TSTP Solution File: SEU144+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU144+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 04:51:42 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 6 unt; 0 def)
% Number of atoms : 141 ( 41 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 168 ( 63 ~; 71 |; 28 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 71 ( 0 sgn 40 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,conjecture,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/tmp/tmpSiCao3/sel_SEU144+1.p_1',l2_zfmisc_1) ).
fof(3,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpSiCao3/sel_SEU144+1.p_1',d1_tarski) ).
fof(5,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpSiCao3/sel_SEU144+1.p_1',d3_tarski) ).
fof(7,negated_conjecture,
~ ! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
inference(assume_negation,[status(cth)],[2]) ).
fof(10,negated_conjecture,
? [X1,X2] :
( ( ~ subset(singleton(X1),X2)
| ~ in(X1,X2) )
& ( subset(singleton(X1),X2)
| in(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(11,negated_conjecture,
? [X3,X4] :
( ( ~ subset(singleton(X3),X4)
| ~ in(X3,X4) )
& ( subset(singleton(X3),X4)
| in(X3,X4) ) ),
inference(variable_rename,[status(thm)],[10]) ).
fof(12,negated_conjecture,
( ( ~ subset(singleton(esk1_0),esk2_0)
| ~ in(esk1_0,esk2_0) )
& ( subset(singleton(esk1_0),esk2_0)
| in(esk1_0,esk2_0) ) ),
inference(skolemize,[status(esa)],[11]) ).
cnf(13,negated_conjecture,
( in(esk1_0,esk2_0)
| subset(singleton(esk1_0),esk2_0) ),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(14,negated_conjecture,
( ~ in(esk1_0,esk2_0)
| ~ subset(singleton(esk1_0),esk2_0) ),
inference(split_conjunct,[status(thm)],[12]) ).
fof(15,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)],[3]) ).
fof(16,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)],[15]) ).
fof(17,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) != X4 )
& ( in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[16]) ).
fof(18,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) != X4 )
& ( in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[17]) ).
fof(19,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[18]) ).
cnf(22,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(23,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[19]) ).
fof(27,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ in(X3,X1)
| in(X3,X2) ) )
& ( ? [X3] :
( in(X3,X1)
& ~ in(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(28,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ? [X7] :
( in(X7,X4)
& ~ in(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[27]) ).
fof(29,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk4_2(X4,X5),X4)
& ~ in(esk4_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[28]) ).
fof(30,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk4_2(X4,X5),X4)
& ~ in(esk4_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[29]) ).
fof(31,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk4_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk4_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[30]) ).
cnf(32,plain,
( subset(X1,X2)
| ~ in(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[31]) ).
cnf(33,plain,
( subset(X1,X2)
| in(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[31]) ).
cnf(34,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[31]) ).
cnf(41,plain,
( in(X1,X2)
| singleton(X1) != X2 ),
inference(er,[status(thm)],[22,theory(equality)]) ).
cnf(43,negated_conjecture,
( in(X1,esk2_0)
| in(esk1_0,esk2_0)
| ~ in(X1,singleton(esk1_0)) ),
inference(spm,[status(thm)],[34,13,theory(equality)]) ).
cnf(44,plain,
( X1 = X2
| ~ in(X2,singleton(X1)) ),
inference(er,[status(thm)],[23,theory(equality)]) ).
cnf(45,plain,
( X1 = esk4_2(singleton(X1),X2)
| subset(singleton(X1),X2) ),
inference(spm,[status(thm)],[44,33,theory(equality)]) ).
cnf(47,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[41,theory(equality)]) ).
cnf(49,negated_conjecture,
in(esk1_0,esk2_0),
inference(spm,[status(thm)],[43,47,theory(equality)]) ).
cnf(55,negated_conjecture,
( $false
| ~ subset(singleton(esk1_0),esk2_0) ),
inference(rw,[status(thm)],[14,49,theory(equality)]) ).
cnf(56,negated_conjecture,
~ subset(singleton(esk1_0),esk2_0),
inference(cn,[status(thm)],[55,theory(equality)]) ).
cnf(58,plain,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[32,45,theory(equality)]) ).
cnf(62,negated_conjecture,
subset(singleton(esk1_0),esk2_0),
inference(spm,[status(thm)],[58,49,theory(equality)]) ).
cnf(66,negated_conjecture,
$false,
inference(sr,[status(thm)],[62,56,theory(equality)]) ).
cnf(67,negated_conjecture,
$false,
66,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU144+1.p
% --creating new selector for []
% -running prover on /tmp/tmpSiCao3/sel_SEU144+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU144+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU144+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU144+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
%
%------------------------------------------------------------------------------