TSTP Solution File: SET916+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET916+1 : TPTP v5.0.0. Released v3.2.0.
% 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 03:51:26 EST 2010
% Result : Theorem 3.25s
% Output : CNFRefutation 3.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 6 unt; 0 def)
% Number of atoms : 253 ( 82 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 335 ( 130 ~; 127 |; 73 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 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 : 136 ( 4 sgn 81 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/tmp/tmpNPJwNR/sel_SET916+1.p_1',symmetry_r1_xboole_0) ).
fof(4,axiom,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/tmp/tmpNPJwNR/sel_SET916+1.p_1',t4_xboole_0) ).
fof(6,conjecture,
! [X1,X2,X3] :
~ ( ~ in(X1,X2)
& ~ in(X3,X2)
& ~ disjoint(unordered_pair(X1,X3),X2) ),
file('/tmp/tmpNPJwNR/sel_SET916+1.p_1',t57_zfmisc_1) ).
fof(9,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/tmp/tmpNPJwNR/sel_SET916+1.p_1',d3_xboole_0) ).
fof(11,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/tmp/tmpNPJwNR/sel_SET916+1.p_1',d2_tarski) ).
fof(12,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( ~ in(X1,X2)
& ~ in(X3,X2)
& ~ disjoint(unordered_pair(X1,X3),X2) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(13,plain,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[4,theory(equality)]) ).
fof(15,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( ~ in(X1,X2)
& ~ in(X3,X2)
& ~ disjoint(unordered_pair(X1,X3),X2) ),
inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).
fof(21,plain,
! [X1,X2] :
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(22,plain,
! [X3,X4] :
( ~ disjoint(X3,X4)
| disjoint(X4,X3) ),
inference(variable_rename,[status(thm)],[21]) ).
cnf(23,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,plain,
! [X1,X2] :
( ( disjoint(X1,X2)
| ? [X3] : in(X3,set_intersection2(X1,X2)) )
& ( ! [X3] : ~ in(X3,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(25,plain,
! [X4,X5] :
( ( disjoint(X4,X5)
| ? [X6] : in(X6,set_intersection2(X4,X5)) )
& ( ! [X7] : ~ in(X7,set_intersection2(X4,X5))
| ~ disjoint(X4,X5) ) ),
inference(variable_rename,[status(thm)],[24]) ).
fof(26,plain,
! [X4,X5] :
( ( disjoint(X4,X5)
| in(esk1_2(X4,X5),set_intersection2(X4,X5)) )
& ( ! [X7] : ~ in(X7,set_intersection2(X4,X5))
| ~ disjoint(X4,X5) ) ),
inference(skolemize,[status(esa)],[25]) ).
fof(27,plain,
! [X4,X5,X7] :
( ( ~ in(X7,set_intersection2(X4,X5))
| ~ disjoint(X4,X5) )
& ( disjoint(X4,X5)
| in(esk1_2(X4,X5),set_intersection2(X4,X5)) ) ),
inference(shift_quantors,[status(thm)],[26]) ).
cnf(28,plain,
( in(esk1_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(33,negated_conjecture,
? [X1,X2,X3] :
( ~ in(X1,X2)
& ~ in(X3,X2)
& ~ disjoint(unordered_pair(X1,X3),X2) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(34,negated_conjecture,
? [X4,X5,X6] :
( ~ in(X4,X5)
& ~ in(X6,X5)
& ~ disjoint(unordered_pair(X4,X6),X5) ),
inference(variable_rename,[status(thm)],[33]) ).
fof(35,negated_conjecture,
( ~ in(esk3_0,esk4_0)
& ~ in(esk5_0,esk4_0)
& ~ disjoint(unordered_pair(esk3_0,esk5_0),esk4_0) ),
inference(skolemize,[status(esa)],[34]) ).
cnf(36,negated_conjecture,
~ disjoint(unordered_pair(esk3_0,esk5_0),esk4_0),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(37,negated_conjecture,
~ in(esk5_0,esk4_0),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(38,negated_conjecture,
~ in(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[35]) ).
fof(44,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)],[9]) ).
fof(45,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)],[44]) ).
fof(46,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(esk7_3(X5,X6,X7),X7)
| ~ in(esk7_3(X5,X6,X7),X5)
| ~ in(esk7_3(X5,X6,X7),X6) )
& ( in(esk7_3(X5,X6,X7),X7)
| ( in(esk7_3(X5,X6,X7),X5)
& in(esk7_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(skolemize,[status(esa)],[45]) ).
fof(47,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(esk7_3(X5,X6,X7),X7)
| ~ in(esk7_3(X5,X6,X7),X5)
| ~ in(esk7_3(X5,X6,X7),X6) )
& ( in(esk7_3(X5,X6,X7),X7)
| ( in(esk7_3(X5,X6,X7),X5)
& in(esk7_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[46]) ).
