TSTP Solution File: SET927+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET927+1 : TPTP v5.0.0. Released v3.2.0.
% 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 03:48:02 EST 2010
% Result : Theorem 0.28s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 51 ( 9 unt; 0 def)
% Number of atoms : 164 ( 87 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 178 ( 65 ~; 82 |; 26 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 2 sgn 28 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmp6WWHsC/sel_SET927+1.p_1',commutativity_k2_tarski) ).
fof(5,conjecture,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
file('/tmp/tmp6WWHsC/sel_SET927+1.p_1',t70_zfmisc_1) ).
fof(6,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
file('/tmp/tmp6WWHsC/sel_SET927+1.p_1',l39_zfmisc_1) ).
fof(7,negated_conjecture,
~ ! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(10,negated_conjecture,
~ ! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(11,plain,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).
fof(15,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[2]) ).
cnf(16,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[15]) ).
fof(23,negated_conjecture,
? [X1,X2,X3] :
( ( set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
| in(X1,X3)
| ( ~ in(X2,X3)
& X1 != X2 ) )
& ( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
| ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(24,negated_conjecture,
? [X4,X5,X6] :
( ( set_difference(unordered_pair(X4,X5),X6) != singleton(X4)
| in(X4,X6)
| ( ~ in(X5,X6)
& X4 != X5 ) )
& ( set_difference(unordered_pair(X4,X5),X6) = singleton(X4)
| ( ~ in(X4,X6)
& ( in(X5,X6)
| X4 = X5 ) ) ) ),
inference(variable_rename,[status(thm)],[23]) ).
fof(25,negated_conjecture,
( ( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0)
| in(esk3_0,esk5_0)
| ( ~ in(esk4_0,esk5_0)
& esk3_0 != esk4_0 ) )
& ( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = singleton(esk3_0)
| ( ~ in(esk3_0,esk5_0)
& ( in(esk4_0,esk5_0)
| esk3_0 = esk4_0 ) ) ) ),
inference(skolemize,[status(esa)],[24]) ).
fof(26,negated_conjecture,
( ( ~ in(esk4_0,esk5_0)
| in(esk3_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0) )
& ( esk3_0 != esk4_0
| in(esk3_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0) )
& ( ~ in(esk3_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = singleton(esk3_0) )
& ( in(esk4_0,esk5_0)
| esk3_0 = esk4_0
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = singleton(esk3_0) ) ),
inference(distribute,[status(thm)],[25]) ).
cnf(27,negated_conjecture,
( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = singleton(esk3_0)
| esk3_0 = esk4_0
| in(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[26]) ).
cnf(28,negated_conjecture,
( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = singleton(esk3_0)
| ~ in(esk3_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[26]) ).
cnf(29,negated_conjecture,
( in(esk3_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0)
| esk3_0 != esk4_0 ),
inference(split_conjunct,[status(thm)],[26]) ).
cnf(30,negated_conjecture,
( in(esk3_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0)
| ~ in(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[26]) ).
fof(31,plain,
! [X1,X2,X3] :
( ( set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
| ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) )
& ( in(X1,X3)
| ( ~ in(X2,X3)
& X1 != X2 )
| set_difference(unordered_pair(X1,X2),X3) = singleton(X1) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(32,plain,
! [X4,X5,X6] :
( ( set_difference(unordered_pair(X4,X5),X6) != singleton(X4)
| ( ~ in(X4,X6)
& ( in(X5,X6)
| X4 = X5 ) ) )
& ( in(X4,X6)
| ( ~ in(X5,X6)
& X4 != X5 )
| set_difference(unordered_pair(X4,X5),X6) = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,plain,
! [X4,X5,X6] :
( ( ~ in(X4,X6)
| set_difference(unordered_pair(X4,X5),X6) != singleton(X4) )
& ( in(X5,X6)
| X4 = X5
| set_difference(unordered_pair(X4,X5),X6) != singleton(X4) )
& ( ~ in(X5,X6)
| in(X4,X6)
| set_difference(unordered_pair(X4,X5),X6) = singleton(X4) )
& ( X4 != X5
| in(X4,X6)
| set_difference(unordered_pair(X4,X5),X6) = singleton(X4) ) ),
inference(distribute,[status(thm)],[32]) ).
cnf(34,plain,
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
| in(X1,X3)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(35,plain,
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
| in(X1,X3)
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(36,plain,
( X1 = X2
| in(X2,X3)
| set_difference(unordered_pair(X1,X2),X3) != singleton(X1) ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(37,plain,
( set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(38,plain,
( set_difference(unordered_pair(X2,X1),X3) != singleton(X1)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[37,16,theory(equality)]) ).
cnf(40,negated_conjecture,
( esk3_0 = esk4_0
| set_difference(unordered_pair(esk4_0,esk3_0),esk5_0) = singleton(esk3_0)
| in(esk4_0,esk5_0) ),
inference(rw,[status(thm)],[27,16,theory(equality)]) ).
cnf(42,negated_conjecture,
( set_difference(unordered_pair(esk4_0,esk3_0),esk5_0) = singleton(esk3_0)
| ~ in(esk3_0,esk5_0) ),
inference(rw,[status(thm)],[28,16,theory(equality)]) ).
cnf(43,plain,
( set_difference(unordered_pair(X1,X1),X2) = singleton(X1)
| in(X1,X2) ),
inference(er,[status(thm)],[34,theory(equality)]) ).
