TSTP Solution File: SEU212+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU212+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 05:39:40 EST 2010
% Result : Theorem 23.62s
% Output : CNFRefutation 23.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 66 ( 18 unt; 0 def)
% Number of atoms : 251 ( 70 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 303 ( 118 ~; 129 |; 40 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 90 ( 3 sgn 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(17,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
file('/tmp/tmpY_w6-T/sel_SEU212+2.p_1',t8_funct_1) ).
fof(54,axiom,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
file('/tmp/tmpY_w6-T/sel_SEU212+2.p_1',t20_relat_1) ).
fof(58,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpY_w6-T/sel_SEU212+2.p_1',commutativity_k2_tarski) ).
fof(61,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/tmp/tmpY_w6-T/sel_SEU212+2.p_1',t69_enumset1) ).
fof(155,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpY_w6-T/sel_SEU212+2.p_1',d5_tarski) ).
fof(163,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
file('/tmp/tmpY_w6-T/sel_SEU212+2.p_1',d4_funct_1) ).
fof(216,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
inference(assume_negation,[status(cth)],[17]) ).
fof(237,plain,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
inference(fof_simplification,[status(thm)],[163,theory(equality)]) ).
fof(309,negated_conjecture,
? [X1,X2,X3] :
( relation(X3)
& function(X3)
& ( ~ in(ordered_pair(X1,X2),X3)
| ~ in(X1,relation_dom(X3))
| X2 != apply(X3,X1) )
& ( in(ordered_pair(X1,X2),X3)
| ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
inference(fof_nnf,[status(thm)],[216]) ).
fof(310,negated_conjecture,
? [X4,X5,X6] :
( relation(X6)
& function(X6)
& ( ~ in(ordered_pair(X4,X5),X6)
| ~ in(X4,relation_dom(X6))
| X5 != apply(X6,X4) )
& ( in(ordered_pair(X4,X5),X6)
| ( in(X4,relation_dom(X6))
& X5 = apply(X6,X4) ) ) ),
inference(variable_rename,[status(thm)],[309]) ).
fof(311,negated_conjecture,
( relation(esk7_0)
& function(esk7_0)
& ( ~ in(ordered_pair(esk5_0,esk6_0),esk7_0)
| ~ in(esk5_0,relation_dom(esk7_0))
| esk6_0 != apply(esk7_0,esk5_0) )
& ( in(ordered_pair(esk5_0,esk6_0),esk7_0)
| ( in(esk5_0,relation_dom(esk7_0))
& esk6_0 = apply(esk7_0,esk5_0) ) ) ),
inference(skolemize,[status(esa)],[310]) ).
fof(312,negated_conjecture,
( relation(esk7_0)
& function(esk7_0)
& ( ~ in(ordered_pair(esk5_0,esk6_0),esk7_0)
| ~ in(esk5_0,relation_dom(esk7_0))
| esk6_0 != apply(esk7_0,esk5_0) )
& ( in(esk5_0,relation_dom(esk7_0))
| in(ordered_pair(esk5_0,esk6_0),esk7_0) )
& ( esk6_0 = apply(esk7_0,esk5_0)
| in(ordered_pair(esk5_0,esk6_0),esk7_0) ) ),
inference(distribute,[status(thm)],[311]) ).
cnf(313,negated_conjecture,
( in(ordered_pair(esk5_0,esk6_0),esk7_0)
| esk6_0 = apply(esk7_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[312]) ).
cnf(314,negated_conjecture,
( in(ordered_pair(esk5_0,esk6_0),esk7_0)
| in(esk5_0,relation_dom(esk7_0)) ),
inference(split_conjunct,[status(thm)],[312]) ).
cnf(315,negated_conjecture,
( esk6_0 != apply(esk7_0,esk5_0)
| ~ in(esk5_0,relation_dom(esk7_0))
| ~ in(ordered_pair(esk5_0,esk6_0),esk7_0) ),
inference(split_conjunct,[status(thm)],[312]) ).
cnf(316,negated_conjecture,
function(esk7_0),
inference(split_conjunct,[status(thm)],[312]) ).
