%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU031+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 04:12:28 EST 2010
% Result : Theorem 71.11s
% Output : CNFRefutation 71.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 12 unt; 0 def)
% Number of atoms : 301 ( 92 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 414 ( 168 ~; 182 |; 49 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 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 : 64 ( 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/tmpVjLvmd/sel_SEU031+1.p_2',t61_funct_1) ).
fof(15,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/tmp/tmpVjLvmd/sel_SEU031+1.p_2',dt_k2_funct_1) ).
fof(22,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X1)
& relation_rng(X2) = relation_dom(X1)
& relation_composition(X2,X1) = identity_relation(relation_rng(X1)) )
=> X2 = function_inverse(X1) ) ) ),
file('/tmp/tmpVjLvmd/sel_SEU031+1.p_2',t64_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/tmpVjLvmd/sel_SEU031+1.p_2',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/tmpVjLvmd/sel_SEU031+1.p_2',l72_funct_1) ).
fof(44,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X1)
& relation_rng(X2) = relation_dom(X1)
& relation_composition(X2,X1) = identity_relation(relation_rng(X1)) )
=> X2 = function_inverse(X1) ) ) ),
inference(assume_negation,[status(cth)],[22]) ).
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(69,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)],[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(126,negated_conjecture,
? [X1] :
( relation(X1)
& function(X1)
& ? [X2] :
( relation(X2)
& function(X2)
& one_to_one(X1)
& relation_rng(X2) = relation_dom(X1)
& relation_composition(X2,X1) = identity_relation(relation_rng(X1))
& X2 != function_inverse(X1) ) ),
inference(fof_nnf,[status(thm)],[44]) ).
fof(127,negated_conjecture,
? [X3] :
( relation(X3)
& function(X3)
& ? [X4] :
( relation(X4)
& function(X4)
& one_to_one(X3)
& relation_rng(X4) = relation_dom(X3)
& relation_composition(X4,X3) = identity_relation(relation_rng(X3))
& X4 != function_inverse(X3) ) ),
inference(variable_rename,[status(thm)],[126]) ).
fof(128,negated_conjecture,
( relation(esk5_0)
& function(esk5_0)
& relation(esk6_0)
& function(esk6_0)
& one_to_one(esk5_0)
& relation_rng(esk6_0) = relation_dom(esk5_0)
& relation_composition(esk6_0,esk5_0) = identity_relation(relation_rng(esk5_0))
& esk6_0 != function_inverse(esk5_0) ),
inference(skolemize,[status(esa)],[127]) ).
cnf(129,negated_conjecture,
esk6_0 != function_inverse(esk5_0),
inference(split_conjunct,[status(thm)],[128]) ).
cnf(130,negated_conjecture,
relation_composition(esk6_0,esk5_0) = identity_relation(relation_rng(esk5_0)),
inference(split_conjunct,[status(thm)],[128]) ).
cnf(131,negated_conjecture,
relation_rng(esk6_0) = relation_dom(esk5_0),
inference(split_conjunct,[status(thm)],[128]) ).
cnf(132,negated_conjecture,
one_to_one(esk5_0),
inference(split_conjunct,[status(thm)],[128]) ).
cnf(133,negated_conjecture,
function(esk6_0),
inference(split_conjunct,[status(thm)],[128]) ).
cnf(134,negated_conjecture,
relation(esk6_0),
inference(split_conjunct,[status(thm)],[128]) ).
cnf(135,negated_conjecture,
function(esk5_0),
inference(split_conjunct,[status(thm)],[128]) ).
cnf(136,negated_conjecture,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[128]) ).
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(195,plain,
( relation_rng(X1) = relation_dom(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(274,negated_conjecture,
( relation_composition(esk5_0,function_inverse(esk5_0)) = identity_relation(relation_rng(esk6_0))
| ~ one_to_one(esk5_0)
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(spm,[status(thm)],[69,131,theory(equality)]) ).
cnf(281,negated_conjecture,
( relation_composition(esk5_0,function_inverse(esk5_0)) = identity_relation(relation_rng(esk6_0))
| $false
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[274,132,theory(equality)]) ).
cnf(282,negated_conjecture,
( relation_composition(esk5_0,function_inverse(esk5_0)) = identity_relation(relation_rng(esk6_0))
| $false
| $false
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[281,135,theory(equality)]) ).
cnf(283,negated_conjecture,
( relation_composition(esk5_0,function_inverse(esk5_0)) = identity_relation(relation_rng(esk6_0))
| $false
| $false
| $false ),
inference(rw,[status(thm)],[282,136,theory(equality)]) ).
