TSTP Solution File: SEU212+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU212+3 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 05:39:52 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 51 ( 10 unt; 0 def)
% Number of atoms : 267 ( 77 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 351 ( 135 ~; 148 |; 51 &)
% ( 8 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 94 ( 2 sgn 56 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
file('/tmp/tmplfQGqf/sel_SEU212+3.p_1',d4_funct_1) ).
fof(21,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/tmp/tmplfQGqf/sel_SEU212+3.p_1',d4_relat_1) ).
fof(23,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
file('/tmp/tmplfQGqf/sel_SEU212+3.p_1',t8_funct_1) ).
fof(29,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmplfQGqf/sel_SEU212+3.p_1',d5_tarski) ).
fof(36,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
inference(assume_negation,[status(cth)],[23]) ).
fof(37,plain,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).
fof(51,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ! [X2,X3] :
( ( ~ in(X2,relation_dom(X1))
| ( ( X3 != apply(X1,X2)
| in(ordered_pair(X2,X3),X1) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X3 = apply(X1,X2) ) ) )
& ( in(X2,relation_dom(X1))
| ( ( X3 != apply(X1,X2)
| X3 = empty_set )
& ( X3 != empty_set
| X3 = apply(X1,X2) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(52,plain,
! [X4] :
( ~ relation(X4)
| ~ function(X4)
| ! [X5,X6] :
( ( ~ in(X5,relation_dom(X4))
| ( ( X6 != apply(X4,X5)
| in(ordered_pair(X5,X6),X4) )
& ( ~ in(ordered_pair(X5,X6),X4)
| X6 = apply(X4,X5) ) ) )
& ( in(X5,relation_dom(X4))
| ( ( X6 != apply(X4,X5)
| X6 = empty_set )
& ( X6 != empty_set
| X6 = apply(X4,X5) ) ) ) ) ),
inference(variable_rename,[status(thm)],[51]) ).
fof(53,plain,
! [X4,X5,X6] :
( ( ( ~ in(X5,relation_dom(X4))
| ( ( X6 != apply(X4,X5)
| in(ordered_pair(X5,X6),X4) )
& ( ~ in(ordered_pair(X5,X6),X4)
| X6 = apply(X4,X5) ) ) )
& ( in(X5,relation_dom(X4))
| ( ( X6 != apply(X4,X5)
| X6 = empty_set )
& ( X6 != empty_set
| X6 = apply(X4,X5) ) ) ) )
| ~ relation(X4)
| ~ function(X4) ),
inference(shift_quantors,[status(thm)],[52]) ).
fof(54,plain,
! [X4,X5,X6] :
( ( X6 != apply(X4,X5)
| in(ordered_pair(X5,X6),X4)
| ~ in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( ~ in(ordered_pair(X5,X6),X4)
| X6 = apply(X4,X5)
| ~ in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( X6 != apply(X4,X5)
| X6 = empty_set
| in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( X6 != empty_set
| X6 = apply(X4,X5)
| in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[53]) ).
cnf(57,plain,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[54]) ).
cnf(58,plain,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
inference(split_conjunct,[status(thm)],[54]) ).
fof(115,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ( X2 != relation_dom(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] : in(ordered_pair(X3,X4),X1) )
& ( ! [X4] : ~ in(ordered_pair(X3,X4),X1)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] : ~ in(ordered_pair(X3,X4),X1) )
& ( in(X3,X2)
| ? [X4] : in(ordered_pair(X3,X4),X1) ) )
| X2 = relation_dom(X1) ) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(116,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_dom(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ? [X8] : in(ordered_pair(X7,X8),X5) )
& ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) ) ) )
& ( ? [X10] :
( ( ~ in(X10,X6)
| ! [X11] : ~ in(ordered_pair(X10,X11),X5) )
& ( in(X10,X6)
| ? [X12] : in(ordered_pair(X10,X12),X5) ) )
| X6 = relation_dom(X5) ) ) ),
inference(variable_rename,[status(thm)],[115]) ).
fof(117,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_dom(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| in(ordered_pair(X7,esk6_3(X5,X6,X7)),X5) )
& ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk7_2(X5,X6),X6)
| ! [X11] : ~ in(ordered_pair(esk7_2(X5,X6),X11),X5) )
& ( in(esk7_2(X5,X6),X6)
| in(ordered_pair(esk7_2(X5,X6),esk8_2(X5,X6)),X5) ) )
| X6 = relation_dom(X5) ) ) ),
inference(skolemize,[status(esa)],[116]) ).
