TSTP Solution File: SEU030+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU030+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 04:12:23 EST 2010
% Result : Theorem 1.07s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of formulae : 64 ( 12 unt; 0 def)
% Number of atoms : 311 ( 86 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 421 ( 174 ~; 183 |; 49 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 32 !; 4 ?)
% 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/tmpLWeqLq/sel_SEU030+1.p_1',t61_funct_1) ).
fof(15,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/tmp/tmpLWeqLq/sel_SEU030+1.p_1',dt_k2_funct_1) ).
fof(23,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X1)
& relation_rng(X1) = relation_dom(X2)
& relation_composition(X1,X2) = identity_relation(relation_dom(X1)) )
=> X2 = function_inverse(X1) ) ) ),
file('/tmp/tmpLWeqLq/sel_SEU030+1.p_1',t63_funct_1) ).
fof(38,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/tmpLWeqLq/sel_SEU030+1.p_1',t55_funct_1) ).
fof(43,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ! [X4] :
( ( relation(X4)
& function(X4) )
=> ( ( relation_rng(X2) = X1
& relation_composition(X2,X3) = identity_relation(relation_dom(X4))
& relation_composition(X3,X4) = identity_relation(X1) )
=> X4 = X2 ) ) ) ),
file('/tmp/tmpLWeqLq/sel_SEU030+1.p_1',l72_funct_1) ).
fof(44,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X1)
& relation_rng(X1) = relation_dom(X2)
& relation_composition(X1,X2) = identity_relation(relation_dom(X1)) )
=> X2 = function_inverse(X1) ) ) ),
inference(assume_negation,[status(cth)],[23]) ).
fof(65,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(66,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)],[65]) ).
fof(67,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)],[66]) ).
cnf(68,plain,
( relation_composition(function_inverse(X1),X1) = identity_relation(relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[67]) ).
fof(103,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(104,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ( relation(function_inverse(X2))
& function(function_inverse(X2)) ) ),
inference(variable_rename,[status(thm)],[103]) ).
fof(105,plain,
! [X2] :
( ( relation(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) )
& ( function(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[104]) ).
cnf(106,plain,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(107,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[105]) ).
fof(129,negated_conjecture,
? [X1] :
( relation(X1)
& function(X1)
& ? [X2] :
( relation(X2)
& function(X2)
& one_to_one(X1)
& relation_rng(X1) = relation_dom(X2)
& relation_composition(X1,X2) = identity_relation(relation_dom(X1))
& X2 != function_inverse(X1) ) ),
inference(fof_nnf,[status(thm)],[44]) ).
fof(130,negated_conjecture,
? [X3] :
( relation(X3)
& function(X3)
& ? [X4] :
( relation(X4)
& function(X4)
& one_to_one(X3)
& relation_rng(X3) = relation_dom(X4)
& relation_composition(X3,X4) = identity_relation(relation_dom(X3))
& X4 != function_inverse(X3) ) ),
inference(variable_rename,[status(thm)],[129]) ).
fof(131,negated_conjecture,
( relation(esk5_0)
& function(esk5_0)
& relation(esk6_0)
& function(esk6_0)
& one_to_one(esk5_0)
& relation_rng(esk5_0) = relation_dom(esk6_0)
& relation_composition(esk5_0,esk6_0) = identity_relation(relation_dom(esk5_0))
& esk6_0 != function_inverse(esk5_0) ),
inference(skolemize,[status(esa)],[130]) ).
cnf(132,negated_conjecture,
esk6_0 != function_inverse(esk5_0),
inference(split_conjunct,[status(thm)],[131]) ).
cnf(133,negated_conjecture,
relation_composition(esk5_0,esk6_0) = identity_relation(relation_dom(esk5_0)),
inference(split_conjunct,[status(thm)],[131]) ).
cnf(134,negated_conjecture,
relation_rng(esk5_0) = relation_dom(esk6_0),
inference(split_conjunct,[status(thm)],[131]) ).
cnf(135,negated_conjecture,
one_to_one(esk5_0),
inference(split_conjunct,[status(thm)],[131]) ).
cnf(136,negated_conjecture,
function(esk6_0),
inference(split_conjunct,[status(thm)],[131]) ).
cnf(137,negated_conjecture,
relation(esk6_0),
inference(split_conjunct,[status(thm)],[131]) ).
cnf(138,negated_conjecture,
function(esk5_0),
inference(split_conjunct,[status(thm)],[131]) ).
cnf(139,negated_conjecture,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[131]) ).
fof(191,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)],[38]) ).
fof(192,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)],[191]) ).
fof(193,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)],[192]) ).
cnf(194,plain,
( relation_dom(X1) = relation_rng(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[193]) ).