cnf(284,negated_conjecture,
relation_composition(esk5_0,function_inverse(esk5_0)) = identity_relation(relation_rng(esk6_0)),
inference(cn,[status(thm)],[283,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(1676,plain,
( X1 = function_inverse(X2)
| identity_relation(relation_rng(X2)) != relation_composition(X1,X3)
| relation_composition(X3,function_inverse(X2)) != identity_relation(relation_rng(X1))
| ~ function(function_inverse(X2))
| ~ function(X3)
| ~ function(X1)
| ~ relation(function_inverse(X2))
| ~ relation(X3)
| ~ relation(X1)
| ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(spm,[status(thm)],[317,195,theory(equality)]) ).
cnf(22808,plain,
( X1 = function_inverse(X2)
| relation_composition(X3,function_inverse(X2)) != identity_relation(relation_rng(X1))
| identity_relation(relation_rng(X2)) != relation_composition(X1,X3)
| ~ one_to_one(X2)
| ~ function(function_inverse(X2))
| ~ function(X2)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(csr,[status(thm)],[1676,107]) ).
cnf(22809,plain,
( X1 = function_inverse(X2)
| relation_composition(X3,function_inverse(X2)) != identity_relation(relation_rng(X1))
| identity_relation(relation_rng(X2)) != relation_composition(X1,X3)
| ~ one_to_one(X2)
| ~ function(X3)
| ~ function(X1)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(csr,[status(thm)],[22808,106]) ).
cnf(22811,negated_conjecture,
( esk6_0 = function_inverse(X1)
| relation_composition(X2,function_inverse(X1)) != relation_composition(esk5_0,function_inverse(esk5_0))
| identity_relation(relation_rng(X1)) != relation_composition(esk6_0,X2)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ function(esk6_0)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(esk6_0)
| ~ relation(X1) ),
inference(spm,[status(thm)],[22809,284,theory(equality)]) ).
cnf(22906,negated_conjecture,
( esk6_0 = function_inverse(X1)
| relation_composition(X2,function_inverse(X1)) != relation_composition(esk5_0,function_inverse(esk5_0))
| identity_relation(relation_rng(X1)) != relation_composition(esk6_0,X2)
| ~ one_to_one(X1)
| ~ function(X2)
| $false
| ~ function(X1)
| ~ relation(X2)
| ~ relation(esk6_0)
| ~ relation(X1) ),
inference(rw,[status(thm)],[22811,133,theory(equality)]) ).
cnf(22907,negated_conjecture,
( esk6_0 = function_inverse(X1)
| relation_composition(X2,function_inverse(X1)) != relation_composition(esk5_0,function_inverse(esk5_0))
| identity_relation(relation_rng(X1)) != relation_composition(esk6_0,X2)
| ~ one_to_one(X1)
| ~ function(X2)
| $false
| ~ function(X1)
| ~ relation(X2)
| $false
| ~ relation(X1) ),
inference(rw,[status(thm)],[22906,134,theory(equality)]) ).
cnf(22908,negated_conjecture,
( esk6_0 = function_inverse(X1)
| relation_composition(X2,function_inverse(X1)) != relation_composition(esk5_0,function_inverse(esk5_0))
| identity_relation(relation_rng(X1)) != relation_composition(esk6_0,X2)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cn,[status(thm)],[22907,theory(equality)]) ).
cnf(838236,negated_conjecture,
( function_inverse(esk5_0) = esk6_0
| identity_relation(relation_rng(esk5_0)) != relation_composition(esk6_0,esk5_0)
| ~ one_to_one(esk5_0)
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(er,[status(thm)],[22908,theory(equality)]) ).
cnf(838522,negated_conjecture,
( function_inverse(esk5_0) = esk6_0
| $false
| ~ one_to_one(esk5_0)
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[838236,130,theory(equality)]) ).
cnf(838523,negated_conjecture,
( function_inverse(esk5_0) = esk6_0
| $false
| $false
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[838522,132,theory(equality)]) ).
cnf(838524,negated_conjecture,
( function_inverse(esk5_0) = esk6_0
| $false
| $false
| $false
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[838523,135,theory(equality)]) ).
cnf(838525,negated_conjecture,
( function_inverse(esk5_0) = esk6_0
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[838524,136,theory(equality)]) ).
cnf(838526,negated_conjecture,
function_inverse(esk5_0) = esk6_0,
inference(cn,[status(thm)],[838525,theory(equality)]) ).
cnf(838527,negated_conjecture,
$false,
inference(sr,[status(thm)],[838526,129,theory(equality)]) ).
cnf(838528,negated_conjecture,
$false,
838527,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU031+1.p
% --creating new selector for []
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpVjLvmd/sel_SEU031+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpVjLvmd/sel_SEU031+1.p_2 with time limit 80
% -prover status Theorem
% Problem SEU031+1.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU031+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU031+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
%
%------------------------------------------------------------------------------