fof(118,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ( ~ in(ordered_pair(esk7_2(X5,X6),X11),X5)
| ~ in(esk7_2(X5,X6),X6) )
& ( in(esk7_2(X5,X6),X6)
| in(ordered_pair(esk7_2(X5,X6),esk8_2(X5,X6)),X5) ) )
| X6 = relation_dom(X5) )
& ( ( ( ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) )
& ( ~ in(X7,X6)
| in(ordered_pair(X7,esk6_3(X5,X6,X7)),X5) ) )
| X6 != relation_dom(X5) ) )
| ~ relation(X5) ),
inference(shift_quantors,[status(thm)],[117]) ).
fof(119,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(ordered_pair(esk7_2(X5,X6),X11),X5)
| ~ in(esk7_2(X5,X6),X6)
| X6 = relation_dom(X5)
| ~ relation(X5) )
& ( in(esk7_2(X5,X6),X6)
| in(ordered_pair(esk7_2(X5,X6),esk8_2(X5,X6)),X5)
| X6 = relation_dom(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6)
| X6 != relation_dom(X5)
| ~ relation(X5) )
& ( ~ in(X7,X6)
| in(ordered_pair(X7,esk6_3(X5,X6,X7)),X5)
| X6 != relation_dom(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[118]) ).
cnf(121,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[119]) ).
fof(127,negated_conjecture,
? [X1,X2,X3] :
( relation(X3)
& function(X3)
& ( ~ in(ordered_pair(X1,X2),X3)
| ~ in(X1,relation_dom(X3))
| X2 != apply(X3,X1) )
& ( in(ordered_pair(X1,X2),X3)
| ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(128,negated_conjecture,
? [X4,X5,X6] :
( relation(X6)
& function(X6)
& ( ~ in(ordered_pair(X4,X5),X6)
| ~ in(X4,relation_dom(X6))
| X5 != apply(X6,X4) )
& ( in(ordered_pair(X4,X5),X6)
| ( in(X4,relation_dom(X6))
& X5 = apply(X6,X4) ) ) ),
inference(variable_rename,[status(thm)],[127]) ).
fof(129,negated_conjecture,
( relation(esk11_0)
& function(esk11_0)
& ( ~ in(ordered_pair(esk9_0,esk10_0),esk11_0)
| ~ in(esk9_0,relation_dom(esk11_0))
| esk10_0 != apply(esk11_0,esk9_0) )
& ( in(ordered_pair(esk9_0,esk10_0),esk11_0)
| ( in(esk9_0,relation_dom(esk11_0))
& esk10_0 = apply(esk11_0,esk9_0) ) ) ),
inference(skolemize,[status(esa)],[128]) ).
fof(130,negated_conjecture,
( relation(esk11_0)
& function(esk11_0)
& ( ~ in(ordered_pair(esk9_0,esk10_0),esk11_0)
| ~ in(esk9_0,relation_dom(esk11_0))
| esk10_0 != apply(esk11_0,esk9_0) )
& ( in(esk9_0,relation_dom(esk11_0))
| in(ordered_pair(esk9_0,esk10_0),esk11_0) )
& ( esk10_0 = apply(esk11_0,esk9_0)
| in(ordered_pair(esk9_0,esk10_0),esk11_0) ) ),
inference(distribute,[status(thm)],[129]) ).
cnf(131,negated_conjecture,
( in(ordered_pair(esk9_0,esk10_0),esk11_0)
| esk10_0 = apply(esk11_0,esk9_0) ),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(132,negated_conjecture,
( in(ordered_pair(esk9_0,esk10_0),esk11_0)
| in(esk9_0,relation_dom(esk11_0)) ),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(133,negated_conjecture,
( esk10_0 != apply(esk11_0,esk9_0)
| ~ in(esk9_0,relation_dom(esk11_0))
| ~ in(ordered_pair(esk9_0,esk10_0),esk11_0) ),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(134,negated_conjecture,
function(esk11_0),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(135,negated_conjecture,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[130]) ).
fof(150,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[29]) ).
cnf(151,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[150]) ).
cnf(170,negated_conjecture,
( apply(esk11_0,esk9_0) = esk10_0
| in(unordered_pair(unordered_pair(esk9_0,esk10_0),singleton(esk9_0)),esk11_0) ),
inference(rw,[status(thm)],[131,151,theory(equality)]),
[unfolding] ).
cnf(171,negated_conjecture,
( in(esk9_0,relation_dom(esk11_0))
| in(unordered_pair(unordered_pair(esk9_0,esk10_0),singleton(esk9_0)),esk11_0) ),
inference(rw,[status(thm)],[132,151,theory(equality)]),
[unfolding] ).