fof(212,plain,
! [X1,X2] :
( ~ relation(X2)
| ~ function(X2)
| ! [X3] :
( ~ relation(X3)
| ~ function(X3)
| ! [X4] :
( ~ relation(X4)
| ~ function(X4)
| relation_rng(X2) != X1
| relation_composition(X2,X3) != identity_relation(relation_dom(X4))
| relation_composition(X3,X4) != identity_relation(X1)
| X4 = X2 ) ) ),
inference(fof_nnf,[status(thm)],[43]) ).
fof(213,plain,
! [X5,X6] :
( ~ relation(X6)
| ~ function(X6)
| ! [X7] :
( ~ relation(X7)
| ~ function(X7)
| ! [X8] :
( ~ relation(X8)
| ~ function(X8)
| relation_rng(X6) != X5
| relation_composition(X6,X7) != identity_relation(relation_dom(X8))
| relation_composition(X7,X8) != identity_relation(X5)
| X8 = X6 ) ) ),
inference(variable_rename,[status(thm)],[212]) ).
fof(214,plain,
! [X5,X6,X7,X8] :
( ~ relation(X8)
| ~ function(X8)
| relation_rng(X6) != X5
| relation_composition(X6,X7) != identity_relation(relation_dom(X8))
| relation_composition(X7,X8) != identity_relation(X5)
| X8 = X6
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) ),
inference(shift_quantors,[status(thm)],[213]) ).
cnf(215,plain,
( X3 = X1
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_composition(X2,X3) != identity_relation(X4)
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| relation_rng(X1) != X4
| ~ function(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[214]) ).
cnf(291,negated_conjecture,
( relation_composition(function_inverse(esk5_0),esk5_0) = identity_relation(relation_dom(esk6_0))
| ~ one_to_one(esk5_0)
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(spm,[status(thm)],[68,134,theory(equality)]) ).
cnf(298,negated_conjecture,
( relation_composition(function_inverse(esk5_0),esk5_0) = identity_relation(relation_dom(esk6_0))
| $false
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[291,135,theory(equality)]) ).
cnf(299,negated_conjecture,
( relation_composition(function_inverse(esk5_0),esk5_0) = identity_relation(relation_dom(esk6_0))
| $false
| $false
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[298,138,theory(equality)]) ).
cnf(300,negated_conjecture,
( relation_composition(function_inverse(esk5_0),esk5_0) = identity_relation(relation_dom(esk6_0))
| $false
| $false
| $false ),
inference(rw,[status(thm)],[299,139,theory(equality)]) ).
cnf(301,negated_conjecture,
relation_composition(function_inverse(esk5_0),esk5_0) = identity_relation(relation_dom(esk6_0)),
inference(cn,[status(thm)],[300,theory(equality)]) ).
cnf(317,plain,
( X1 = X2
| identity_relation(relation_dom(X2)) != relation_composition(X1,X3)
| relation_composition(X3,X2) != identity_relation(relation_rng(X1))
| ~ function(X2)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X1) ),
inference(er,[status(thm)],[215,theory(equality)]) ).
cnf(1737,negated_conjecture,
( X1 = esk6_0
| relation_composition(function_inverse(esk5_0),esk5_0) != relation_composition(X1,X2)
| relation_composition(X2,esk6_0) != identity_relation(relation_rng(X1))
| ~ function(esk6_0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(esk6_0)
| ~ relation(X2)
| ~ relation(X1) ),
inference(spm,[status(thm)],[317,301,theory(equality)]) ).
cnf(1756,negated_conjecture,
( X1 = esk6_0
| relation_composition(function_inverse(esk5_0),esk5_0) != relation_composition(X1,X2)
| relation_composition(X2,esk6_0) != identity_relation(relation_rng(X1))
| $false
| ~ function(X2)
| ~ function(X1)
| ~ relation(esk6_0)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[1737,136,theory(equality)]) ).
cnf(1757,negated_conjecture,
( X1 = esk6_0
| relation_composition(function_inverse(esk5_0),esk5_0) != relation_composition(X1,X2)
| relation_composition(X2,esk6_0) != identity_relation(relation_rng(X1))
| $false
| ~ function(X2)
| ~ function(X1)
| $false
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[1756,137,theory(equality)]) ).
cnf(1758,negated_conjecture,
( X1 = esk6_0
| relation_composition(function_inverse(esk5_0),esk5_0) != relation_composition(X1,X2)
| relation_composition(X2,esk6_0) != identity_relation(relation_rng(X1))
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cn,[status(thm)],[1757,theory(equality)]) ).
