TSTP Solution File: SEU009+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU009+1 : TPTP v5.0.0. Released v3.2.0.
% 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 04:06:21 EST 2010
% Result : Theorem 0.30s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of formulae : 65 ( 12 unt; 0 def)
% Number of atoms : 328 ( 42 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 439 ( 176 ~; 203 |; 50 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 92 ( 2 sgn 43 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(8,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_composition(X3,identity_relation(X1))))
<=> ( in(X2,relation_dom(X3))
& in(apply(X3,X2),X1) ) ) ),
file('/tmp/tmpwYUPg6/sel_SEU009+1.p_1',t40_funct_1) ).
fof(15,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(X1,relation_dom(X3))
& in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
file('/tmp/tmpwYUPg6/sel_SEU009+1.p_1',t21_funct_1) ).
fof(22,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/tmp/tmpwYUPg6/sel_SEU009+1.p_1',t34_funct_1) ).
fof(29,axiom,
! [X1] : relation(identity_relation(X1)),
file('/tmp/tmpwYUPg6/sel_SEU009+1.p_1',dt_k6_relat_1) ).
fof(30,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/tmp/tmpwYUPg6/sel_SEU009+1.p_1',fc2_funct_1) ).
fof(37,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_composition(X3,identity_relation(X1))))
<=> ( in(X2,relation_dom(X3))
& in(apply(X3,X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[8]) ).
fof(72,negated_conjecture,
? [X1,X2,X3] :
( relation(X3)
& function(X3)
& ( ~ in(X2,relation_dom(relation_composition(X3,identity_relation(X1))))
| ~ in(X2,relation_dom(X3))
| ~ in(apply(X3,X2),X1) )
& ( in(X2,relation_dom(relation_composition(X3,identity_relation(X1))))
| ( in(X2,relation_dom(X3))
& in(apply(X3,X2),X1) ) ) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(73,negated_conjecture,
? [X4,X5,X6] :
( relation(X6)
& function(X6)
& ( ~ in(X5,relation_dom(relation_composition(X6,identity_relation(X4))))
| ~ in(X5,relation_dom(X6))
| ~ in(apply(X6,X5),X4) )
& ( in(X5,relation_dom(relation_composition(X6,identity_relation(X4))))
| ( in(X5,relation_dom(X6))
& in(apply(X6,X5),X4) ) ) ),
inference(variable_rename,[status(thm)],[72]) ).
fof(74,negated_conjecture,
( relation(esk7_0)
& function(esk7_0)
& ( ~ in(esk6_0,relation_dom(relation_composition(esk7_0,identity_relation(esk5_0))))
| ~ in(esk6_0,relation_dom(esk7_0))
| ~ in(apply(esk7_0,esk6_0),esk5_0) )
& ( in(esk6_0,relation_dom(relation_composition(esk7_0,identity_relation(esk5_0))))
| ( in(esk6_0,relation_dom(esk7_0))
& in(apply(esk7_0,esk6_0),esk5_0) ) ) ),
inference(skolemize,[status(esa)],[73]) ).
fof(75,negated_conjecture,
( relation(esk7_0)
& function(esk7_0)
& ( ~ in(esk6_0,relation_dom(relation_composition(esk7_0,identity_relation(esk5_0))))
| ~ in(esk6_0,relation_dom(esk7_0))
| ~ in(apply(esk7_0,esk6_0),esk5_0) )
& ( in(esk6_0,relation_dom(esk7_0))
| in(esk6_0,relation_dom(relation_composition(esk7_0,identity_relation(esk5_0)))) )
& ( in(apply(esk7_0,esk6_0),esk5_0)
| in(esk6_0,relation_dom(relation_composition(esk7_0,identity_relation(esk5_0)))) ) ),
inference(distribute,[status(thm)],[74]) ).
cnf(76,negated_conjecture,
( in(esk6_0,relation_dom(relation_composition(esk7_0,identity_relation(esk5_0))))
| in(apply(esk7_0,esk6_0),esk5_0) ),
inference(split_conjunct,[status(thm)],[75]) ).
cnf(77,negated_conjecture,
( in(esk6_0,relation_dom(relation_composition(esk7_0,identity_relation(esk5_0))))
| in(esk6_0,relation_dom(esk7_0)) ),
inference(split_conjunct,[status(thm)],[75]) ).
cnf(78,negated_conjecture,
( ~ in(apply(esk7_0,esk6_0),esk5_0)
| ~ in(esk6_0,relation_dom(esk7_0))
| ~ in(esk6_0,relation_dom(relation_composition(esk7_0,identity_relation(esk5_0)))) ),
inference(split_conjunct,[status(thm)],[75]) ).
cnf(79,negated_conjecture,
function(esk7_0),
inference(split_conjunct,[status(thm)],[75]) ).
