%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU034+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 04:13:11 EST 2010
% Result : Theorem 2.05s
% Output : CNFRefutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 19 unt; 0 def)
% Number of atoms : 196 ( 65 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 249 ( 107 ~; 112 |; 22 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 54 ( 3 sgn 30 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_composition(X1,function_inverse(X1)) = identity_relation(relation_dom(X1))
& relation_composition(function_inverse(X1),X1) = identity_relation(relation_rng(X1)) ) ) ),
file('/tmp/tmpTHdoU6/sel_SEU034+1.p_1',t61_funct_1) ).
fof(11,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( relation_rng(X1) = relation_dom(X2)
& relation_composition(X1,X2) = X1 )
=> X2 = identity_relation(relation_dom(X2)) ) ) ),
file('/tmp/tmpTHdoU6/sel_SEU034+1.p_1',t44_funct_1) ).
fof(16,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/tmp/tmpTHdoU6/sel_SEU034+1.p_1',dt_k2_funct_1) ).
fof(18,axiom,
! [X1] : one_to_one(identity_relation(X1)),
file('/tmp/tmpTHdoU6/sel_SEU034+1.p_1',t52_funct_1) ).
fof(34,axiom,
! [X1] : relation(identity_relation(X1)),
file('/tmp/tmpTHdoU6/sel_SEU034+1.p_1',dt_k6_relat_1) ).
fof(35,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/tmp/tmpTHdoU6/sel_SEU034+1.p_1',fc2_funct_1) ).
fof(37,axiom,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
file('/tmp/tmpTHdoU6/sel_SEU034+1.p_1',t71_relat_1) ).
fof(40,conjecture,
! [X1] : function_inverse(identity_relation(X1)) = identity_relation(X1),
file('/tmp/tmpTHdoU6/sel_SEU034+1.p_1',t67_funct_1) ).
fof(41,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_rng(X1) = relation_dom(function_inverse(X1))
& relation_dom(X1) = relation_rng(function_inverse(X1)) ) ) ),
file('/tmp/tmpTHdoU6/sel_SEU034+1.p_1',t55_funct_1) ).
fof(46,negated_conjecture,
~ ! [X1] : function_inverse(identity_relation(X1)) = identity_relation(X1),
inference(assume_negation,[status(cth)],[40]) ).
fof(67,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| ( relation_composition(X1,function_inverse(X1)) = identity_relation(relation_dom(X1))
& relation_composition(function_inverse(X1),X1) = identity_relation(relation_rng(X1)) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(68,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X2)
| ( relation_composition(X2,function_inverse(X2)) = identity_relation(relation_dom(X2))
& relation_composition(function_inverse(X2),X2) = identity_relation(relation_rng(X2)) ) ),
inference(variable_rename,[status(thm)],[67]) ).
fof(69,plain,
! [X2] :
( ( relation_composition(X2,function_inverse(X2)) = identity_relation(relation_dom(X2))
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) )
& ( relation_composition(function_inverse(X2),X2) = identity_relation(relation_rng(X2))
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[68]) ).
cnf(71,plain,
( relation_composition(X1,function_inverse(X1)) = identity_relation(relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[69]) ).
fof(94,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ! [X2] :
( ~ relation(X2)
| ~ function(X2)
| relation_rng(X1) != relation_dom(X2)
| relation_composition(X1,X2) != X1
| X2 = identity_relation(relation_dom(X2)) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(95,plain,
! [X3] :
( ~ relation(X3)
| ~ function(X3)
| ! [X4] :
( ~ relation(X4)
| ~ function(X4)
| relation_rng(X3) != relation_dom(X4)
| relation_composition(X3,X4) != X3
| X4 = identity_relation(relation_dom(X4)) ) ),
inference(variable_rename,[status(thm)],[94]) ).
fof(96,plain,
! [X3,X4] :
( ~ relation(X4)
| ~ function(X4)
| relation_rng(X3) != relation_dom(X4)
| relation_composition(X3,X4) != X3
| X4 = identity_relation(relation_dom(X4))
| ~ relation(X3)
| ~ function(X3) ),
inference(shift_quantors,[status(thm)],[95]) ).
cnf(97,plain,
( X2 = identity_relation(relation_dom(X2))
| ~ function(X1)
| ~ relation(X1)
| relation_composition(X1,X2) != X1
| relation_rng(X1) != relation_dom(X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[96]) ).
fof(109,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(110,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ( relation(function_inverse(X2))
& function(function_inverse(X2)) ) ),
inference(variable_rename,[status(thm)],[109]) ).
fof(111,plain,
! [X2] :
( ( relation(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) )
& ( function(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[110]) ).
cnf(112,plain,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(113,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[111]) ).
fof(117,plain,
! [X2] : one_to_one(identity_relation(X2)),
inference(variable_rename,[status(thm)],[18]) ).
cnf(118,plain,
one_to_one(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[117]) ).
fof(172,plain,
! [X2] : relation(identity_relation(X2)),
inference(variable_rename,[status(thm)],[34]) ).
cnf(173,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[172]) ).