cnf(21809,negated_conjecture,
( function_inverse(esk5_0) = esk6_0
| relation_composition(esk5_0,esk6_0) != identity_relation(relation_rng(function_inverse(esk5_0)))
| ~ function(esk5_0)
| ~ function(function_inverse(esk5_0))
| ~ relation(esk5_0)
| ~ relation(function_inverse(esk5_0)) ),
inference(er,[status(thm)],[1758,theory(equality)]) ).
cnf(21886,negated_conjecture,
( function_inverse(esk5_0) = esk6_0
| relation_composition(esk5_0,esk6_0) != identity_relation(relation_rng(function_inverse(esk5_0)))
| $false
| ~ function(function_inverse(esk5_0))
| ~ relation(esk5_0)
| ~ relation(function_inverse(esk5_0)) ),
inference(rw,[status(thm)],[21809,138,theory(equality)]) ).
cnf(21887,negated_conjecture,
( function_inverse(esk5_0) = esk6_0
| relation_composition(esk5_0,esk6_0) != identity_relation(relation_rng(function_inverse(esk5_0)))
| $false
| ~ function(function_inverse(esk5_0))
| $false
| ~ relation(function_inverse(esk5_0)) ),
inference(rw,[status(thm)],[21886,139,theory(equality)]) ).
cnf(21888,negated_conjecture,
( function_inverse(esk5_0) = esk6_0
| relation_composition(esk5_0,esk6_0) != identity_relation(relation_rng(function_inverse(esk5_0)))
| ~ function(function_inverse(esk5_0))
| ~ relation(function_inverse(esk5_0)) ),
inference(cn,[status(thm)],[21887,theory(equality)]) ).
cnf(21889,negated_conjecture,
( identity_relation(relation_rng(function_inverse(esk5_0))) != relation_composition(esk5_0,esk6_0)
| ~ function(function_inverse(esk5_0))
| ~ relation(function_inverse(esk5_0)) ),
inference(sr,[status(thm)],[21888,132,theory(equality)]) ).
cnf(21985,negated_conjecture,
( identity_relation(relation_dom(esk5_0)) != relation_composition(esk5_0,esk6_0)
| ~ function(function_inverse(esk5_0))
| ~ relation(function_inverse(esk5_0))
| ~ one_to_one(esk5_0)
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(spm,[status(thm)],[21889,194,theory(equality)]) ).
cnf(22018,negated_conjecture,
( $false
| ~ function(function_inverse(esk5_0))
| ~ relation(function_inverse(esk5_0))
| ~ one_to_one(esk5_0)
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[21985,133,theory(equality)]) ).
cnf(22019,negated_conjecture,
( $false
| ~ function(function_inverse(esk5_0))
| ~ relation(function_inverse(esk5_0))
| $false
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[22018,135,theory(equality)]) ).
cnf(22020,negated_conjecture,
( $false
| ~ function(function_inverse(esk5_0))
| ~ relation(function_inverse(esk5_0))
| $false
| $false
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[22019,138,theory(equality)]) ).
cnf(22021,negated_conjecture,
( $false
| ~ function(function_inverse(esk5_0))
| ~ relation(function_inverse(esk5_0))
| $false
| $false
| $false ),
inference(rw,[status(thm)],[22020,139,theory(equality)]) ).
cnf(22022,negated_conjecture,
( ~ function(function_inverse(esk5_0))
| ~ relation(function_inverse(esk5_0)) ),
inference(cn,[status(thm)],[22021,theory(equality)]) ).
cnf(22056,negated_conjecture,
( ~ relation(function_inverse(esk5_0))
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(spm,[status(thm)],[22022,106,theory(equality)]) ).
cnf(22065,negated_conjecture,
( ~ relation(function_inverse(esk5_0))
| $false
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[22056,138,theory(equality)]) ).
cnf(22066,negated_conjecture,
( ~ relation(function_inverse(esk5_0))
| $false
| $false ),
inference(rw,[status(thm)],[22065,139,theory(equality)]) ).
cnf(22067,negated_conjecture,
~ relation(function_inverse(esk5_0)),
inference(cn,[status(thm)],[22066,theory(equality)]) ).
cnf(22325,negated_conjecture,
( ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(spm,[status(thm)],[22067,107,theory(equality)]) ).
cnf(22333,negated_conjecture,
( $false
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[22325,138,theory(equality)]) ).
cnf(22334,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[22333,139,theory(equality)]) ).
cnf(22335,negated_conjecture,
$false,
inference(cn,[status(thm)],[22334,theory(equality)]) ).
cnf(22336,negated_conjecture,
$false,
22335,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU030+1.p
% --creating new selector for []
% -running prover on /tmp/tmpLWeqLq/sel_SEU030+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU030+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU030+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU030+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
%
%------------------------------------------------------------------------------