cnf(80,negated_conjecture,
relation(esk7_0),
inference(split_conjunct,[status(thm)],[75]) ).
fof(99,plain,
! [X1,X2] :
( ~ relation(X2)
| ~ function(X2)
| ! [X3] :
( ~ relation(X3)
| ~ function(X3)
| ( ( ~ in(X1,relation_dom(relation_composition(X3,X2)))
| ( in(X1,relation_dom(X3))
& in(apply(X3,X1),relation_dom(X2)) ) )
& ( ~ in(X1,relation_dom(X3))
| ~ in(apply(X3,X1),relation_dom(X2))
| in(X1,relation_dom(relation_composition(X3,X2))) ) ) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(100,plain,
! [X4,X5] :
( ~ relation(X5)
| ~ function(X5)
| ! [X6] :
( ~ relation(X6)
| ~ function(X6)
| ( ( ~ in(X4,relation_dom(relation_composition(X6,X5)))
| ( in(X4,relation_dom(X6))
& in(apply(X6,X4),relation_dom(X5)) ) )
& ( ~ in(X4,relation_dom(X6))
| ~ in(apply(X6,X4),relation_dom(X5))
| in(X4,relation_dom(relation_composition(X6,X5))) ) ) ) ),
inference(variable_rename,[status(thm)],[99]) ).
fof(101,plain,
! [X4,X5,X6] :
( ~ relation(X6)
| ~ function(X6)
| ( ( ~ in(X4,relation_dom(relation_composition(X6,X5)))
| ( in(X4,relation_dom(X6))
& in(apply(X6,X4),relation_dom(X5)) ) )
& ( ~ in(X4,relation_dom(X6))
| ~ in(apply(X6,X4),relation_dom(X5))
| in(X4,relation_dom(relation_composition(X6,X5))) ) )
| ~ relation(X5)
| ~ function(X5) ),
inference(shift_quantors,[status(thm)],[100]) ).
fof(102,plain,
! [X4,X5,X6] :
( ( in(X4,relation_dom(X6))
| ~ in(X4,relation_dom(relation_composition(X6,X5)))
| ~ relation(X6)
| ~ function(X6)
| ~ relation(X5)
| ~ function(X5) )
& ( in(apply(X6,X4),relation_dom(X5))
| ~ in(X4,relation_dom(relation_composition(X6,X5)))
| ~ relation(X6)
| ~ function(X6)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(X4,relation_dom(X6))
| ~ in(apply(X6,X4),relation_dom(X5))
| in(X4,relation_dom(relation_composition(X6,X5)))
| ~ relation(X6)
| ~ function(X6)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[101]) ).
cnf(103,plain,
( in(X3,relation_dom(relation_composition(X2,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(apply(X2,X3),relation_dom(X1))
| ~ in(X3,relation_dom(X2)) ),
inference(split_conjunct,[status(thm)],[102]) ).
cnf(104,plain,
( in(apply(X2,X3),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
inference(split_conjunct,[status(thm)],[102]) ).
cnf(105,plain,
( in(X3,relation_dom(X2))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
inference(split_conjunct,[status(thm)],[102]) ).
fof(124,plain,
! [X1,X2] :
( ~ relation(X2)
| ~ function(X2)
| ( ( X2 != identity_relation(X1)
| ( relation_dom(X2) = X1
& ! [X3] :
( ~ in(X3,X1)
| apply(X2,X3) = X3 ) ) )
& ( relation_dom(X2) != X1
| ? [X3] :
( in(X3,X1)
& apply(X2,X3) != X3 )
| X2 = identity_relation(X1) ) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(125,plain,
! [X4,X5] :
( ~ relation(X5)
| ~ function(X5)
| ( ( X5 != identity_relation(X4)
| ( relation_dom(X5) = X4
& ! [X6] :
( ~ in(X6,X4)
| apply(X5,X6) = X6 ) ) )
& ( relation_dom(X5) != X4
| ? [X7] :
( in(X7,X4)
& apply(X5,X7) != X7 )
| X5 = identity_relation(X4) ) ) ),
inference(variable_rename,[status(thm)],[124]) ).
fof(126,plain,
! [X4,X5] :
( ~ relation(X5)
| ~ function(X5)
| ( ( X5 != identity_relation(X4)
| ( relation_dom(X5) = X4
& ! [X6] :
( ~ in(X6,X4)
| apply(X5,X6) = X6 ) ) )
& ( relation_dom(X5) != X4
| ( in(esk9_2(X4,X5),X4)
& apply(X5,esk9_2(X4,X5)) != esk9_2(X4,X5) )
| X5 = identity_relation(X4) ) ) ),
inference(skolemize,[status(esa)],[125]) ).
