TSTP Solution File: SEU154+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU154+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 04:58:28 EST 2010
% Result : Theorem 0.33s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 11 unt; 0 def)
% Number of atoms : 236 ( 70 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 288 ( 104 ~; 118 |; 56 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 124 ( 3 sgn 78 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/tmp/tmpplrVXo/sel_SEU154+1.p_1',commutativity_k3_xboole_0) ).
fof(3,axiom,
! [X1] : subset(empty_set,X1),
file('/tmp/tmpplrVXo/sel_SEU154+1.p_1',t2_xboole_1) ).
fof(8,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/tmp/tmpplrVXo/sel_SEU154+1.p_1',d7_xboole_0) ).
fof(11,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpplrVXo/sel_SEU154+1.p_1',d1_tarski) ).
fof(13,conjecture,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/tmp/tmpplrVXo/sel_SEU154+1.p_1',l28_zfmisc_1) ).
fof(14,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/tmp/tmpplrVXo/sel_SEU154+1.p_1',d3_xboole_0) ).
fof(16,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpplrVXo/sel_SEU154+1.p_1',d3_tarski) ).
fof(19,negated_conjecture,
~ ! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(assume_negation,[status(cth)],[13]) ).
fof(21,negated_conjecture,
~ ! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[19,theory(equality)]) ).
fof(23,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(24,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[23]) ).
fof(27,plain,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[3]) ).
cnf(28,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[27]) ).
fof(40,plain,
! [X1,X2] :
( ( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set )
& ( set_intersection2(X1,X2) != empty_set
| disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(41,plain,
! [X3,X4] :
( ( ~ disjoint(X3,X4)
| set_intersection2(X3,X4) = empty_set )
& ( set_intersection2(X3,X4) != empty_set
| disjoint(X3,X4) ) ),
inference(variable_rename,[status(thm)],[40]) ).
cnf(42,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(48,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)],[11]) ).
fof(49,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)],[48]) ).
fof(50,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) != X4 )
& ( in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[49]) ).
fof(51,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) != X4 )
& ( in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[50]) ).
fof(52,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[51]) ).
cnf(56,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(60,negated_conjecture,
? [X1,X2] :
( ~ in(X1,X2)
& ~ disjoint(singleton(X1),X2) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(61,negated_conjecture,
? [X3,X4] :
( ~ in(X3,X4)
& ~ disjoint(singleton(X3),X4) ),
inference(variable_rename,[status(thm)],[60]) ).
fof(62,negated_conjecture,
( ~ in(esk4_0,esk5_0)
& ~ disjoint(singleton(esk4_0),esk5_0) ),
inference(skolemize,[status(esa)],[61]) ).
cnf(63,negated_conjecture,
~ disjoint(singleton(esk4_0),esk5_0),
inference(split_conjunct,[status(thm)],[62]) ).
cnf(64,negated_conjecture,
~ in(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[62]) ).
fof(65,plain,
! [X1,X2,X3] :
( ( X3 != set_intersection2(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_intersection2(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(66,plain,
! [X5,X6,X7] :
( ( X7 != set_intersection2(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_intersection2(X5,X6) ) ),
inference(variable_rename,[status(thm)],[65]) ).
fof(67,plain,
! [X5,X6,X7] :
( ( X7 != set_intersection2(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& in(X8,X6) ) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk6_3(X5,X6,X7),X7)
| ~ in(esk6_3(X5,X6,X7),X5)
| ~ in(esk6_3(X5,X6,X7),X6) )
& ( in(esk6_3(X5,X6,X7),X7)
| ( in(esk6_3(X5,X6,X7),X5)
& in(esk6_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(skolemize,[status(esa)],[66]) ).
fof(68,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_intersection2(X5,X6) )
& ( ( ( ~ in(esk6_3(X5,X6,X7),X7)
| ~ in(esk6_3(X5,X6,X7),X5)
| ~ in(esk6_3(X5,X6,X7),X6) )
& ( in(esk6_3(X5,X6,X7),X7)
| ( in(esk6_3(X5,X6,X7),X5)
& in(esk6_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[67]) ).
fof(69,plain,
! [X5,X6,X7,X8] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( in(X8,X6)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(esk6_3(X5,X6,X7),X7)
| ~ in(esk6_3(X5,X6,X7),X5)
| ~ in(esk6_3(X5,X6,X7),X6)
| X7 = set_intersection2(X5,X6) )
& ( in(esk6_3(X5,X6,X7),X5)
| in(esk6_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) )
& ( in(esk6_3(X5,X6,X7),X6)
| in(esk6_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) ) ),
inference(distribute,[status(thm)],[68]) ).
cnf(70,plain,
( X1 = set_intersection2(X2,X3)
| in(esk6_3(X2,X3,X1),X1)
| in(esk6_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[69]) ).
cnf(71,plain,
( X1 = set_intersection2(X2,X3)
| in(esk6_3(X2,X3,X1),X1)
| in(esk6_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[69]) ).
fof(79,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)],[16]) ).
fof(80,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)],[79]) ).
fof(81,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk7_2(X4,X5),X4)
& ~ in(esk7_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[80]) ).
fof(82,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk7_2(X4,X5),X4)
& ~ in(esk7_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[81]) ).
fof(83,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk7_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk7_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[82]) ).
cnf(86,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[83]) ).
cnf(95,plain,
( X1 = X2
| ~ in(X2,singleton(X1)) ),
inference(er,[status(thm)],[56,theory(equality)]) ).
cnf(99,plain,
( disjoint(X1,X2)
| set_intersection2(X2,X1) != empty_set ),
inference(spm,[status(thm)],[42,24,theory(equality)]) ).
cnf(104,plain,
( in(X1,X2)
| ~ in(X1,empty_set) ),
inference(spm,[status(thm)],[86,28,theory(equality)]) ).
cnf(152,plain,
( in(esk6_3(X1,X2,empty_set),X3)
| set_intersection2(X1,X2) = empty_set
| in(esk6_3(X1,X2,empty_set),X2) ),
inference(spm,[status(thm)],[104,70,theory(equality)]) ).
cnf(1302,plain,
( set_intersection2(X4,X5) = empty_set
| in(esk6_3(X4,X5,empty_set),X5) ),
inference(ef,[status(thm)],[152,theory(equality)]) ).
cnf(1359,plain,
( X1 = esk6_3(X2,singleton(X1),empty_set)
| set_intersection2(X2,singleton(X1)) = empty_set ),
inference(spm,[status(thm)],[95,1302,theory(equality)]) ).
cnf(1375,plain,
( set_intersection2(X1,singleton(X2)) = empty_set
| in(X2,empty_set)
| in(X2,X1) ),
inference(spm,[status(thm)],[71,1359,theory(equality)]) ).
cnf(2279,plain,
( set_intersection2(X1,singleton(X2)) = empty_set
| in(X2,X1) ),
inference(csr,[status(thm)],[1375,104]) ).
cnf(2289,plain,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
inference(spm,[status(thm)],[99,2279,theory(equality)]) ).
cnf(2352,negated_conjecture,
in(esk4_0,esk5_0),
inference(spm,[status(thm)],[63,2289,theory(equality)]) ).
cnf(2355,negated_conjecture,
$false,
inference(sr,[status(thm)],[2352,64,theory(equality)]) ).
cnf(2356,negated_conjecture,
$false,
2355,
[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/SEU154+1.p
% --creating new selector for []
% -running prover on /tmp/tmpplrVXo/sel_SEU154+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU154+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU154+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU154+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
%
%------------------------------------------------------------------------------