fof(48,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(esk7_3(X5,X6,X7),X7)
| ~ in(esk7_3(X5,X6,X7),X5)
| ~ in(esk7_3(X5,X6,X7),X6)
| X7 = set_intersection2(X5,X6) )
& ( in(esk7_3(X5,X6,X7),X5)
| in(esk7_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) )
& ( in(esk7_3(X5,X6,X7),X6)
| in(esk7_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) ) ),
inference(distribute,[status(thm)],[47]) ).
cnf(53,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(54,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(58,plain,
! [X1,X2,X3] :
( ( X3 != unordered_pair(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| X4 = X1
| X4 = X2 )
& ( ( X4 != X1
& X4 != X2 )
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ( X4 != X1
& X4 != X2 ) )
& ( in(X4,X3)
| X4 = X1
| X4 = X2 ) )
| X3 = unordered_pair(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(59,plain,
! [X5,X6,X7] :
( ( X7 != unordered_pair(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ( X9 != X5
& X9 != X6 ) )
& ( in(X9,X7)
| X9 = X5
| X9 = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(variable_rename,[status(thm)],[58]) ).
fof(60,plain,
! [X5,X6,X7] :
( ( X7 != unordered_pair(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
| ( esk8_3(X5,X6,X7) != X5
& esk8_3(X5,X6,X7) != X6 ) )
& ( in(esk8_3(X5,X6,X7),X7)
| esk8_3(X5,X6,X7) = X5
| esk8_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(skolemize,[status(esa)],[59]) ).
fof(61,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) )
| X7 != unordered_pair(X5,X6) )
& ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
| ( esk8_3(X5,X6,X7) != X5
& esk8_3(X5,X6,X7) != X6 ) )
& ( in(esk8_3(X5,X6,X7),X7)
| esk8_3(X5,X6,X7) = X5
| esk8_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[60]) ).
fof(62,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6
| X7 != unordered_pair(X5,X6) )
& ( X8 != X5
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( X8 != X6
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( esk8_3(X5,X6,X7) != X5
| ~ in(esk8_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( esk8_3(X5,X6,X7) != X6
| ~ in(esk8_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( in(esk8_3(X5,X6,X7),X7)
| esk8_3(X5,X6,X7) = X5
| esk8_3(X5,X6,X7) = X6
| X7 = unordered_pair(X5,X6) ) ),
inference(distribute,[status(thm)],[61]) ).
cnf(68,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[62]) ).
cnf(78,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[53,theory(equality)]) ).
cnf(83,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[54,theory(equality)]) ).
cnf(88,plain,
( X1 = X2
| X3 = X2
| ~ in(X2,unordered_pair(X1,X3)) ),
inference(er,[status(thm)],[68,theory(equality)]) ).
cnf(170,plain,
( in(esk1_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(spm,[status(thm)],[78,28,theory(equality)]) ).
cnf(189,plain,
( X1 = esk1_2(X2,unordered_pair(X3,X1))
| X3 = esk1_2(X2,unordered_pair(X3,X1))
| disjoint(X2,unordered_pair(X3,X1)) ),
inference(spm,[status(thm)],[88,170,theory(equality)]) ).
cnf(194,plain,
( in(esk1_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(spm,[status(thm)],[83,28,theory(equality)]) ).
cnf(1419,plain,
( in(X2,X1)
| disjoint(X1,unordered_pair(X2,X3))
| esk1_2(X1,unordered_pair(X2,X3)) = X3 ),
inference(spm,[status(thm)],[194,189,theory(equality)]) ).
cnf(70163,plain,
( in(X3,X1)
| disjoint(X1,unordered_pair(X2,X3))
| in(X2,X1) ),
inference(spm,[status(thm)],[194,1419,theory(equality)]) ).
cnf(70857,plain,
( disjoint(unordered_pair(X1,X2),X3)
| in(X1,X3)
| in(X2,X3) ),
inference(spm,[status(thm)],[23,70163,theory(equality)]) ).
cnf(71263,negated_conjecture,
( in(esk5_0,esk4_0)
| in(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[36,70857,theory(equality)]) ).
cnf(71564,negated_conjecture,
in(esk3_0,esk4_0),
inference(sr,[status(thm)],[71263,37,theory(equality)]) ).
cnf(71565,negated_conjecture,
$false,
inference(sr,[status(thm)],[71564,38,theory(equality)]) ).
cnf(71566,negated_conjecture,
$false,
71565,
[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/SET/SET916+1.p
% --creating new selector for []
% -running prover on /tmp/tmpNPJwNR/sel_SET916+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET916+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET916+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET916+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
%
%------------------------------------------------------------------------------