fof(127,plain,
! [X4,X5,X6] :
( ( ( ( ( ~ in(X6,X4)
| apply(X5,X6) = X6 )
& relation_dom(X5) = X4 )
| X5 != identity_relation(X4) )
& ( relation_dom(X5) != X4
| ( in(esk9_2(X4,X5),X4)
& apply(X5,esk9_2(X4,X5)) != esk9_2(X4,X5) )
| X5 = identity_relation(X4) ) )
| ~ relation(X5)
| ~ function(X5) ),
inference(shift_quantors,[status(thm)],[126]) ).
fof(128,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| apply(X5,X6) = X6
| X5 != identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( relation_dom(X5) = X4
| X5 != identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk9_2(X4,X5),X4)
| relation_dom(X5) != X4
| X5 = identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( apply(X5,esk9_2(X4,X5)) != esk9_2(X4,X5)
| relation_dom(X5) != X4
| X5 = identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[127]) ).
cnf(131,plain,
( relation_dom(X1) = X2
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2) ),
inference(split_conjunct,[status(thm)],[128]) ).
fof(156,plain,
! [X2] : relation(identity_relation(X2)),
inference(variable_rename,[status(thm)],[29]) ).
cnf(157,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[156]) ).
fof(158,plain,
! [X2] :
( relation(identity_relation(X2))
& function(identity_relation(X2)) ),
inference(variable_rename,[status(thm)],[30]) ).
cnf(159,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[158]) ).
cnf(205,plain,
( relation_dom(identity_relation(X1)) = X1
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1)) ),
inference(er,[status(thm)],[131,theory(equality)]) ).
cnf(206,plain,
( relation_dom(identity_relation(X1)) = X1
| $false
| ~ relation(identity_relation(X1)) ),
inference(rw,[status(thm)],[205,159,theory(equality)]) ).
cnf(207,plain,
( relation_dom(identity_relation(X1)) = X1
| $false
| $false ),
inference(rw,[status(thm)],[206,157,theory(equality)]) ).
cnf(208,plain,
relation_dom(identity_relation(X1)) = X1,
inference(cn,[status(thm)],[207,theory(equality)]) ).
cnf(228,negated_conjecture,
( in(esk6_0,relation_dom(esk7_0))
| ~ function(esk7_0)
| ~ function(identity_relation(esk5_0))
| ~ relation(esk7_0)
| ~ relation(identity_relation(esk5_0)) ),
inference(spm,[status(thm)],[105,77,theory(equality)]) ).
cnf(230,negated_conjecture,
( in(esk6_0,relation_dom(esk7_0))
| $false
| ~ function(identity_relation(esk5_0))
| ~ relation(esk7_0)
| ~ relation(identity_relation(esk5_0)) ),
inference(rw,[status(thm)],[228,79,theory(equality)]) ).
cnf(231,negated_conjecture,
( in(esk6_0,relation_dom(esk7_0))
| $false
| $false
| ~ relation(esk7_0)
| ~ relation(identity_relation(esk5_0)) ),
inference(rw,[status(thm)],[230,159,theory(equality)]) ).
cnf(232,negated_conjecture,
( in(esk6_0,relation_dom(esk7_0))
| $false
| $false
| $false
| ~ relation(identity_relation(esk5_0)) ),
inference(rw,[status(thm)],[231,80,theory(equality)]) ).
cnf(233,negated_conjecture,
( in(esk6_0,relation_dom(esk7_0))
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[232,157,theory(equality)]) ).
cnf(234,negated_conjecture,
in(esk6_0,relation_dom(esk7_0)),
inference(cn,[status(thm)],[233,theory(equality)]) ).
cnf(277,negated_conjecture,
( ~ in(esk6_0,relation_dom(relation_composition(esk7_0,identity_relation(esk5_0))))
| ~ in(apply(esk7_0,esk6_0),esk5_0)
| $false ),
inference(rw,[status(thm)],[78,234,theory(equality)]) ).
cnf(278,negated_conjecture,
( ~ in(esk6_0,relation_dom(relation_composition(esk7_0,identity_relation(esk5_0))))
| ~ in(apply(esk7_0,esk6_0),esk5_0) ),
inference(cn,[status(thm)],[277,theory(equality)]) ).
cnf(287,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,relation_dom(relation_composition(X1,identity_relation(X3))))
| ~ function(X1)
| ~ function(identity_relation(X3))
| ~ relation(X1)
| ~ relation(identity_relation(X3)) ),
inference(spm,[status(thm)],[104,208,theory(equality)]) ).
