%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET889+1 : TPTP v5.0.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 03:44:01 EST 2010
% Result : Theorem 0.43s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 19 unt; 0 def)
% Number of atoms : 244 ( 144 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 287 ( 97 ~; 139 |; 46 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 121 ( 7 sgn 60 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1] : powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1)),
file('/tmp/tmpfxr7kR/sel_SET889+1.p_1',t30_zfmisc_1) ).
fof(4,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/tmp/tmpfxr7kR/sel_SET889+1.p_1',d1_zfmisc_1) ).
fof(5,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpfxr7kR/sel_SET889+1.p_1',commutativity_k2_tarski) ).
fof(6,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/tmp/tmpfxr7kR/sel_SET889+1.p_1',l4_zfmisc_1) ).
fof(9,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/tmp/tmpfxr7kR/sel_SET889+1.p_1',d2_tarski) ).
fof(11,axiom,
! [X1,X2] : subset(X1,X1),
file('/tmp/tmpfxr7kR/sel_SET889+1.p_1',reflexivity_r1_tarski) ).
fof(12,negated_conjecture,
~ ! [X1] : powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1)),
inference(assume_negation,[status(cth)],[1]) ).
fof(15,negated_conjecture,
? [X1] : powerset(singleton(X1)) != unordered_pair(empty_set,singleton(X1)),
inference(fof_nnf,[status(thm)],[12]) ).
fof(16,negated_conjecture,
? [X2] : powerset(singleton(X2)) != unordered_pair(empty_set,singleton(X2)),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,negated_conjecture,
powerset(singleton(esk1_0)) != unordered_pair(empty_set,singleton(esk1_0)),
inference(skolemize,[status(esa)],[16]) ).
cnf(18,negated_conjecture,
powerset(singleton(esk1_0)) != unordered_pair(empty_set,singleton(esk1_0)),
inference(split_conjunct,[status(thm)],[17]) ).
fof(28,plain,
! [X1,X2] :
( ( X2 != powerset(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| subset(X3,X1) )
& ( ~ subset(X3,X1)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ~ subset(X3,X1) )
& ( in(X3,X2)
| subset(X3,X1) ) )
| X2 = powerset(X1) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(29,plain,
! [X4,X5] :
( ( X5 != powerset(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| ~ subset(X7,X4) )
& ( in(X7,X5)
| subset(X7,X4) ) )
| X5 = powerset(X4) ) ),
inference(variable_rename,[status(thm)],[28]) ).
fof(30,plain,
! [X4,X5] :
( ( X5 != powerset(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk4_2(X4,X5),X5)
| ~ subset(esk4_2(X4,X5),X4) )
& ( in(esk4_2(X4,X5),X5)
| subset(esk4_2(X4,X5),X4) ) )
| X5 = powerset(X4) ) ),
inference(skolemize,[status(esa)],[29]) ).
fof(31,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) )
| X5 != powerset(X4) )
& ( ( ( ~ in(esk4_2(X4,X5),X5)
| ~ subset(esk4_2(X4,X5),X4) )
& ( in(esk4_2(X4,X5),X5)
| subset(esk4_2(X4,X5),X4) ) )
| X5 = powerset(X4) ) ),
inference(shift_quantors,[status(thm)],[30]) ).
fof(32,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| subset(X6,X4)
| X5 != powerset(X4) )
& ( ~ subset(X6,X4)
| in(X6,X5)
| X5 != powerset(X4) )
& ( ~ in(esk4_2(X4,X5),X5)
| ~ subset(esk4_2(X4,X5),X4)
| X5 = powerset(X4) )
& ( in(esk4_2(X4,X5),X5)
| subset(esk4_2(X4,X5),X4)
| X5 = powerset(X4) ) ),
inference(distribute,[status(thm)],[31]) ).
cnf(33,plain,
( X1 = powerset(X2)
| subset(esk4_2(X2,X1),X2)
| in(esk4_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(34,plain,
( X1 = powerset(X2)
| ~ subset(esk4_2(X2,X1),X2)
| ~ in(esk4_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[32]) ).
