TSTP Solution File: SET873+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET873+1 : TPTP v5.0.0. Released v3.2.0.
% 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 03:42:23 EST 2010
% Result : Theorem 0.26s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 12 unt; 0 def)
% Number of atoms : 96 ( 54 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 103 ( 39 ~; 41 |; 18 &)
% ( 2 <=>; 3 =>; 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; 2 con; 0-2 aty)
% Number of variables : 53 ( 2 sgn 36 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2] :
( set_union2(singleton(X1),singleton(X2)) = singleton(X1)
=> X1 = X2 ),
file('/tmp/tmpL9JAmR/sel_SET873+1.p_1',t13_zfmisc_1) ).
fof(4,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/tmp/tmpL9JAmR/sel_SET873+1.p_1',commutativity_k2_xboole_0) ).
fof(6,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpL9JAmR/sel_SET873+1.p_1',d1_tarski) ).
fof(10,axiom,
! [X1,X2] :
( subset(set_union2(singleton(X1),X2),X2)
=> in(X1,X2) ),
file('/tmp/tmpL9JAmR/sel_SET873+1.p_1',l21_zfmisc_1) ).
fof(11,axiom,
! [X1,X2] : subset(X1,X1),
file('/tmp/tmpL9JAmR/sel_SET873+1.p_1',reflexivity_r1_tarski) ).
fof(12,negated_conjecture,
~ ! [X1,X2] :
( set_union2(singleton(X1),singleton(X2)) = singleton(X1)
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[1]) ).
fof(17,negated_conjecture,
? [X1,X2] :
( set_union2(singleton(X1),singleton(X2)) = singleton(X1)
& X1 != X2 ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(18,negated_conjecture,
? [X3,X4] :
( set_union2(singleton(X3),singleton(X4)) = singleton(X3)
& X3 != X4 ),
inference(variable_rename,[status(thm)],[17]) ).
fof(19,negated_conjecture,
( set_union2(singleton(esk1_0),singleton(esk2_0)) = singleton(esk1_0)
& esk1_0 != esk2_0 ),
inference(skolemize,[status(esa)],[18]) ).
cnf(20,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[19]) ).
cnf(21,negated_conjecture,
set_union2(singleton(esk1_0),singleton(esk2_0)) = singleton(esk1_0),
inference(split_conjunct,[status(thm)],[19]) ).
fof(28,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[4]) ).
cnf(29,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[28]) ).
fof(33,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)],[6]) ).
fof(34,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)],[33]) ).
fof(35,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)],[34]) ).
fof(36,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)],[35]) ).
fof(37,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)],[36]) ).
cnf(41,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(50,plain,
! [X1,X2] :
( ~ subset(set_union2(singleton(X1),X2),X2)
| in(X1,X2) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(51,plain,
! [X3,X4] :
( ~ subset(set_union2(singleton(X3),X4),X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[50]) ).
cnf(52,plain,
( in(X1,X2)
| ~ subset(set_union2(singleton(X1),X2),X2) ),
inference(split_conjunct,[status(thm)],[51]) ).
fof(53,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[11]) ).
cnf(54,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(70,plain,
( in(X1,X2)
| ~ subset(set_union2(X2,singleton(X1)),X2) ),
inference(spm,[status(thm)],[52,29,theory(equality)]) ).
cnf(91,negated_conjecture,
( in(esk2_0,singleton(esk1_0))
| ~ subset(singleton(esk1_0),singleton(esk1_0)) ),
inference(spm,[status(thm)],[70,21,theory(equality)]) ).
cnf(97,negated_conjecture,
( in(esk2_0,singleton(esk1_0))
| $false ),
inference(rw,[status(thm)],[91,54,theory(equality)]) ).
cnf(98,negated_conjecture,
in(esk2_0,singleton(esk1_0)),
inference(cn,[status(thm)],[97,theory(equality)]) ).
cnf(100,negated_conjecture,
( X1 = esk2_0
| singleton(X1) != singleton(esk1_0) ),
inference(spm,[status(thm)],[41,98,theory(equality)]) ).
cnf(103,negated_conjecture,
esk1_0 = esk2_0,
inference(er,[status(thm)],[100,theory(equality)]) ).
cnf(104,negated_conjecture,
$false,
inference(sr,[status(thm)],[103,20,theory(equality)]) ).
cnf(105,negated_conjecture,
$false,
104,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET873+1.p
% --creating new selector for []
% -running prover on /tmp/tmpL9JAmR/sel_SET873+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET873+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET873+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET873+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
%
%------------------------------------------------------------------------------