fof(174,plain,
! [X2] :
( relation(identity_relation(X2))
& function(identity_relation(X2)) ),
inference(variable_rename,[status(thm)],[35]) ).
cnf(175,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[174]) ).
fof(181,plain,
! [X2] :
( relation_dom(identity_relation(X2)) = X2
& relation_rng(identity_relation(X2)) = X2 ),
inference(variable_rename,[status(thm)],[37]) ).
cnf(182,plain,
relation_rng(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[181]) ).
cnf(183,plain,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[181]) ).
fof(191,negated_conjecture,
? [X1] : function_inverse(identity_relation(X1)) != identity_relation(X1),
inference(fof_nnf,[status(thm)],[46]) ).
fof(192,negated_conjecture,
? [X2] : function_inverse(identity_relation(X2)) != identity_relation(X2),
inference(variable_rename,[status(thm)],[191]) ).
fof(193,negated_conjecture,
function_inverse(identity_relation(esk9_0)) != identity_relation(esk9_0),
inference(skolemize,[status(esa)],[192]) ).
cnf(194,negated_conjecture,
function_inverse(identity_relation(esk9_0)) != identity_relation(esk9_0),
inference(split_conjunct,[status(thm)],[193]) ).
fof(195,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| ( relation_rng(X1) = relation_dom(function_inverse(X1))
& relation_dom(X1) = relation_rng(function_inverse(X1)) ) ),
inference(fof_nnf,[status(thm)],[41]) ).
fof(196,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X2)
| ( relation_rng(X2) = relation_dom(function_inverse(X2))
& relation_dom(X2) = relation_rng(function_inverse(X2)) ) ),
inference(variable_rename,[status(thm)],[195]) ).
fof(197,plain,
! [X2] :
( ( relation_rng(X2) = relation_dom(function_inverse(X2))
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) )
& ( relation_dom(X2) = relation_rng(function_inverse(X2))
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[196]) ).
cnf(199,plain,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[197]) ).
cnf(306,plain,
( identity_relation(relation_dom(function_inverse(X1))) = function_inverse(X1)
| relation_rng(X1) != relation_dom(function_inverse(X1))
| identity_relation(relation_dom(X1)) != X1
| ~ function(function_inverse(X1))
| ~ function(X1)
| ~ relation(function_inverse(X1))
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(spm,[status(thm)],[97,71,theory(equality)]) ).
cnf(1338,plain,
( identity_relation(relation_dom(function_inverse(X1))) = function_inverse(X1)
| relation_dom(function_inverse(X1)) != relation_rng(X1)
| identity_relation(relation_dom(X1)) != X1
| ~ one_to_one(X1)
| ~ function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[306,113]) ).
cnf(1339,plain,
( identity_relation(relation_dom(function_inverse(X1))) = function_inverse(X1)
| relation_dom(function_inverse(X1)) != relation_rng(X1)
| identity_relation(relation_dom(X1)) != X1
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[1338,112]) ).
cnf(1340,plain,
( identity_relation(relation_dom(function_inverse(X1))) = function_inverse(X1)
| identity_relation(relation_dom(X1)) != X1
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[1339,199]) ).
cnf(1345,plain,
( identity_relation(relation_rng(X1)) = function_inverse(X1)
| identity_relation(relation_dom(X1)) != X1
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[1340,199,theory(equality)]) ).
cnf(48920,plain,
( identity_relation(X1) = function_inverse(identity_relation(X1))
| identity_relation(relation_dom(identity_relation(X1))) != identity_relation(X1)
| ~ one_to_one(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1)) ),
inference(spm,[status(thm)],[1345,182,theory(equality)]) ).
cnf(49118,plain,
( identity_relation(X1) = function_inverse(identity_relation(X1))
| $false
| ~ one_to_one(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1)) ),
inference(rw,[status(thm)],[48920,183,theory(equality)]) ).
cnf(49119,plain,
( identity_relation(X1) = function_inverse(identity_relation(X1))
| $false
| $false
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1)) ),
inference(rw,[status(thm)],[49118,118,theory(equality)]) ).
cnf(49120,plain,
( identity_relation(X1) = function_inverse(identity_relation(X1))
| $false
| $false
| $false
| ~ relation(identity_relation(X1)) ),
inference(rw,[status(thm)],[49119,175,theory(equality)]) ).
cnf(49121,plain,
( identity_relation(X1) = function_inverse(identity_relation(X1))
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[49120,173,theory(equality)]) ).
cnf(49122,plain,
identity_relation(X1) = function_inverse(identity_relation(X1)),
inference(cn,[status(thm)],[49121,theory(equality)]) ).
cnf(49355,negated_conjecture,
$false,
inference(rw,[status(thm)],[194,49122,theory(equality)]) ).
cnf(49356,negated_conjecture,
$false,
inference(cn,[status(thm)],[49355,theory(equality)]) ).
cnf(49357,negated_conjecture,
$false,
49356,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU034+1.p
% --creating new selector for []
% -running prover on /tmp/tmpTHdoU6/sel_SEU034+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU034+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU034+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU034+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
%
%------------------------------------------------------------------------------