TSTP Solution File: SET882+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET882+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 03:43:16 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 12 unt; 0 def)
% Number of atoms : 129 ( 78 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 154 ( 60 ~; 59 |; 29 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 41 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmp0srrwe/sel_SET882+1.p_1',commutativity_k2_tarski) ).
fof(3,conjecture,
! [X1,X2] :
( X1 != X2
=> set_difference(unordered_pair(X1,X2),singleton(X2)) = singleton(X1) ),
file('/tmp/tmp0srrwe/sel_SET882+1.p_1',t23_zfmisc_1) ).
fof(4,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmp0srrwe/sel_SET882+1.p_1',d1_tarski) ).
fof(7,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
file('/tmp/tmp0srrwe/sel_SET882+1.p_1',l39_zfmisc_1) ).
fof(8,negated_conjecture,
~ ! [X1,X2] :
( X1 != X2
=> set_difference(unordered_pair(X1,X2),singleton(X2)) = singleton(X1) ),
inference(assume_negation,[status(cth)],[3]) ).
fof(11,plain,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(15,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[2]) ).
cnf(16,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[15]) ).
fof(17,negated_conjecture,
? [X1,X2] :
( X1 != X2
& set_difference(unordered_pair(X1,X2),singleton(X2)) != singleton(X1) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(18,negated_conjecture,
? [X3,X4] :
( X3 != X4
& set_difference(unordered_pair(X3,X4),singleton(X4)) != singleton(X3) ),
inference(variable_rename,[status(thm)],[17]) ).
fof(19,negated_conjecture,
( esk2_0 != esk3_0
& set_difference(unordered_pair(esk2_0,esk3_0),singleton(esk3_0)) != singleton(esk2_0) ),
inference(skolemize,[status(esa)],[18]) ).
cnf(20,negated_conjecture,
set_difference(unordered_pair(esk2_0,esk3_0),singleton(esk3_0)) != singleton(esk2_0),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(21,negated_conjecture,
esk2_0 != esk3_0,
inference(split_conjunct,[status(thm)],[19]) ).
fof(22,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)],[4]) ).
fof(23,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)],[22]) ).
fof(24,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) != X4 )
& ( in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[23]) ).
fof(25,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) != X4 )
& ( in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[24]) ).
fof(26,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[25]) ).
cnf(29,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[26]) ).
cnf(30,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[26]) ).
fof(37,plain,
! [X1,X2,X3] :
( ( set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
| ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) )
& ( in(X1,X3)
| ( ~ in(X2,X3)
& X1 != X2 )
| set_difference(unordered_pair(X1,X2),X3) = singleton(X1) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(38,plain,
! [X4,X5,X6] :
( ( set_difference(unordered_pair(X4,X5),X6) != singleton(X4)
| ( ~ in(X4,X6)
& ( in(X5,X6)
| X4 = X5 ) ) )
& ( in(X4,X6)
| ( ~ in(X5,X6)
& X4 != X5 )
| set_difference(unordered_pair(X4,X5),X6) = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[37]) ).
fof(39,plain,
! [X4,X5,X6] :
( ( ~ in(X4,X6)
| set_difference(unordered_pair(X4,X5),X6) != singleton(X4) )
& ( in(X5,X6)
| X4 = X5
| set_difference(unordered_pair(X4,X5),X6) != singleton(X4) )
& ( ~ in(X5,X6)
| in(X4,X6)
| set_difference(unordered_pair(X4,X5),X6) = singleton(X4) )
& ( X4 != X5
| in(X4,X6)
| set_difference(unordered_pair(X4,X5),X6) = singleton(X4) ) ),
inference(distribute,[status(thm)],[38]) ).
cnf(41,plain,
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
| in(X1,X3)
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[39]) ).
cnf(46,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk2_0),singleton(esk3_0)) != singleton(esk2_0),
inference(rw,[status(thm)],[20,16,theory(equality)]) ).
cnf(50,plain,
( X1 = X2
| ~ in(X2,singleton(X1)) ),
inference(er,[status(thm)],[30,theory(equality)]) ).
cnf(53,plain,
( in(X1,X2)
| singleton(X1) != X2 ),
inference(er,[status(thm)],[29,theory(equality)]) ).
cnf(55,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[53,theory(equality)]) ).
cnf(57,plain,
( set_difference(unordered_pair(X1,X2),singleton(X2)) = singleton(X1)
| in(X1,singleton(X2)) ),
inference(spm,[status(thm)],[41,55,theory(equality)]) ).
cnf(66,plain,
( set_difference(unordered_pair(X2,X1),singleton(X2)) = singleton(X1)
| in(X1,singleton(X2)) ),
inference(spm,[status(thm)],[57,16,theory(equality)]) ).
cnf(77,negated_conjecture,
in(esk2_0,singleton(esk3_0)),
inference(spm,[status(thm)],[46,66,theory(equality)]) ).
cnf(87,negated_conjecture,
esk3_0 = esk2_0,
inference(spm,[status(thm)],[50,77,theory(equality)]) ).
cnf(92,negated_conjecture,
$false,
inference(rw,[status(thm)],[21,87,theory(equality)]) ).
cnf(93,negated_conjecture,
$false,
inference(cn,[status(thm)],[92,theory(equality)]) ).
cnf(94,negated_conjecture,
$false,
93,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET882+1.p
% --creating new selector for []
% -running prover on /tmp/tmp0srrwe/sel_SET882+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET882+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET882+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET882+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
%
%------------------------------------------------------------------------------