cnf(44,negated_conjecture,
( in(esk3_0,esk5_0)
| esk3_0 != esk4_0
| set_difference(unordered_pair(esk4_0,esk3_0),esk5_0) != singleton(esk3_0) ),
inference(rw,[status(thm)],[29,16,theory(equality)]) ).
cnf(45,plain,
( X1 = X2
| in(X2,X3)
| set_difference(unordered_pair(X2,X1),X3) != singleton(X1) ),
inference(spm,[status(thm)],[36,16,theory(equality)]) ).
cnf(48,negated_conjecture,
( in(esk3_0,esk5_0)
| set_difference(unordered_pair(esk4_0,esk3_0),esk5_0) != singleton(esk3_0)
| ~ in(esk4_0,esk5_0) ),
inference(rw,[status(thm)],[30,16,theory(equality)]) ).
cnf(51,negated_conjecture,
( esk3_0 = esk4_0
| in(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[45,40,theory(equality)]) ).
cnf(53,negated_conjecture,
( set_difference(unordered_pair(X1,esk4_0),esk5_0) = singleton(X1)
| in(X1,esk5_0)
| esk3_0 = esk4_0 ),
inference(spm,[status(thm)],[35,51,theory(equality)]) ).
cnf(54,negated_conjecture,
( in(esk3_0,esk5_0)
| esk3_0 = esk4_0
| set_difference(unordered_pair(esk4_0,esk3_0),esk5_0) != singleton(esk3_0) ),
inference(spm,[status(thm)],[48,51,theory(equality)]) ).
cnf(55,negated_conjecture,
( in(esk3_0,esk5_0)
| set_difference(unordered_pair(esk4_0,esk3_0),esk5_0) != singleton(esk3_0) ),
inference(csr,[status(thm)],[54,44]) ).
cnf(59,negated_conjecture,
( set_difference(unordered_pair(esk4_0,X1),esk5_0) = singleton(X1)
| esk3_0 = esk4_0
| in(X1,esk5_0) ),
inference(spm,[status(thm)],[53,16,theory(equality)]) ).
cnf(69,negated_conjecture,
( in(esk3_0,esk5_0)
| esk3_0 = esk4_0 ),
inference(spm,[status(thm)],[55,59,theory(equality)]) ).
cnf(71,negated_conjecture,
( set_difference(unordered_pair(esk4_0,esk3_0),esk5_0) = singleton(esk3_0)
| esk3_0 = esk4_0 ),
inference(spm,[status(thm)],[42,69,theory(equality)]) ).
cnf(82,negated_conjecture,
( esk3_0 = esk4_0
| ~ in(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[38,71,theory(equality)]) ).
cnf(83,negated_conjecture,
esk3_0 = esk4_0,
inference(csr,[status(thm)],[82,69]) ).
cnf(93,negated_conjecture,
( in(esk4_0,esk5_0)
| set_difference(unordered_pair(esk4_0,esk3_0),esk5_0) != singleton(esk3_0) ),
inference(rw,[status(thm)],[55,83,theory(equality)]) ).
cnf(94,negated_conjecture,
( in(esk4_0,esk5_0)
| set_difference(unordered_pair(esk4_0,esk4_0),esk5_0) != singleton(esk3_0) ),
inference(rw,[status(thm)],[93,83,theory(equality)]) ).
cnf(95,negated_conjecture,
( in(esk4_0,esk5_0)
| set_difference(unordered_pair(esk4_0,esk4_0),esk5_0) != singleton(esk4_0) ),
inference(rw,[status(thm)],[94,83,theory(equality)]) ).
cnf(98,negated_conjecture,
( set_difference(unordered_pair(esk4_0,esk4_0),esk5_0) = singleton(esk3_0)
| ~ in(esk3_0,esk5_0) ),
inference(rw,[status(thm)],[42,83,theory(equality)]) ).
cnf(99,negated_conjecture,
( set_difference(unordered_pair(esk4_0,esk4_0),esk5_0) = singleton(esk4_0)
| ~ in(esk3_0,esk5_0) ),
inference(rw,[status(thm)],[98,83,theory(equality)]) ).
cnf(100,negated_conjecture,
( set_difference(unordered_pair(esk4_0,esk4_0),esk5_0) = singleton(esk4_0)
| ~ in(esk4_0,esk5_0) ),
inference(rw,[status(thm)],[99,83,theory(equality)]) ).
cnf(101,negated_conjecture,
set_difference(unordered_pair(esk4_0,esk4_0),esk5_0) = singleton(esk4_0),
inference(csr,[status(thm)],[100,43]) ).
cnf(104,negated_conjecture,
~ in(esk4_0,esk5_0),
inference(spm,[status(thm)],[37,101,theory(equality)]) ).
cnf(108,negated_conjecture,
( in(esk4_0,esk5_0)
| $false ),
inference(rw,[status(thm)],[95,101,theory(equality)]) ).
cnf(109,negated_conjecture,
in(esk4_0,esk5_0),
inference(cn,[status(thm)],[108,theory(equality)]) ).
cnf(110,negated_conjecture,
$false,
inference(sr,[status(thm)],[109,104,theory(equality)]) ).
cnf(111,negated_conjecture,
$false,
110,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET927+1.p
% --creating new selector for []
% -running prover on /tmp/tmp6WWHsC/sel_SET927+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET927+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET927+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET927+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
%
%------------------------------------------------------------------------------