TSTP Solution File: SEU025+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU025+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 04:11:51 EST 2010
% Result : Theorem 0.74s
% Output : CNFRefutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 9 unt; 0 def)
% Number of atoms : 212 ( 53 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 279 ( 122 ~; 121 |; 23 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 50 ( 2 sgn 30 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(10,axiom,
! [X1,X2] : subset(X1,X1),
file('/tmp/tmp4gLgjK/sel_SEU025+1.p_1',reflexivity_r1_tarski) ).
fof(14,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/tmp/tmp4gLgjK/sel_SEU025+1.p_1',dt_k2_funct_1) ).
fof(16,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ) ),
file('/tmp/tmp4gLgjK/sel_SEU025+1.p_1',t46_relat_1) ).
fof(19,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_dom(X1),relation_rng(X2))
=> relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ) ),
file('/tmp/tmp4gLgjK/sel_SEU025+1.p_1',t47_relat_1) ).
fof(24,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_dom(relation_composition(X1,function_inverse(X1))) = relation_dom(X1)
& relation_rng(relation_composition(X1,function_inverse(X1))) = relation_dom(X1) ) ) ),
file('/tmp/tmp4gLgjK/sel_SEU025+1.p_1',t58_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/tmp4gLgjK/sel_SEU025+1.p_1',t55_funct_1) ).
fof(42,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_dom(relation_composition(X1,function_inverse(X1))) = relation_dom(X1)
& relation_rng(relation_composition(X1,function_inverse(X1))) = relation_dom(X1) ) ) ),
inference(assume_negation,[status(cth)],[24]) ).
fof(85,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[10]) ).
cnf(86,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[85]) ).
fof(96,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(97,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ( relation(function_inverse(X2))
& function(function_inverse(X2)) ) ),
inference(variable_rename,[status(thm)],[96]) ).
fof(98,plain,
! [X2] :
( ( relation(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) )
& ( function(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[97]) ).
cnf(100,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[98]) ).
fof(104,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ~ subset(relation_rng(X1),relation_dom(X2))
| relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(105,plain,
! [X3] :
( ~ relation(X3)
| ! [X4] :
( ~ relation(X4)
| ~ subset(relation_rng(X3),relation_dom(X4))
| relation_dom(relation_composition(X3,X4)) = relation_dom(X3) ) ),
inference(variable_rename,[status(thm)],[104]) ).
fof(106,plain,
! [X3,X4] :
( ~ relation(X4)
| ~ subset(relation_rng(X3),relation_dom(X4))
| relation_dom(relation_composition(X3,X4)) = relation_dom(X3)
| ~ relation(X3) ),
inference(shift_quantors,[status(thm)],[105]) ).
cnf(107,plain,
( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
| ~ relation(X1)
| ~ subset(relation_rng(X1),relation_dom(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[106]) ).
fof(113,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ~ subset(relation_dom(X1),relation_rng(X2))
| relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(114,plain,
! [X3] :
( ~ relation(X3)
| ! [X4] :
( ~ relation(X4)
| ~ subset(relation_dom(X3),relation_rng(X4))
| relation_rng(relation_composition(X4,X3)) = relation_rng(X3) ) ),
inference(variable_rename,[status(thm)],[113]) ).
fof(115,plain,
! [X3,X4] :
( ~ relation(X4)
| ~ subset(relation_dom(X3),relation_rng(X4))
| relation_rng(relation_composition(X4,X3)) = relation_rng(X3)
| ~ relation(X3) ),
inference(shift_quantors,[status(thm)],[114]) ).
cnf(116,plain,
( relation_rng(relation_composition(X2,X1)) = relation_rng(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),relation_rng(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[115]) ).
fof(130,negated_conjecture,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& ( relation_dom(relation_composition(X1,function_inverse(X1))) != relation_dom(X1)
| relation_rng(relation_composition(X1,function_inverse(X1))) != relation_dom(X1) ) ),
inference(fof_nnf,[status(thm)],[42]) ).
fof(131,negated_conjecture,
? [X2] :
( relation(X2)
& function(X2)
& one_to_one(X2)
& ( relation_dom(relation_composition(X2,function_inverse(X2))) != relation_dom(X2)
| relation_rng(relation_composition(X2,function_inverse(X2))) != relation_dom(X2) ) ),
inference(variable_rename,[status(thm)],[130]) ).
fof(132,negated_conjecture,
( relation(esk5_0)
& function(esk5_0)
& one_to_one(esk5_0)
& ( relation_dom(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0)
| relation_rng(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0) ) ),
inference(skolemize,[status(esa)],[131]) ).
