TSTP Solution File: SEU032+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU032+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 04:12:35 EST 2010
% Result : Theorem 0.24s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 6 unt; 0 def)
% Number of atoms : 215 ( 55 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 294 ( 126 ~; 123 |; 31 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 41 ( 0 sgn 25 !; 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/tmp-S2Baw/sel_SEU032+1.p_1',t61_funct_1) ).
fof(11,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
file('/tmp/tmp-S2Baw/sel_SEU032+1.p_1',t62_funct_1) ).
fof(16,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/tmp/tmp-S2Baw/sel_SEU032+1.p_1',dt_k2_funct_1) ).
fof(24,axiom,
! [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/tmp-S2Baw/sel_SEU032+1.p_1',t63_funct_1) ).
fof(31,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(function_inverse(X1)) = X1 ) ),
file('/tmp/tmp-S2Baw/sel_SEU032+1.p_1',t65_funct_1) ).
fof(40,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/tmp-S2Baw/sel_SEU032+1.p_1',t55_funct_1) ).
fof(45,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(function_inverse(X1)) = X1 ) ),
inference(assume_negation,[status(cth)],[31]) ).
fof(66,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(67,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)],[66]) ).
fof(68,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)],[67]) ).
cnf(69,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)],[68]) ).
fof(93,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| one_to_one(function_inverse(X1)) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(94,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X2)
| one_to_one(function_inverse(X2)) ),
inference(variable_rename,[status(thm)],[93]) ).
cnf(95,plain,
( one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[94]) ).
fof(107,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(108,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ( relation(function_inverse(X2))
& function(function_inverse(X2)) ) ),
inference(variable_rename,[status(thm)],[107]) ).
fof(109,plain,
! [X2] :
( ( relation(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) )
& ( function(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[108]) ).
cnf(110,plain,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[109]) ).
cnf(111,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[109]) ).
fof(133,plain,
! [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)],[24]) ).
fof(134,plain,
! [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)],[133]) ).
fof(135,plain,
! [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)
| ~ relation(X3)
| ~ function(X3) ),
inference(shift_quantors,[status(thm)],[134]) ).
cnf(136,plain,
( X2 = function_inverse(X1)
| ~ function(X1)
| ~ relation(X1)
| relation_composition(X1,X2) != identity_relation(relation_dom(X1))
| relation_rng(X1) != relation_dom(X2)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[135]) ).
fof(162,negated_conjecture,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& function_inverse(function_inverse(X1)) != X1 ),
inference(fof_nnf,[status(thm)],[45]) ).
fof(163,negated_conjecture,
? [X2] :
( relation(X2)
& function(X2)
& one_to_one(X2)
& function_inverse(function_inverse(X2)) != X2 ),
inference(variable_rename,[status(thm)],[162]) ).
fof(164,negated_conjecture,
( relation(esk5_0)
& function(esk5_0)
& one_to_one(esk5_0)
& function_inverse(function_inverse(esk5_0)) != esk5_0 ),
inference(skolemize,[status(esa)],[163]) ).
cnf(165,negated_conjecture,
function_inverse(function_inverse(esk5_0)) != esk5_0,
inference(split_conjunct,[status(thm)],[164]) ).
cnf(166,negated_conjecture,
one_to_one(esk5_0),
inference(split_conjunct,[status(thm)],[164]) ).
cnf(167,negated_conjecture,
function(esk5_0),
inference(split_conjunct,[status(thm)],[164]) ).
cnf(168,negated_conjecture,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[164]) ).
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)],[40]) ).
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(198,plain,
( relation_dom(X1) = relation_rng(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[197]) ).
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(303,plain,
( function_inverse(function_inverse(X1)) = X1
| identity_relation(relation_dom(function_inverse(X1))) != identity_relation(relation_rng(X1))
| relation_rng(function_inverse(X1)) != relation_dom(X1)
| ~ one_to_one(function_inverse(X1))
| ~ function(X1)
| ~ function(function_inverse(X1))
| ~ relation(X1)
| ~ relation(function_inverse(X1))
| ~ one_to_one(X1) ),
inference(spm,[status(thm)],[136,69,theory(equality)]) ).
cnf(1208,plain,
( function_inverse(function_inverse(X1)) = X1
| identity_relation(relation_dom(function_inverse(X1))) != identity_relation(relation_rng(X1))
| relation_rng(function_inverse(X1)) != relation_dom(X1)
| ~ one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[303,111]) ).
cnf(1209,plain,
( function_inverse(function_inverse(X1)) = X1
| identity_relation(relation_dom(function_inverse(X1))) != identity_relation(relation_rng(X1))
| relation_rng(function_inverse(X1)) != relation_dom(X1)
| ~ one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[1208,110]) ).
cnf(1210,plain,
( function_inverse(function_inverse(X1)) = X1
| identity_relation(relation_dom(function_inverse(X1))) != identity_relation(relation_rng(X1))
| relation_rng(function_inverse(X1)) != relation_dom(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[1209,95]) ).
cnf(1211,plain,
( function_inverse(function_inverse(X1)) = X1
| identity_relation(relation_dom(function_inverse(X1))) != identity_relation(relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[1210,198]) ).
cnf(1212,plain,
( function_inverse(function_inverse(X1)) = X1
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[1211,199,theory(equality)]) ).
cnf(1227,negated_conjecture,
( ~ one_to_one(esk5_0)
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(spm,[status(thm)],[165,1212,theory(equality)]) ).
cnf(1261,negated_conjecture,
( $false
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[1227,166,theory(equality)]) ).
cnf(1262,negated_conjecture,
( $false
| $false
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[1261,167,theory(equality)]) ).
cnf(1263,negated_conjecture,
( $false
| $false
| $false ),
inference(rw,[status(thm)],[1262,168,theory(equality)]) ).
cnf(1264,negated_conjecture,
$false,
inference(cn,[status(thm)],[1263,theory(equality)]) ).
cnf(1265,negated_conjecture,
$false,
1264,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU032+1.p
% --creating new selector for []
% -running prover on /tmp/tmp-S2Baw/sel_SEU032+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU032+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU032+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU032+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
%
%------------------------------------------------------------------------------