%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU145+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 04:56:15 EST 2010
% Result : Theorem 6.33s
% Output : CNFRefutation 6.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 64 ( 8 unt; 0 def)
% Number of atoms : 275 ( 65 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 329 ( 118 ~; 143 |; 58 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 167 ( 7 sgn 70 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
file('/tmp/tmpCKLE2O/sel_SEU145+1.p_1',l3_zfmisc_1) ).
fof(4,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/tmp/tmpCKLE2O/sel_SEU145+1.p_1',d4_xboole_0) ).
fof(5,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpCKLE2O/sel_SEU145+1.p_1',d1_tarski) ).
fof(7,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpCKLE2O/sel_SEU145+1.p_1',d3_tarski) ).
fof(9,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(10,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[4,theory(equality)]) ).
fof(12,negated_conjecture,
? [X1,X2,X3] :
( subset(X1,X2)
& ~ in(X3,X1)
& ~ subset(X1,set_difference(X2,singleton(X3))) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(13,negated_conjecture,
? [X4,X5,X6] :
( subset(X4,X5)
& ~ in(X6,X4)
& ~ subset(X4,set_difference(X5,singleton(X6))) ),
inference(variable_rename,[status(thm)],[12]) ).
fof(14,negated_conjecture,
( subset(esk1_0,esk2_0)
& ~ in(esk3_0,esk1_0)
& ~ subset(esk1_0,set_difference(esk2_0,singleton(esk3_0))) ),
inference(skolemize,[status(esa)],[13]) ).
cnf(15,negated_conjecture,
~ subset(esk1_0,set_difference(esk2_0,singleton(esk3_0))),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(16,negated_conjecture,
~ in(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(17,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[14]) ).
fof(20,plain,
! [X1,X2,X3] :
( ( X3 != set_difference(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| ( in(X4,X1)
& ~ in(X4,X2) ) )
& ( ~ in(X4,X1)
| in(X4,X2)
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ~ in(X4,X1)
| in(X4,X2) )
& ( in(X4,X3)
| ( in(X4,X1)
& ~ in(X4,X2) ) ) )
| X3 = set_difference(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(21,plain,
! [X5,X6,X7] :
( ( X7 != set_difference(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& ~ in(X8,X6) ) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ~ in(X9,X5)
| in(X9,X6) )
& ( in(X9,X7)
| ( in(X9,X5)
& ~ in(X9,X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(variable_rename,[status(thm)],[20]) ).
fof(22,plain,
! [X5,X6,X7] :
( ( X7 != set_difference(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& ~ in(X8,X6) ) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk4_3(X5,X6,X7),X7)
| ~ in(esk4_3(X5,X6,X7),X5)
| in(esk4_3(X5,X6,X7),X6) )
& ( in(esk4_3(X5,X6,X7),X7)
| ( in(esk4_3(X5,X6,X7),X5)
& ~ in(esk4_3(X5,X6,X7),X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(skolemize,[status(esa)],[21]) ).
fof(23,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| ( in(X8,X5)
& ~ in(X8,X6) ) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7) ) )
| X7 != set_difference(X5,X6) )
& ( ( ( ~ in(esk4_3(X5,X6,X7),X7)
| ~ in(esk4_3(X5,X6,X7),X5)
| in(esk4_3(X5,X6,X7),X6) )
& ( in(esk4_3(X5,X6,X7),X7)
| ( in(esk4_3(X5,X6,X7),X5)
& ~ in(esk4_3(X5,X6,X7),X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[22]) ).
fof(24,plain,
! [X5,X6,X7,X8] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X8,X6)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(esk4_3(X5,X6,X7),X7)
| ~ in(esk4_3(X5,X6,X7),X5)
| in(esk4_3(X5,X6,X7),X6)
| X7 = set_difference(X5,X6) )
& ( in(esk4_3(X5,X6,X7),X5)
| in(esk4_3(X5,X6,X7),X7)
| X7 = set_difference(X5,X6) )
& ( ~ in(esk4_3(X5,X6,X7),X6)
| in(esk4_3(X5,X6,X7),X7)
| X7 = set_difference(X5,X6) ) ),
inference(distribute,[status(thm)],[23]) ).
cnf(26,plain,
( X1 = set_difference(X2,X3)
| in(esk4_3(X2,X3,X1),X1)
| in(esk4_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[24]) ).
cnf(27,plain,
( X1 = set_difference(X2,X3)
| in(esk4_3(X2,X3,X1),X3)
| ~ in(esk4_3(X2,X3,X1),X2)
| ~ in(esk4_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[24]) ).
cnf(28,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[24]) ).
cnf(29,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[24]) ).
cnf(30,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(31,plain,
! [X1,X2] :
( ( X2 != singleton(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1 )
& ( X3 != X1
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| X3 != X1 )
& ( in(X3,X2)
| X3 = X1 ) )
| X2 = singleton(X1) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(32,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| X7 != X4 )
& ( in(X7,X5)
| X7 = X4 ) )
| X5 = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) != X4 )
& ( in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[32]) ).
fof(34,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) != X4 )
& ( in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[33]) ).
fof(35,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[34]) ).
cnf(39,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[35]) ).
fof(43,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)],[7]) ).
fof(44,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)],[43]) ).
fof(45,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk6_2(X4,X5),X4)
& ~ in(esk6_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[44]) ).
fof(46,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk6_2(X4,X5),X4)
& ~ in(esk6_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[45]) ).
fof(47,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk6_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk6_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[46]) ).
cnf(48,plain,
( subset(X1,X2)
| ~ in(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[47]) ).
cnf(49,plain,
( subset(X1,X2)
| in(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[47]) ).