fof(37,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(38,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,plain,
! [X1,X2] :
( ( ~ subset(X1,singleton(X2))
| X1 = empty_set
| X1 = singleton(X2) )
& ( ( X1 != empty_set
& X1 != singleton(X2) )
| subset(X1,singleton(X2)) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(40,plain,
! [X3,X4] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( ( X3 != empty_set
& X3 != singleton(X4) )
| subset(X3,singleton(X4)) ) ),
inference(variable_rename,[status(thm)],[39]) ).
fof(41,plain,
! [X3,X4] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( X3 != empty_set
| subset(X3,singleton(X4)) )
& ( X3 != singleton(X4)
| subset(X3,singleton(X4)) ) ),
inference(distribute,[status(thm)],[40]) ).
cnf(43,plain,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[41]) ).
cnf(44,plain,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(51,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)],[9]) ).
fof(52,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)],[51]) ).
fof(53,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(esk6_3(X5,X6,X7),X7)
| ( esk6_3(X5,X6,X7) != X5
& esk6_3(X5,X6,X7) != X6 ) )
& ( in(esk6_3(X5,X6,X7),X7)
| esk6_3(X5,X6,X7) = X5
| esk6_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(skolemize,[status(esa)],[52]) ).
fof(54,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(esk6_3(X5,X6,X7),X7)
| ( esk6_3(X5,X6,X7) != X5
& esk6_3(X5,X6,X7) != X6 ) )
& ( in(esk6_3(X5,X6,X7),X7)
| esk6_3(X5,X6,X7) = X5
| esk6_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[53]) ).
fof(55,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) )
& ( esk6_3(X5,X6,X7) != X5
| ~ in(esk6_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( esk6_3(X5,X6,X7) != X6
| ~ in(esk6_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( in(esk6_3(X5,X6,X7),X7)
| esk6_3(X5,X6,X7) = X5
| esk6_3(X5,X6,X7) = X6
| X7 = unordered_pair(X5,X6) ) ),
inference(distribute,[status(thm)],[54]) ).
cnf(59,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(61,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[55]) ).
fof(63,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[11]) ).
cnf(64,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[63]) ).
cnf(67,plain,
( in(X1,X2)
| unordered_pair(X3,X1) != X2 ),
inference(er,[status(thm)],[59,theory(equality)]) ).
cnf(69,plain,
( X1 = X2
| X3 = X2
| ~ in(X2,unordered_pair(X1,X3)) ),
inference(er,[status(thm)],[61,theory(equality)]) ).
cnf(82,plain,
( singleton(X1) = esk4_2(singleton(X1),X2)
| empty_set = esk4_2(singleton(X1),X2)
| powerset(singleton(X1)) = X2
| in(esk4_2(singleton(X1),X2),X2) ),
inference(spm,[status(thm)],[44,33,theory(equality)]) ).
cnf(86,plain,
( powerset(singleton(X1)) = X2
| ~ in(esk4_2(singleton(X1),X2),X2)
| empty_set != esk4_2(singleton(X1),X2) ),
inference(spm,[status(thm)],[34,43,theory(equality)]) ).
cnf(98,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[67,theory(equality)]) ).
cnf(101,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[98,38,theory(equality)]) ).
cnf(195,plain,
( X1 = esk4_2(singleton(X2),unordered_pair(X3,X1))
| X3 = esk4_2(singleton(X2),unordered_pair(X3,X1))
| esk4_2(singleton(X2),unordered_pair(X3,X1)) = singleton(X2)
| esk4_2(singleton(X2),unordered_pair(X3,X1)) = empty_set
| powerset(singleton(X2)) = unordered_pair(X3,X1) ),
inference(spm,[status(thm)],[69,82,theory(equality)]) ).