cnf(133,negated_conjecture,
( relation_rng(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0)
| relation_dom(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0) ),
inference(split_conjunct,[status(thm)],[132]) ).
cnf(134,negated_conjecture,
one_to_one(esk5_0),
inference(split_conjunct,[status(thm)],[132]) ).
cnf(135,negated_conjecture,
function(esk5_0),
inference(split_conjunct,[status(thm)],[132]) ).
cnf(136,negated_conjecture,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[132]) ).
fof(186,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(187,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)],[186]) ).
fof(188,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)],[187]) ).
cnf(189,plain,
( relation_dom(X1) = relation_rng(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[188]) ).
cnf(190,plain,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[188]) ).
cnf(243,plain,
( relation_dom(relation_composition(X1,function_inverse(X2))) = relation_dom(X1)
| ~ subset(relation_rng(X1),relation_rng(X2))
| ~ relation(function_inverse(X2))
| ~ relation(X1)
| ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(spm,[status(thm)],[107,190,theory(equality)]) ).
cnf(253,plain,
( relation_rng(relation_composition(X1,function_inverse(X2))) = relation_rng(function_inverse(X2))
| ~ subset(relation_rng(X2),relation_rng(X1))
| ~ relation(X1)
| ~ relation(function_inverse(X2))
| ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(spm,[status(thm)],[116,190,theory(equality)]) ).
cnf(580,plain,
( relation_dom(relation_composition(X1,function_inverse(X2))) = relation_dom(X1)
| ~ one_to_one(X2)
| ~ subset(relation_rng(X1),relation_rng(X2))
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(csr,[status(thm)],[243,100]) ).
cnf(581,plain,
( relation_dom(relation_composition(X1,function_inverse(X1))) = relation_dom(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[580,86,theory(equality)]) ).
cnf(741,plain,
( relation_rng(relation_composition(X1,function_inverse(X2))) = relation_rng(function_inverse(X2))
| ~ one_to_one(X2)
| ~ subset(relation_rng(X2),relation_rng(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(csr,[status(thm)],[253,100]) ).
cnf(742,plain,
( relation_rng(relation_composition(X1,function_inverse(X1))) = relation_rng(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[741,86,theory(equality)]) ).
cnf(10999,negated_conjecture,
( relation_dom(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0)
| relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0)
| ~ one_to_one(esk5_0)
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(spm,[status(thm)],[133,742,theory(equality)]) ).
cnf(11063,negated_conjecture,
( relation_dom(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0)
| relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0)
| $false
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[10999,134,theory(equality)]) ).
cnf(11064,negated_conjecture,
( relation_dom(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0)
| relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0)
| $false
| $false
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[11063,135,theory(equality)]) ).
cnf(11065,negated_conjecture,
( relation_dom(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0)
| relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[11064,136,theory(equality)]) ).
cnf(11066,negated_conjecture,
( relation_dom(relation_composition(esk5_0,function_inverse(esk5_0))) != relation_dom(esk5_0)
| relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0) ),
inference(cn,[status(thm)],[11065,theory(equality)]) ).
cnf(13237,negated_conjecture,
( relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0)
| ~ one_to_one(esk5_0)
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(spm,[status(thm)],[11066,581,theory(equality)]) ).
cnf(13273,negated_conjecture,
( relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0)
| $false
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[13237,134,theory(equality)]) ).
cnf(13274,negated_conjecture,
( relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0)
| $false
| $false
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[13273,135,theory(equality)]) ).
cnf(13275,negated_conjecture,
( relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[13274,136,theory(equality)]) ).
cnf(13276,negated_conjecture,
relation_rng(function_inverse(esk5_0)) != relation_dom(esk5_0),
inference(cn,[status(thm)],[13275,theory(equality)]) ).
cnf(13284,negated_conjecture,
( ~ one_to_one(esk5_0)
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(spm,[status(thm)],[13276,189,theory(equality)]) ).
cnf(13305,negated_conjecture,
( $false
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[13284,134,theory(equality)]) ).
cnf(13306,negated_conjecture,
( $false
| $false
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[13305,135,theory(equality)]) ).
cnf(13307,negated_conjecture,
( $false
| $false
| $false ),
inference(rw,[status(thm)],[13306,136,theory(equality)]) ).
cnf(13308,negated_conjecture,
$false,
inference(cn,[status(thm)],[13307,theory(equality)]) ).
cnf(13309,negated_conjecture,
$false,
13308,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU025+1.p
% --creating new selector for []
% -running prover on /tmp/tmp4gLgjK/sel_SEU025+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU025+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU025+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU025+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
%
%------------------------------------------------------------------------------