cnf(317,negated_conjecture,
relation(esk7_0),
inference(split_conjunct,[status(thm)],[312]) ).
fof(450,plain,
! [X1,X2,X3] :
( ~ relation(X3)
| ~ in(ordered_pair(X1,X2),X3)
| ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ),
inference(fof_nnf,[status(thm)],[54]) ).
fof(451,plain,
! [X4,X5,X6] :
( ~ relation(X6)
| ~ in(ordered_pair(X4,X5),X6)
| ( in(X4,relation_dom(X6))
& in(X5,relation_rng(X6)) ) ),
inference(variable_rename,[status(thm)],[450]) ).
fof(452,plain,
! [X4,X5,X6] :
( ( in(X4,relation_dom(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) )
& ( in(X5,relation_rng(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[451]) ).
cnf(454,plain,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[452]) ).
fof(466,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[58]) ).
cnf(467,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[466]) ).
fof(479,plain,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[61]) ).
cnf(480,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[479]) ).
fof(861,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[155]) ).
cnf(862,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[861]) ).
fof(892,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ! [X2,X3] :
( ( ~ in(X2,relation_dom(X1))
| ( ( X3 != apply(X1,X2)
| in(ordered_pair(X2,X3),X1) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X3 = apply(X1,X2) ) ) )
& ( in(X2,relation_dom(X1))
| ( ( X3 != apply(X1,X2)
| X3 = empty_set )
& ( X3 != empty_set
| X3 = apply(X1,X2) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[237]) ).
fof(893,plain,
! [X4] :
( ~ relation(X4)
| ~ function(X4)
| ! [X5,X6] :
( ( ~ in(X5,relation_dom(X4))
| ( ( X6 != apply(X4,X5)
| in(ordered_pair(X5,X6),X4) )
& ( ~ in(ordered_pair(X5,X6),X4)
| X6 = apply(X4,X5) ) ) )
& ( in(X5,relation_dom(X4))
| ( ( X6 != apply(X4,X5)
| X6 = empty_set )
& ( X6 != empty_set
| X6 = apply(X4,X5) ) ) ) ) ),
inference(variable_rename,[status(thm)],[892]) ).
fof(894,plain,
! [X4,X5,X6] :
( ( ( ~ in(X5,relation_dom(X4))
| ( ( X6 != apply(X4,X5)
| in(ordered_pair(X5,X6),X4) )
& ( ~ in(ordered_pair(X5,X6),X4)
| X6 = apply(X4,X5) ) ) )
& ( in(X5,relation_dom(X4))
| ( ( X6 != apply(X4,X5)
| X6 = empty_set )
& ( X6 != empty_set
| X6 = apply(X4,X5) ) ) ) )
| ~ relation(X4)
| ~ function(X4) ),
inference(shift_quantors,[status(thm)],[893]) ).
fof(895,plain,
! [X4,X5,X6] :
( ( X6 != apply(X4,X5)
| in(ordered_pair(X5,X6),X4)
| ~ in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( ~ in(ordered_pair(X5,X6),X4)
| X6 = apply(X4,X5)
| ~ in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( X6 != apply(X4,X5)
| X6 = empty_set
| in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( X6 != empty_set
| X6 = apply(X4,X5)
| in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[894]) ).
cnf(898,plain,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[895]) ).
cnf(899,plain,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
inference(split_conjunct,[status(thm)],[895]) ).
cnf(1126,plain,
unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[862,480,theory(equality)]),
[unfolding] ).
cnf(1174,negated_conjecture,
( apply(esk7_0,esk5_0) = esk6_0
| in(unordered_pair(unordered_pair(esk5_0,esk6_0),unordered_pair(esk5_0,esk5_0)),esk7_0) ),
inference(rw,[status(thm)],[313,1126,theory(equality)]),
[unfolding] ).
cnf(1175,negated_conjecture,
( in(esk5_0,relation_dom(esk7_0))
| in(unordered_pair(unordered_pair(esk5_0,esk6_0),unordered_pair(esk5_0,esk5_0)),esk7_0) ),
inference(rw,[status(thm)],[314,1126,theory(equality)]),
[unfolding] ).
