TSTP Solution File: SEU212+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU212+1 : TPTP v5.0.0. Released v3.3.0.
% 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 05:39:33 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% 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/tmpGxWR5p/sel_SEU212+1.p_1',d4_funct_1) ).
fof(17,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/tmp/tmpGxWR5p/sel_SEU212+1.p_1',d4_relat_1) ).
fof(20,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/tmpGxWR5p/sel_SEU212+1.p_1',t8_funct_1) ).
fof(33,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpGxWR5p/sel_SEU212+1.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)],[20]) ).
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(49,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(50,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)],[49]) ).
fof(51,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)],[50]) ).
fof(52,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)],[51]) ).
cnf(55,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)],[52]) ).
cnf(56,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)],[52]) ).
fof(95,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)],[17]) ).
fof(96,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)],[95]) ).
fof(97,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_dom(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| in(ordered_pair(X7,esk4_3(X5,X6,X7)),X5) )
& ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk5_2(X5,X6),X6)
| ! [X11] : ~ in(ordered_pair(esk5_2(X5,X6),X11),X5) )
& ( in(esk5_2(X5,X6),X6)
| in(ordered_pair(esk5_2(X5,X6),esk6_2(X5,X6)),X5) ) )
| X6 = relation_dom(X5) ) ) ),
inference(skolemize,[status(esa)],[96]) ).
fof(98,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ( ~ in(ordered_pair(esk5_2(X5,X6),X11),X5)
| ~ in(esk5_2(X5,X6),X6) )
& ( in(esk5_2(X5,X6),X6)
| in(ordered_pair(esk5_2(X5,X6),esk6_2(X5,X6)),X5) ) )
| X6 = relation_dom(X5) )
& ( ( ( ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) )
& ( ~ in(X7,X6)
| in(ordered_pair(X7,esk4_3(X5,X6,X7)),X5) ) )
| X6 != relation_dom(X5) ) )
| ~ relation(X5) ),
inference(shift_quantors,[status(thm)],[97]) ).
fof(99,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(ordered_pair(esk5_2(X5,X6),X11),X5)
| ~ in(esk5_2(X5,X6),X6)
| X6 = relation_dom(X5)
| ~ relation(X5) )
& ( in(esk5_2(X5,X6),X6)
| in(ordered_pair(esk5_2(X5,X6),esk6_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,esk4_3(X5,X6,X7)),X5)
| X6 != relation_dom(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[98]) ).
cnf(101,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[99]) ).
fof(108,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(109,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)],[108]) ).
fof(110,negated_conjecture,
( relation(esk9_0)
& function(esk9_0)
& ( ~ in(ordered_pair(esk7_0,esk8_0),esk9_0)
| ~ in(esk7_0,relation_dom(esk9_0))
| esk8_0 != apply(esk9_0,esk7_0) )
& ( in(ordered_pair(esk7_0,esk8_0),esk9_0)
| ( in(esk7_0,relation_dom(esk9_0))
& esk8_0 = apply(esk9_0,esk7_0) ) ) ),
inference(skolemize,[status(esa)],[109]) ).
fof(111,negated_conjecture,
( relation(esk9_0)
& function(esk9_0)
& ( ~ in(ordered_pair(esk7_0,esk8_0),esk9_0)
| ~ in(esk7_0,relation_dom(esk9_0))
| esk8_0 != apply(esk9_0,esk7_0) )
& ( in(esk7_0,relation_dom(esk9_0))
| in(ordered_pair(esk7_0,esk8_0),esk9_0) )
& ( esk8_0 = apply(esk9_0,esk7_0)
| in(ordered_pair(esk7_0,esk8_0),esk9_0) ) ),
inference(distribute,[status(thm)],[110]) ).
cnf(112,negated_conjecture,
( in(ordered_pair(esk7_0,esk8_0),esk9_0)
| esk8_0 = apply(esk9_0,esk7_0) ),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(113,negated_conjecture,
( in(ordered_pair(esk7_0,esk8_0),esk9_0)
| in(esk7_0,relation_dom(esk9_0)) ),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(114,negated_conjecture,
( esk8_0 != apply(esk9_0,esk7_0)
| ~ in(esk7_0,relation_dom(esk9_0))
| ~ in(ordered_pair(esk7_0,esk8_0),esk9_0) ),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(115,negated_conjecture,
function(esk9_0),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(116,negated_conjecture,
relation(esk9_0),
inference(split_conjunct,[status(thm)],[111]) ).
fof(142,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[33]) ).
cnf(143,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[142]) ).
cnf(151,negated_conjecture,
( apply(esk9_0,esk7_0) = esk8_0
| in(unordered_pair(unordered_pair(esk7_0,esk8_0),singleton(esk7_0)),esk9_0) ),
inference(rw,[status(thm)],[112,143,theory(equality)]),
[unfolding] ).
