TSTP Solution File: SET881+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET881+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 03:43:12 EST 2010
% Result : Theorem 0.19s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 15 unt; 0 def)
% Number of atoms : 112 ( 76 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 136 ( 51 ~; 55 |; 27 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 61 ( 5 sgn 38 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( set_difference(singleton(X1),X2) = empty_set
<=> in(X1,X2) ),
file('/tmp/tmpCesMYd/sel_SET881+1.p_1',l36_zfmisc_1) ).
fof(2,conjecture,
! [X1,X2] : set_difference(singleton(X1),unordered_pair(X1,X2)) = empty_set,
file('/tmp/tmpCesMYd/sel_SET881+1.p_1',t22_zfmisc_1) ).
fof(4,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpCesMYd/sel_SET881+1.p_1',commutativity_k2_tarski) ).
fof(7,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/tmp/tmpCesMYd/sel_SET881+1.p_1',d2_tarski) ).
fof(9,negated_conjecture,
~ ! [X1,X2] : set_difference(singleton(X1),unordered_pair(X1,X2)) = empty_set,
inference(assume_negation,[status(cth)],[2]) ).
fof(12,plain,
! [X1,X2] :
( ( set_difference(singleton(X1),X2) != empty_set
| in(X1,X2) )
& ( ~ in(X1,X2)
| set_difference(singleton(X1),X2) = empty_set ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(13,plain,
! [X3,X4] :
( ( set_difference(singleton(X3),X4) != empty_set
| in(X3,X4) )
& ( ~ in(X3,X4)
| set_difference(singleton(X3),X4) = empty_set ) ),
inference(variable_rename,[status(thm)],[12]) ).
cnf(14,plain,
( set_difference(singleton(X1),X2) = empty_set
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[13]) ).
fof(16,negated_conjecture,
? [X1,X2] : set_difference(singleton(X1),unordered_pair(X1,X2)) != empty_set,
inference(fof_nnf,[status(thm)],[9]) ).
fof(17,negated_conjecture,
? [X3,X4] : set_difference(singleton(X3),unordered_pair(X3,X4)) != empty_set,
inference(variable_rename,[status(thm)],[16]) ).
fof(18,negated_conjecture,
set_difference(singleton(esk1_0),unordered_pair(esk1_0,esk2_0)) != empty_set,
inference(skolemize,[status(esa)],[17]) ).
cnf(19,negated_conjecture,
set_difference(singleton(esk1_0),unordered_pair(esk1_0,esk2_0)) != empty_set,
inference(split_conjunct,[status(thm)],[18]) ).
fof(23,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[4]) ).
cnf(24,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[23]) ).
fof(31,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)],[7]) ).
fof(32,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)],[31]) ).
fof(33,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(esk5_3(X5,X6,X7),X7)
| ( esk5_3(X5,X6,X7) != X5
& esk5_3(X5,X6,X7) != X6 ) )
& ( in(esk5_3(X5,X6,X7),X7)
| esk5_3(X5,X6,X7) = X5
| esk5_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(skolemize,[status(esa)],[32]) ).
fof(34,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(esk5_3(X5,X6,X7),X7)
| ( esk5_3(X5,X6,X7) != X5
& esk5_3(X5,X6,X7) != X6 ) )
& ( in(esk5_3(X5,X6,X7),X7)
| esk5_3(X5,X6,X7) = X5
| esk5_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[33]) ).
fof(35,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) )
& ( esk5_3(X5,X6,X7) != X5
| ~ in(esk5_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( esk5_3(X5,X6,X7) != X6
| ~ in(esk5_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( in(esk5_3(X5,X6,X7),X7)
| esk5_3(X5,X6,X7) = X5
| esk5_3(X5,X6,X7) = X6
| X7 = unordered_pair(X5,X6) ) ),
inference(distribute,[status(thm)],[34]) ).
cnf(39,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(43,plain,
( in(X1,X2)
| unordered_pair(X3,X1) != X2 ),
inference(er,[status(thm)],[39,theory(equality)]) ).
cnf(50,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[43,theory(equality)]) ).
cnf(53,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[50,24,theory(equality)]) ).
cnf(59,plain,
set_difference(singleton(X1),unordered_pair(X1,X2)) = empty_set,
inference(spm,[status(thm)],[14,53,theory(equality)]) ).
cnf(78,negated_conjecture,
$false,
inference(rw,[status(thm)],[19,59,theory(equality)]) ).
cnf(79,negated_conjecture,
$false,
inference(cn,[status(thm)],[78,theory(equality)]) ).
cnf(80,negated_conjecture,
$false,
79,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET881+1.p
% --creating new selector for []
% -running prover on /tmp/tmpCesMYd/sel_SET881+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET881+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET881+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET881+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
%
%------------------------------------------------------------------------------