cnf(173,plain,
( in(X3,X2)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X1) ),
inference(rw,[status(thm)],[121,151,theory(equality)]),
[unfolding] ).
cnf(176,plain,
( apply(X1,X2) = X3
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X1) ),
inference(rw,[status(thm)],[57,151,theory(equality)]),
[unfolding] ).
cnf(177,plain,
( in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X1)
| apply(X1,X2) != X3
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(rw,[status(thm)],[58,151,theory(equality)]),
[unfolding] ).
cnf(179,negated_conjecture,
( apply(esk11_0,esk9_0) != esk10_0
| ~ in(esk9_0,relation_dom(esk11_0))
| ~ in(unordered_pair(unordered_pair(esk9_0,esk10_0),singleton(esk9_0)),esk11_0) ),
inference(rw,[status(thm)],[133,151,theory(equality)]),
[unfolding] ).
cnf(246,negated_conjecture,
( apply(esk11_0,esk9_0) = esk10_0
| ~ in(esk9_0,relation_dom(esk11_0))
| ~ function(esk11_0)
| ~ relation(esk11_0) ),
inference(spm,[status(thm)],[176,170,theory(equality)]) ).
cnf(251,negated_conjecture,
( apply(esk11_0,esk9_0) = esk10_0
| ~ in(esk9_0,relation_dom(esk11_0))
| $false
| ~ relation(esk11_0) ),
inference(rw,[status(thm)],[246,134,theory(equality)]) ).
cnf(252,negated_conjecture,
( apply(esk11_0,esk9_0) = esk10_0
| ~ in(esk9_0,relation_dom(esk11_0))
| $false
| $false ),
inference(rw,[status(thm)],[251,135,theory(equality)]) ).
cnf(253,negated_conjecture,
( apply(esk11_0,esk9_0) = esk10_0
| ~ in(esk9_0,relation_dom(esk11_0)) ),
inference(cn,[status(thm)],[252,theory(equality)]) ).
cnf(259,negated_conjecture,
( apply(esk11_0,esk9_0) != esk10_0
| ~ in(esk9_0,relation_dom(esk11_0))
| ~ function(esk11_0)
| ~ relation(esk11_0) ),
inference(spm,[status(thm)],[179,177,theory(equality)]) ).
cnf(260,negated_conjecture,
( apply(esk11_0,esk9_0) != esk10_0
| ~ in(esk9_0,relation_dom(esk11_0))
| $false
| ~ relation(esk11_0) ),
inference(rw,[status(thm)],[259,134,theory(equality)]) ).
cnf(261,negated_conjecture,
( apply(esk11_0,esk9_0) != esk10_0
| ~ in(esk9_0,relation_dom(esk11_0))
| $false
| $false ),
inference(rw,[status(thm)],[260,135,theory(equality)]) ).
cnf(262,negated_conjecture,
( apply(esk11_0,esk9_0) != esk10_0
| ~ in(esk9_0,relation_dom(esk11_0)) ),
inference(cn,[status(thm)],[261,theory(equality)]) ).
cnf(300,negated_conjecture,
~ in(esk9_0,relation_dom(esk11_0)),
inference(csr,[status(thm)],[262,253]) ).
cnf(302,negated_conjecture,
in(unordered_pair(unordered_pair(esk9_0,esk10_0),singleton(esk9_0)),esk11_0),
inference(sr,[status(thm)],[171,300,theory(equality)]) ).
cnf(308,negated_conjecture,
( in(esk9_0,X1)
| relation_dom(esk11_0) != X1
| ~ relation(esk11_0) ),
inference(spm,[status(thm)],[173,302,theory(equality)]) ).
cnf(313,negated_conjecture,
( in(esk9_0,X1)
| relation_dom(esk11_0) != X1
| $false ),
inference(rw,[status(thm)],[308,135,theory(equality)]) ).
cnf(314,negated_conjecture,
( in(esk9_0,X1)
| relation_dom(esk11_0) != X1 ),
inference(cn,[status(thm)],[313,theory(equality)]) ).
cnf(318,negated_conjecture,
in(esk9_0,relation_dom(esk11_0)),
inference(er,[status(thm)],[314,theory(equality)]) ).
cnf(319,negated_conjecture,
$false,
inference(sr,[status(thm)],[318,300,theory(equality)]) ).
cnf(320,negated_conjecture,
$false,
319,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU212+3.p
% --creating new selector for []
% -running prover on /tmp/tmplfQGqf/sel_SEU212+3.p_1 with time limit 29
% -prover status Theorem
% Problem SEU212+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU212+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU212+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
%
%------------------------------------------------------------------------------