cnf(152,negated_conjecture,
( in(esk7_0,relation_dom(esk9_0))
| in(unordered_pair(unordered_pair(esk7_0,esk8_0),singleton(esk7_0)),esk9_0) ),
inference(rw,[status(thm)],[113,143,theory(equality)]),
[unfolding] ).
cnf(154,plain,
( in(X3,X2)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X1) ),
inference(rw,[status(thm)],[101,143,theory(equality)]),
[unfolding] ).
cnf(157,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)],[55,143,theory(equality)]),
[unfolding] ).
cnf(158,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)],[56,143,theory(equality)]),
[unfolding] ).
cnf(160,negated_conjecture,
( apply(esk9_0,esk7_0) != esk8_0
| ~ in(esk7_0,relation_dom(esk9_0))
| ~ in(unordered_pair(unordered_pair(esk7_0,esk8_0),singleton(esk7_0)),esk9_0) ),
inference(rw,[status(thm)],[114,143,theory(equality)]),
[unfolding] ).
cnf(201,negated_conjecture,
( apply(esk9_0,esk7_0) != esk8_0
| ~ in(esk7_0,relation_dom(esk9_0))
| ~ function(esk9_0)
| ~ relation(esk9_0) ),
inference(spm,[status(thm)],[160,158,theory(equality)]) ).
cnf(202,negated_conjecture,
( apply(esk9_0,esk7_0) != esk8_0
| ~ in(esk7_0,relation_dom(esk9_0))
| $false
| ~ relation(esk9_0) ),
inference(rw,[status(thm)],[201,115,theory(equality)]) ).
cnf(203,negated_conjecture,
( apply(esk9_0,esk7_0) != esk8_0
| ~ in(esk7_0,relation_dom(esk9_0))
| $false
| $false ),
inference(rw,[status(thm)],[202,116,theory(equality)]) ).
cnf(204,negated_conjecture,
( apply(esk9_0,esk7_0) != esk8_0
| ~ in(esk7_0,relation_dom(esk9_0)) ),
inference(cn,[status(thm)],[203,theory(equality)]) ).
cnf(210,negated_conjecture,
( apply(esk9_0,esk7_0) = esk8_0
| ~ in(esk7_0,relation_dom(esk9_0))
| ~ function(esk9_0)
| ~ relation(esk9_0) ),
inference(spm,[status(thm)],[157,151,theory(equality)]) ).
cnf(215,negated_conjecture,
( apply(esk9_0,esk7_0) = esk8_0
| ~ in(esk7_0,relation_dom(esk9_0))
| $false
| ~ relation(esk9_0) ),
inference(rw,[status(thm)],[210,115,theory(equality)]) ).
cnf(216,negated_conjecture,
( apply(esk9_0,esk7_0) = esk8_0
| ~ in(esk7_0,relation_dom(esk9_0))
| $false
| $false ),
inference(rw,[status(thm)],[215,116,theory(equality)]) ).
cnf(217,negated_conjecture,
( apply(esk9_0,esk7_0) = esk8_0
| ~ in(esk7_0,relation_dom(esk9_0)) ),
inference(cn,[status(thm)],[216,theory(equality)]) ).
cnf(254,negated_conjecture,
~ in(esk7_0,relation_dom(esk9_0)),
inference(csr,[status(thm)],[204,217]) ).
cnf(257,negated_conjecture,
in(unordered_pair(unordered_pair(esk7_0,esk8_0),singleton(esk7_0)),esk9_0),
inference(sr,[status(thm)],[152,254,theory(equality)]) ).
cnf(260,negated_conjecture,
( in(esk7_0,X1)
| relation_dom(esk9_0) != X1
| ~ relation(esk9_0) ),
inference(spm,[status(thm)],[154,257,theory(equality)]) ).
cnf(265,negated_conjecture,
( in(esk7_0,X1)
| relation_dom(esk9_0) != X1
| $false ),
inference(rw,[status(thm)],[260,116,theory(equality)]) ).
cnf(266,negated_conjecture,
( in(esk7_0,X1)
| relation_dom(esk9_0) != X1 ),
inference(cn,[status(thm)],[265,theory(equality)]) ).
cnf(270,negated_conjecture,
in(esk7_0,relation_dom(esk9_0)),
inference(er,[status(thm)],[266,theory(equality)]) ).
cnf(272,negated_conjecture,
$false,
inference(sr,[status(thm)],[270,254,theory(equality)]) ).
cnf(273,negated_conjecture,
$false,
272,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU212+1.p
% --creating new selector for []
% -running prover on /tmp/tmpGxWR5p/sel_SEU212+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU212+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU212+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU212+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
%
%------------------------------------------------------------------------------