cnf(50,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[47]) ).
cnf(53,negated_conjecture,
( in(X1,esk2_0)
| ~ in(X1,esk1_0) ),
inference(spm,[status(thm)],[50,17,theory(equality)]) ).
cnf(57,plain,
( X1 = esk6_2(X2,X3)
| subset(X2,X3)
| singleton(X1) != X2 ),
inference(spm,[status(thm)],[39,49,theory(equality)]) ).
cnf(60,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[30,theory(equality)]) ).
cnf(61,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(er,[status(thm)],[29,theory(equality)]) ).
cnf(62,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[28,theory(equality)]) ).
cnf(66,plain,
( set_difference(X4,X5) = X4
| in(esk4_3(X4,X5,X4),X4) ),
inference(ef,[status(thm)],[26,theory(equality)]) ).
cnf(75,plain,
( subset(set_difference(X1,X2),X3)
| ~ in(esk6_2(set_difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[61,49,theory(equality)]) ).
cnf(81,negated_conjecture,
( subset(X1,esk2_0)
| ~ in(esk6_2(X1,esk2_0),esk1_0) ),
inference(spm,[status(thm)],[48,53,theory(equality)]) ).
cnf(90,plain,
( X1 = esk6_2(singleton(X1),X2)
| subset(singleton(X1),X2) ),
inference(er,[status(thm)],[57,theory(equality)]) ).
cnf(94,plain,
( in(esk6_2(set_difference(X1,X2),X3),X1)
| subset(set_difference(X1,X2),X3) ),
inference(spm,[status(thm)],[60,49,theory(equality)]) ).
cnf(107,plain,
( subset(X1,set_difference(X2,X3))
| in(esk6_2(X1,set_difference(X2,X3)),X3)
| ~ in(esk6_2(X1,set_difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[48,62,theory(equality)]) ).
cnf(152,plain,
( set_difference(X1,X2) = X1
| in(esk4_3(X1,X2,X1),X2)
| ~ in(esk4_3(X1,X2,X1),X1) ),
inference(spm,[status(thm)],[27,66,theory(equality)]) ).
cnf(166,negated_conjecture,
subset(set_difference(esk1_0,X1),esk2_0),
inference(spm,[status(thm)],[81,94,theory(equality)]) ).
cnf(192,negated_conjecture,
( in(X1,esk2_0)
| ~ in(X1,set_difference(esk1_0,X2)) ),
inference(spm,[status(thm)],[50,166,theory(equality)]) ).
cnf(193,negated_conjecture,
( in(esk6_2(set_difference(esk1_0,X1),X2),esk2_0)
| subset(set_difference(esk1_0,X1),X2) ),
inference(spm,[status(thm)],[192,49,theory(equality)]) ).
cnf(1040,plain,
( in(esk6_2(X1,set_difference(X1,X2)),X2)
| subset(X1,set_difference(X1,X2)) ),
inference(spm,[status(thm)],[107,49,theory(equality)]) ).
cnf(1045,negated_conjecture,
( in(esk6_2(set_difference(esk1_0,X1),set_difference(esk2_0,X2)),X2)
| subset(set_difference(esk1_0,X1),set_difference(esk2_0,X2)) ),
inference(spm,[status(thm)],[107,193,theory(equality)]) ).
cnf(1063,plain,
( in(X1,X2)
| subset(singleton(X1),set_difference(singleton(X1),X2)) ),
inference(spm,[status(thm)],[1040,90,theory(equality)]) ).
cnf(1163,plain,
( in(X1,set_difference(singleton(X2),X3))
| in(X2,X3)
| ~ in(X1,singleton(X2)) ),
inference(spm,[status(thm)],[50,1063,theory(equality)]) ).
cnf(1540,plain,
( subset(set_difference(X1,set_difference(singleton(X2),X3)),X4)
| in(X2,X3)
| ~ in(esk6_2(set_difference(X1,set_difference(singleton(X2),X3)),X4),singleton(X2)) ),
inference(spm,[status(thm)],[75,1163,theory(equality)]) ).
cnf(2358,plain,
( set_difference(X1,X2) = X1
| in(esk4_3(X1,X2,X1),X2) ),
inference(csr,[status(thm)],[152,66]) ).
cnf(2365,plain,
( set_difference(X1,set_difference(X2,X3)) = X1
| ~ in(esk4_3(X1,set_difference(X2,X3),X1),X3) ),
inference(spm,[status(thm)],[61,2358,theory(equality)]) ).
cnf(32812,negated_conjecture,
( in(X1,X2)
| subset(set_difference(esk1_0,set_difference(singleton(X1),X2)),set_difference(esk2_0,singleton(X1))) ),
inference(spm,[status(thm)],[1540,1045,theory(equality)]) ).
cnf(102040,plain,
set_difference(X1,set_difference(X2,X1)) = X1,
inference(spm,[status(thm)],[2365,66,theory(equality)]) ).
cnf(102730,negated_conjecture,
( in(X1,esk1_0)
| subset(esk1_0,set_difference(esk2_0,singleton(X1))) ),
inference(spm,[status(thm)],[32812,102040,theory(equality)]) ).
cnf(106065,negated_conjecture,
in(esk3_0,esk1_0),
inference(spm,[status(thm)],[15,102730,theory(equality)]) ).
cnf(106067,negated_conjecture,
$false,
inference(sr,[status(thm)],[106065,16,theory(equality)]) ).
cnf(106068,negated_conjecture,
$false,
106067,
[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/SEU145+1.p
% --creating new selector for []
% -running prover on /tmp/tmpCKLE2O/sel_SEU145+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU145+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU145+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU145+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
%
%------------------------------------------------------------------------------