cnf(704,plain,
( esk4_2(singleton(X7),unordered_pair(X8,X9)) = empty_set
| esk4_2(singleton(X7),unordered_pair(X8,X9)) = X8
| esk4_2(singleton(X7),unordered_pair(X8,X9)) = X9
| powerset(singleton(X7)) = unordered_pair(X8,X9)
| singleton(X7) != X8 ),
inference(ef,[status(thm)],[195,theory(equality)]) ).
cnf(2780,plain,
( esk4_2(singleton(X1),unordered_pair(singleton(X1),X2)) = empty_set
| esk4_2(singleton(X1),unordered_pair(singleton(X1),X2)) = X2
| esk4_2(singleton(X1),unordered_pair(singleton(X1),X2)) = singleton(X1)
| powerset(singleton(X1)) = unordered_pair(singleton(X1),X2) ),
inference(er,[status(thm)],[704,theory(equality)]) ).
cnf(2806,plain,
( powerset(singleton(X1)) = unordered_pair(singleton(X1),X2)
| esk4_2(singleton(X1),unordered_pair(singleton(X1),X2)) = empty_set
| esk4_2(singleton(X1),unordered_pair(singleton(X1),X2)) = X2
| ~ subset(singleton(X1),singleton(X1))
| ~ in(singleton(X1),unordered_pair(singleton(X1),X2)) ),
inference(spm,[status(thm)],[34,2780,theory(equality)]) ).
cnf(2829,plain,
( powerset(singleton(X1)) = unordered_pair(singleton(X1),X2)
| esk4_2(singleton(X1),unordered_pair(singleton(X1),X2)) = empty_set
| esk4_2(singleton(X1),unordered_pair(singleton(X1),X2)) = X2
| $false
| ~ in(singleton(X1),unordered_pair(singleton(X1),X2)) ),
inference(rw,[status(thm)],[2806,64,theory(equality)]) ).
cnf(2830,plain,
( powerset(singleton(X1)) = unordered_pair(singleton(X1),X2)
| esk4_2(singleton(X1),unordered_pair(singleton(X1),X2)) = empty_set
| esk4_2(singleton(X1),unordered_pair(singleton(X1),X2)) = X2
| $false
| $false ),
inference(rw,[status(thm)],[2829,101,theory(equality)]) ).
cnf(2831,plain,
( powerset(singleton(X1)) = unordered_pair(singleton(X1),X2)
| esk4_2(singleton(X1),unordered_pair(singleton(X1),X2)) = empty_set
| esk4_2(singleton(X1),unordered_pair(singleton(X1),X2)) = X2 ),
inference(cn,[status(thm)],[2830,theory(equality)]) ).
cnf(2852,plain,
( esk4_2(singleton(X5),unordered_pair(singleton(X5),X6)) = empty_set
| powerset(singleton(X5)) = unordered_pair(singleton(X5),X6)
| X6 != empty_set ),
inference(ef,[status(thm)],[2831,theory(equality)]) ).
cnf(2897,plain,
( powerset(singleton(X1)) = unordered_pair(singleton(X1),X2)
| ~ in(empty_set,unordered_pair(singleton(X1),X2))
| X2 != empty_set ),
inference(spm,[status(thm)],[86,2852,theory(equality)]) ).
cnf(2910,plain,
powerset(singleton(X1)) = unordered_pair(singleton(X1),empty_set),
inference(spm,[status(thm)],[2897,98,theory(equality)]) ).
cnf(2915,plain,
powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1)),
inference(rw,[status(thm)],[2910,38,theory(equality)]) ).
cnf(3003,negated_conjecture,
$false,
inference(rw,[status(thm)],[18,2915,theory(equality)]) ).
cnf(3004,negated_conjecture,
$false,
inference(cn,[status(thm)],[3003,theory(equality)]) ).
cnf(3005,negated_conjecture,
$false,
3004,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET889+1.p
% --creating new selector for []
% -running prover on /tmp/tmpfxr7kR/sel_SET889+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET889+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET889+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET889+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
%
%------------------------------------------------------------------------------