TSTP Solution File: SEU019+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU019+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 04:11:17 EST 2010
% Result : Theorem 0.46s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 15 unt; 0 def)
% Number of atoms : 258 ( 82 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 333 ( 128 ~; 157 |; 42 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 83 ( 4 sgn 42 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(10,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
file('/tmp/tmpAIHrMJ/sel_SEU019+1.p_1',d8_funct_1) ).
fof(14,conjecture,
! [X1] : one_to_one(identity_relation(X1)),
file('/tmp/tmpAIHrMJ/sel_SEU019+1.p_1',t52_funct_1) ).
fof(20,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/tmpAIHrMJ/sel_SEU019+1.p_1',t34_funct_1) ).
fof(25,axiom,
! [X1] : relation(identity_relation(X1)),
file('/tmp/tmpAIHrMJ/sel_SEU019+1.p_1',dt_k6_relat_1) ).
fof(26,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/tmp/tmpAIHrMJ/sel_SEU019+1.p_1',fc2_funct_1) ).
fof(33,negated_conjecture,
~ ! [X1] : one_to_one(identity_relation(X1)),
inference(assume_negation,[status(cth)],[14]) ).
fof(72,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ( ( ~ one_to_one(X1)
| ! [X2,X3] :
( ~ in(X2,relation_dom(X1))
| ~ in(X3,relation_dom(X1))
| apply(X1,X2) != apply(X1,X3)
| X2 = X3 ) )
& ( ? [X2,X3] :
( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3)
& X2 != X3 )
| one_to_one(X1) ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(73,plain,
! [X4] :
( ~ relation(X4)
| ~ function(X4)
| ( ( ~ one_to_one(X4)
| ! [X5,X6] :
( ~ in(X5,relation_dom(X4))
| ~ in(X6,relation_dom(X4))
| apply(X4,X5) != apply(X4,X6)
| X5 = X6 ) )
& ( ? [X7,X8] :
( in(X7,relation_dom(X4))
& in(X8,relation_dom(X4))
& apply(X4,X7) = apply(X4,X8)
& X7 != X8 )
| one_to_one(X4) ) ) ),
inference(variable_rename,[status(thm)],[72]) ).
fof(74,plain,
! [X4] :
( ~ relation(X4)
| ~ function(X4)
| ( ( ~ one_to_one(X4)
| ! [X5,X6] :
( ~ in(X5,relation_dom(X4))
| ~ in(X6,relation_dom(X4))
| apply(X4,X5) != apply(X4,X6)
| X5 = X6 ) )
& ( ( in(esk5_1(X4),relation_dom(X4))
& in(esk6_1(X4),relation_dom(X4))
& apply(X4,esk5_1(X4)) = apply(X4,esk6_1(X4))
& esk5_1(X4) != esk6_1(X4) )
| one_to_one(X4) ) ) ),
inference(skolemize,[status(esa)],[73]) ).
fof(75,plain,
! [X4,X5,X6] :
( ( ( ~ in(X5,relation_dom(X4))
| ~ in(X6,relation_dom(X4))
| apply(X4,X5) != apply(X4,X6)
| X5 = X6
| ~ one_to_one(X4) )
& ( ( in(esk5_1(X4),relation_dom(X4))
& in(esk6_1(X4),relation_dom(X4))
& apply(X4,esk5_1(X4)) = apply(X4,esk6_1(X4))
& esk5_1(X4) != esk6_1(X4) )
| one_to_one(X4) ) )
| ~ relation(X4)
| ~ function(X4) ),
inference(shift_quantors,[status(thm)],[74]) ).
fof(76,plain,
! [X4,X5,X6] :
( ( ~ in(X5,relation_dom(X4))
| ~ in(X6,relation_dom(X4))
| apply(X4,X5) != apply(X4,X6)
| X5 = X6
| ~ one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( in(esk5_1(X4),relation_dom(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( in(esk6_1(X4),relation_dom(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( apply(X4,esk5_1(X4)) = apply(X4,esk6_1(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( esk5_1(X4) != esk6_1(X4)
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[75]) ).
cnf(77,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| esk5_1(X1) != esk6_1(X1) ),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(78,plain,
( one_to_one(X1)
| apply(X1,esk5_1(X1)) = apply(X1,esk6_1(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(79,plain,
( one_to_one(X1)
| in(esk6_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(80,plain,
( one_to_one(X1)
| in(esk5_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[76]) ).
fof(91,negated_conjecture,
? [X1] : ~ one_to_one(identity_relation(X1)),
inference(fof_nnf,[status(thm)],[33]) ).
fof(92,negated_conjecture,
? [X2] : ~ one_to_one(identity_relation(X2)),
inference(variable_rename,[status(thm)],[91]) ).
fof(93,negated_conjecture,
~ one_to_one(identity_relation(esk7_0)),
inference(skolemize,[status(esa)],[92]) ).
cnf(94,negated_conjecture,
~ one_to_one(identity_relation(esk7_0)),
inference(split_conjunct,[status(thm)],[93]) ).
fof(110,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)],[20]) ).
fof(111,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)],[110]) ).
fof(112,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)],[111]) ).
fof(113,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)],[112]) ).
fof(114,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)],[113]) ).
cnf(117,plain,
( relation_dom(X1) = X2
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2) ),
inference(split_conjunct,[status(thm)],[114]) ).
cnf(118,plain,
( apply(X1,X3) = X3
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[114]) ).
