TSTP Solution File: SEU148+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU148+3 : 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 04:52:47 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 116 ( 75 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 137 ( 53 ~; 55 |; 24 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 1 sgn 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,conjecture,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('/tmp/tmpKZarHh/sel_SEU148+3.p_1',t6_zfmisc_1) ).
fof(3,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/tmp/tmpKZarHh/sel_SEU148+3.p_1',l4_zfmisc_1) ).
fof(4,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpKZarHh/sel_SEU148+3.p_1',d1_tarski) ).
fof(5,axiom,
! [X1] : singleton(X1) != empty_set,
file('/tmp/tmpKZarHh/sel_SEU148+3.p_1',l1_zfmisc_1) ).
fof(10,negated_conjecture,
~ ! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[2]) ).
fof(16,negated_conjecture,
? [X1,X2] :
( subset(singleton(X1),singleton(X2))
& X1 != X2 ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(17,negated_conjecture,
? [X3,X4] :
( subset(singleton(X3),singleton(X4))
& X3 != X4 ),
inference(variable_rename,[status(thm)],[16]) ).
fof(18,negated_conjecture,
( subset(singleton(esk2_0),singleton(esk3_0))
& esk2_0 != esk3_0 ),
inference(skolemize,[status(esa)],[17]) ).
cnf(19,negated_conjecture,
esk2_0 != esk3_0,
inference(split_conjunct,[status(thm)],[18]) ).
cnf(20,negated_conjecture,
subset(singleton(esk2_0),singleton(esk3_0)),
inference(split_conjunct,[status(thm)],[18]) ).
fof(21,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)],[3]) ).
fof(22,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)],[21]) ).
fof(23,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)],[22]) ).
cnf(26,plain,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(27,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(28,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)],[27]) ).
fof(29,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)],[28]) ).
fof(30,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)],[29]) ).
fof(31,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)],[30]) ).
cnf(34,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[31]) ).
cnf(35,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[31]) ).
fof(36,plain,
! [X2] : singleton(X2) != empty_set,
inference(variable_rename,[status(thm)],[5]) ).
cnf(37,plain,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[36]) ).
cnf(47,plain,
( in(X1,X2)
| singleton(X1) != X2 ),
inference(er,[status(thm)],[34,theory(equality)]) ).
cnf(48,negated_conjecture,
( singleton(esk3_0) = singleton(esk2_0)
| empty_set = singleton(esk2_0) ),
inference(spm,[status(thm)],[26,20,theory(equality)]) ).
cnf(51,negated_conjecture,
singleton(esk3_0) = singleton(esk2_0),
inference(sr,[status(thm)],[48,37,theory(equality)]) ).
cnf(61,plain,
( X1 = X2
| singleton(X1) != X3
| singleton(X2) != X3 ),
inference(spm,[status(thm)],[35,47,theory(equality)]) ).
cnf(67,plain,
( X1 = X2
| singleton(X2) != singleton(X1) ),
inference(er,[status(thm)],[61,theory(equality)]) ).
cnf(70,negated_conjecture,
( X1 = esk3_0
| singleton(esk2_0) != singleton(X1) ),
inference(spm,[status(thm)],[67,51,theory(equality)]) ).
cnf(74,negated_conjecture,
esk2_0 = esk3_0,
inference(er,[status(thm)],[70,theory(equality)]) ).
cnf(75,negated_conjecture,
$false,
inference(sr,[status(thm)],[74,19,theory(equality)]) ).
cnf(76,negated_conjecture,
$false,
75,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU148+3.p
% --creating new selector for []
% -running prover on /tmp/tmpKZarHh/sel_SEU148+3.p_1 with time limit 29
% -prover status Theorem
% Problem SEU148+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU148+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU148+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
%
%------------------------------------------------------------------------------