm)],[48,120,theory(equality)]) ).
cnf(127,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[126,120,theory(equality)]),59,theory(equality)]) ).
cnf(128,negated_conjecture,
$false,
inference(cn,[status(thm)],[127,theory(equality)]) ).
cnf(129,negated_conjecture,
$false,
128,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU146+1.p
% --creating new selector for []
% -running prover on /tmp/tmpVaKAwa/sel_SEU146+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU146+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU146+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU146+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
%
%------------------------------------------------------------------------------