fof(132,plain,
! [X2] : relation(identity_relation(X2)),
inference(variable_rename,[status(thm)],[25]) ).
cnf(133,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[132]) ).
fof(134,plain,
! [X2] :
( relation(identity_relation(X2))
& function(identity_relation(X2)) ),
inference(variable_rename,[status(thm)],[26]) ).
cnf(135,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[134]) ).
cnf(168,plain,
( relation_dom(identity_relation(X1)) = X1
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1)) ),
inference(er,[status(thm)],[117,theory(equality)]) ).
cnf(169,plain,
( relation_dom(identity_relation(X1)) = X1
| $false
| ~ relation(identity_relation(X1)) ),
inference(rw,[status(thm)],[168,135,theory(equality)]) ).
cnf(170,plain,
( relation_dom(identity_relation(X1)) = X1
| $false
| $false ),
inference(rw,[status(thm)],[169,133,theory(equality)]) ).
cnf(171,plain,
relation_dom(identity_relation(X1)) = X1,
inference(cn,[status(thm)],[170,theory(equality)]) ).
cnf(201,plain,
( apply(X1,esk6_1(X2)) = esk6_1(X2)
| one_to_one(X2)
| identity_relation(relation_dom(X2)) != X1
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(spm,[status(thm)],[118,79,theory(equality)]) ).
cnf(226,plain,
( one_to_one(identity_relation(X1))
| in(esk5_1(identity_relation(X1)),X1)
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1)) ),
inference(spm,[status(thm)],[80,171,theory(equality)]) ).
cnf(230,plain,
( one_to_one(identity_relation(X1))
| in(esk5_1(identity_relation(X1)),X1)
| $false
| ~ relation(identity_relation(X1)) ),
inference(rw,[status(thm)],[226,135,theory(equality)]) ).
cnf(231,plain,
( one_to_one(identity_relation(X1))
| in(esk5_1(identity_relation(X1)),X1)
| $false
| $false ),
inference(rw,[status(thm)],[230,133,theory(equality)]) ).
cnf(232,plain,
( one_to_one(identity_relation(X1))
| in(esk5_1(identity_relation(X1)),X1) ),
inference(cn,[status(thm)],[231,theory(equality)]) ).
cnf(411,plain,
( apply(X1,esk5_1(identity_relation(X2))) = esk5_1(identity_relation(X2))
| one_to_one(identity_relation(X2))
| identity_relation(X2) != X1
| ~ function(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[118,232,theory(equality)]) ).
cnf(649,plain,
( esk6_1(X1) = apply(X1,esk5_1(X1))
| one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| identity_relation(relation_dom(X1)) != X1 ),
inference(spm,[status(thm)],[78,201,theory(equality)]) ).
cnf(5046,plain,
( esk6_1(identity_relation(X1)) = esk5_1(identity_relation(X1))
| one_to_one(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1))
| identity_relation(relation_dom(identity_relation(X1))) != identity_relation(X1) ),
inference(spm,[status(thm)],[411,649,theory(equality)]) ).
cnf(5051,plain,
( esk6_1(identity_relation(X1)) = esk5_1(identity_relation(X1))
| one_to_one(identity_relation(X1))
| $false
| ~ relation(identity_relation(X1))
| identity_relation(relation_dom(identity_relation(X1))) != identity_relation(X1) ),
inference(rw,[status(thm)],[5046,135,theory(equality)]) ).
cnf(5052,plain,
( esk6_1(identity_relation(X1)) = esk5_1(identity_relation(X1))
| one_to_one(identity_relation(X1))
| $false
| $false
| identity_relation(relation_dom(identity_relation(X1))) != identity_relation(X1) ),
inference(rw,[status(thm)],[5051,133,theory(equality)]) ).
cnf(5053,plain,
( esk6_1(identity_relation(X1)) = esk5_1(identity_relation(X1))
| one_to_one(identity_relation(X1))
| $false
| $false
| $false ),
inference(rw,[status(thm)],[5052,171,theory(equality)]) ).
cnf(5054,plain,
( esk6_1(identity_relation(X1)) = esk5_1(identity_relation(X1))
| one_to_one(identity_relation(X1)) ),
inference(cn,[status(thm)],[5053,theory(equality)]) ).
cnf(5064,plain,
( one_to_one(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1)) ),
inference(spm,[status(thm)],[77,5054,theory(equality)]) ).
cnf(5092,plain,
( one_to_one(identity_relation(X1))
| $false
| ~ relation(identity_relation(X1)) ),
inference(rw,[status(thm)],[5064,135,theory(equality)]) ).
cnf(5093,plain,
( one_to_one(identity_relation(X1))
| $false
| $false ),
inference(rw,[status(thm)],[5092,133,theory(equality)]) ).
cnf(5094,plain,
one_to_one(identity_relation(X1)),
inference(cn,[status(thm)],[5093,theory(equality)]) ).
cnf(5125,negated_conjecture,
$false,
inference(rw,[status(thm)],[94,5094,theory(equality)]) ).
cnf(5126,negated_conjecture,
$false,
inference(cn,[status(thm)],[5125,theory(equality)]) ).
cnf(5127,negated_conjecture,
$false,
5126,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU019+1.p
% --creating new selector for []
% -running prover on /tmp/tmpAIHrMJ/sel_SEU019+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU019+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU019+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU019+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
%
%------------------------------------------------------------------------------