cnf(288,plain,
( in(X1,relation_dom(relation_composition(X2,identity_relation(X3))))
| ~ in(apply(X2,X1),X3)
| ~ in(X1,relation_dom(X2))
| ~ function(X2)
| ~ function(identity_relation(X3))
| ~ relation(X2)
| ~ relation(identity_relation(X3)) ),
inference(spm,[status(thm)],[103,208,theory(equality)]) ).
cnf(291,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,relation_dom(relation_composition(X1,identity_relation(X3))))
| ~ function(X1)
| $false
| ~ relation(X1)
| ~ relation(identity_relation(X3)) ),
inference(rw,[status(thm)],[287,159,theory(equality)]) ).
cnf(292,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,relation_dom(relation_composition(X1,identity_relation(X3))))
| ~ function(X1)
| $false
| ~ relation(X1)
| $false ),
inference(rw,[status(thm)],[291,157,theory(equality)]) ).
cnf(293,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,relation_dom(relation_composition(X1,identity_relation(X3))))
| ~ function(X1)
| ~ relation(X1) ),
inference(cn,[status(thm)],[292,theory(equality)]) ).
cnf(294,plain,
( in(X1,relation_dom(relation_composition(X2,identity_relation(X3))))
| ~ in(apply(X2,X1),X3)
| ~ in(X1,relation_dom(X2))
| ~ function(X2)
| $false
| ~ relation(X2)
| ~ relation(identity_relation(X3)) ),
inference(rw,[status(thm)],[288,159,theory(equality)]) ).
cnf(295,plain,
( in(X1,relation_dom(relation_composition(X2,identity_relation(X3))))
| ~ in(apply(X2,X1),X3)
| ~ in(X1,relation_dom(X2))
| ~ function(X2)
| $false
| ~ relation(X2)
| $false ),
inference(rw,[status(thm)],[294,157,theory(equality)]) ).
cnf(296,plain,
( in(X1,relation_dom(relation_composition(X2,identity_relation(X3))))
| ~ in(apply(X2,X1),X3)
| ~ in(X1,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ),
inference(cn,[status(thm)],[295,theory(equality)]) ).
cnf(1182,negated_conjecture,
( in(apply(esk7_0,esk6_0),esk5_0)
| ~ function(esk7_0)
| ~ relation(esk7_0) ),
inference(spm,[status(thm)],[293,76,theory(equality)]) ).
cnf(1198,negated_conjecture,
( in(apply(esk7_0,esk6_0),esk5_0)
| $false
| ~ relation(esk7_0) ),
inference(rw,[status(thm)],[1182,79,theory(equality)]) ).
cnf(1199,negated_conjecture,
( in(apply(esk7_0,esk6_0),esk5_0)
| $false
| $false ),
inference(rw,[status(thm)],[1198,80,theory(equality)]) ).
cnf(1200,negated_conjecture,
in(apply(esk7_0,esk6_0),esk5_0),
inference(cn,[status(thm)],[1199,theory(equality)]) ).
cnf(1233,negated_conjecture,
( ~ in(esk6_0,relation_dom(relation_composition(esk7_0,identity_relation(esk5_0))))
| $false ),
inference(rw,[status(thm)],[278,1200,theory(equality)]) ).
cnf(1234,negated_conjecture,
~ in(esk6_0,relation_dom(relation_composition(esk7_0,identity_relation(esk5_0)))),
inference(cn,[status(thm)],[1233,theory(equality)]) ).
cnf(1256,negated_conjecture,
( ~ in(apply(esk7_0,esk6_0),esk5_0)
| ~ in(esk6_0,relation_dom(esk7_0))
| ~ function(esk7_0)
| ~ relation(esk7_0) ),
inference(spm,[status(thm)],[1234,296,theory(equality)]) ).
cnf(1276,negated_conjecture,
( $false
| ~ in(esk6_0,relation_dom(esk7_0))
| ~ function(esk7_0)
| ~ relation(esk7_0) ),
inference(rw,[status(thm)],[1256,1200,theory(equality)]) ).
cnf(1277,negated_conjecture,
( $false
| $false
| ~ function(esk7_0)
| ~ relation(esk7_0) ),
inference(rw,[status(thm)],[1276,234,theory(equality)]) ).
cnf(1278,negated_conjecture,
( $false
| $false
| $false
| ~ relation(esk7_0) ),
inference(rw,[status(thm)],[1277,79,theory(equality)]) ).
cnf(1279,negated_conjecture,
( $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[1278,80,theory(equality)]) ).
cnf(1280,negated_conjecture,
$false,
inference(cn,[status(thm)],[1279,theory(equality)]) ).
cnf(1281,negated_conjecture,
$false,
1280,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU009+1.p
% --creating new selector for []
% -running prover on /tmp/tmpwYUPg6/sel_SEU009+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU009+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU009+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU009+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
%
%------------------------------------------------------------------------------