TSTP Solution File: SEU147+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU147+3 : TPTP v5.0.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 04:52:32 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 166 ( 78 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 195 ( 70 ~; 90 |; 30 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 68 ( 2 sgn 43 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/tmp/tmpZ2SD7K/sel_SEU147+3.p_1',t3_xboole_1) ).
fof(4,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/tmp/tmpZ2SD7K/sel_SEU147+3.p_1',d1_zfmisc_1) ).
fof(5,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpZ2SD7K/sel_SEU147+3.p_1',d1_tarski) ).
fof(8,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/tmp/tmpZ2SD7K/sel_SEU147+3.p_1',t1_zfmisc_1) ).
fof(10,axiom,
! [X1,X2] : subset(X1,X1),
file('/tmp/tmpZ2SD7K/sel_SEU147+3.p_1',reflexivity_r1_tarski) ).
fof(11,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(assume_negation,[status(cth)],[8]) ).
fof(14,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(15,plain,
! [X1] :
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(16,plain,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[15]) ).
cnf(17,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[16]) ).
fof(27,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(28,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)],[27]) ).
fof(29,plain,
! [X4,X5] :
( ( X5 != powerset(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk3_2(X4,X5),X5)
| ~ subset(esk3_2(X4,X5),X4) )
& ( in(esk3_2(X4,X5),X5)
| subset(esk3_2(X4,X5),X4) ) )
| X5 = powerset(X4) ) ),
inference(skolemize,[status(esa)],[28]) ).
fof(30,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) )
| X5 != powerset(X4) )
& ( ( ( ~ in(esk3_2(X4,X5),X5)
| ~ subset(esk3_2(X4,X5),X4) )
& ( in(esk3_2(X4,X5),X5)
| subset(esk3_2(X4,X5),X4) ) )
| X5 = powerset(X4) ) ),
inference(shift_quantors,[status(thm)],[29]) ).
fof(31,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| subset(X6,X4)
| X5 != powerset(X4) )
& ( ~ subset(X6,X4)
| in(X6,X5)
| X5 != powerset(X4) )
& ( ~ in(esk3_2(X4,X5),X5)
| ~ subset(esk3_2(X4,X5),X4)
| X5 = powerset(X4) )
& ( in(esk3_2(X4,X5),X5)
| subset(esk3_2(X4,X5),X4)
| X5 = powerset(X4) ) ),
inference(distribute,[status(thm)],[30]) ).
cnf(32,plain,
( X1 = powerset(X2)
| subset(esk3_2(X2,X1),X2)
| in(esk3_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[31]) ).
cnf(33,plain,
( X1 = powerset(X2)
| ~ subset(esk3_2(X2,X1),X2)
| ~ in(esk3_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[31]) ).
fof(36,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(37,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)],[36]) ).
fof(38,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)],[37]) ).
fof(39,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)],[38]) ).
fof(40,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)],[39]) ).
cnf(43,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(44,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(51,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(split_conjunct,[status(thm)],[14]) ).
fof(53,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[10]) ).
cnf(54,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(61,plain,
( X1 = X2
| ~ in(X2,singleton(X1)) ),
inference(er,[status(thm)],[44,theory(equality)]) ).
cnf(63,plain,
( in(X1,X2)
| singleton(X1) != X2 ),
inference(er,[status(thm)],[43,theory(equality)]) ).
cnf(70,plain,
( X1 = esk3_2(X2,singleton(X1))
| powerset(X2) = singleton(X1)
| subset(esk3_2(X2,singleton(X1)),X2) ),
inference(spm,[status(thm)],[61,32,theory(equality)]) ).
cnf(71,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[63,theory(equality)]) ).
cnf(89,plain,
( empty_set = esk3_2(empty_set,singleton(X1))
| esk3_2(empty_set,singleton(X1)) = X1
| powerset(empty_set) = singleton(X1) ),
inference(spm,[status(thm)],[17,70,theory(equality)]) ).
cnf(127,plain,
( esk3_2(empty_set,singleton(X2)) = X2
| powerset(empty_set) = singleton(X2)
| empty_set != X2 ),
inference(ef,[status(thm)],[89,theory(equality)]) ).
cnf(151,plain,
( esk3_2(empty_set,singleton(empty_set)) = empty_set
| powerset(empty_set) = singleton(empty_set) ),
inference(er,[status(thm)],[127,theory(equality)]) ).
cnf(152,plain,
esk3_2(empty_set,singleton(empty_set)) = empty_set,
inference(sr,[status(thm)],[151,51,theory(equality)]) ).
cnf(154,plain,
( powerset(empty_set) = singleton(empty_set)
| ~ in(empty_set,singleton(empty_set))
| ~ subset(empty_set,empty_set) ),
inference(spm,[status(thm)],[33,152,theory(equality)]) ).
cnf(160,plain,
( powerset(empty_set) = singleton(empty_set)
| $false
| ~ subset(empty_set,empty_set) ),
inference(rw,[status(thm)],[154,71,theory(equality)]) ).
cnf(161,plain,
( powerset(empty_set) = singleton(empty_set)
| $false
| $false ),
inference(rw,[status(thm)],[160,54,theory(equality)]) ).
cnf(162,plain,
powerset(empty_set) = singleton(empty_set),
inference(cn,[status(thm)],[161,theory(equality)]) ).
cnf(163,plain,
$false,
inference(sr,[status(thm)],[162,51,theory(equality)]) ).
cnf(164,plain,
$false,
163,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU147+3.p
% --creating new selector for []
% -running prover on /tmp/tmpZ2SD7K/sel_SEU147+3.p_1 with time limit 29
% -prover status Theorem
% Problem SEU147+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU147+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU147+3.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
%
%------------------------------------------------------------------------------