cnf(1194,plain,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
inference(rw,[status(thm)],[454,1126,theory(equality)]),
[unfolding] ).
cnf(1230,plain,
( apply(X1,X2) = X3
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
inference(rw,[status(thm)],[898,1126,theory(equality)]),
[unfolding] ).
cnf(1233,plain,
( in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1)
| apply(X1,X2) != X3
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(rw,[status(thm)],[899,1126,theory(equality)]),
[unfolding] ).
cnf(1254,negated_conjecture,
( apply(esk7_0,esk5_0) != esk6_0
| ~ in(esk5_0,relation_dom(esk7_0))
| ~ in(unordered_pair(unordered_pair(esk5_0,esk6_0),unordered_pair(esk5_0,esk5_0)),esk7_0) ),
inference(rw,[status(thm)],[315,1126,theory(equality)]),
[unfolding] ).
cnf(1302,negated_conjecture,
( in(esk5_0,relation_dom(esk7_0))
| in(unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)),esk7_0) ),
inference(rw,[status(thm)],[1175,467,theory(equality)]) ).
cnf(1331,negated_conjecture,
( apply(esk7_0,esk5_0) = esk6_0
| in(unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)),esk7_0) ),
inference(rw,[status(thm)],[1174,467,theory(equality)]) ).
cnf(1897,plain,
( in(X1,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X3)),X2)
| ~ relation(X2) ),
inference(spm,[status(thm)],[1194,467,theory(equality)]) ).
cnf(3306,negated_conjecture,
( apply(esk7_0,esk5_0) != esk6_0
| ~ in(esk5_0,relation_dom(esk7_0))
| ~ in(unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)),esk7_0) ),
inference(rw,[status(thm)],[1254,467,theory(equality)]) ).
cnf(3377,plain,
( in(unordered_pair(unordered_pair(X1,apply(X2,X1)),unordered_pair(X1,X1)),X2)
| ~ function(X2)
| ~ in(X1,relation_dom(X2))
| ~ relation(X2) ),
inference(er,[status(thm)],[1233,theory(equality)]) ).
cnf(3380,plain,
( in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,apply(X2,X1))),X2)
| ~ function(X2)
| ~ in(X1,relation_dom(X2))
| ~ relation(X2) ),
inference(rw,[status(thm)],[3377,467,theory(equality)]) ).
cnf(3440,plain,
( apply(X1,X2) = X3
| ~ function(X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[1230,1194]) ).
cnf(3445,plain,
( apply(X1,X2) = X3
| ~ function(X1)
| ~ in(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,X3)),X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[3440,467,theory(equality)]) ).
cnf(283320,negated_conjecture,
( in(unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)),esk7_0)
| ~ function(esk7_0)
| ~ in(esk5_0,relation_dom(esk7_0))
| ~ relation(esk7_0) ),
inference(spm,[status(thm)],[3380,1331,theory(equality)]) ).
cnf(283667,negated_conjecture,
( in(unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)),esk7_0)
| $false
| ~ in(esk5_0,relation_dom(esk7_0))
| ~ relation(esk7_0) ),
inference(rw,[status(thm)],[283320,316,theory(equality)]) ).
cnf(283668,negated_conjecture,
( in(unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)),esk7_0)
| $false
| ~ in(esk5_0,relation_dom(esk7_0))
| $false ),
inference(rw,[status(thm)],[283667,317,theory(equality)]) ).
cnf(283669,negated_conjecture,
( in(unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)),esk7_0)
| ~ in(esk5_0,relation_dom(esk7_0)) ),
inference(cn,[status(thm)],[283668,theory(equality)]) ).
cnf(283688,negated_conjecture,
in(unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)),esk7_0),
inference(csr,[status(thm)],[283669,1302]) ).
cnf(283709,negated_conjecture,
( in(esk5_0,relation_dom(esk7_0))
| ~ relation(esk7_0) ),
inference(spm,[status(thm)],[1897,283688,theory(equality)]) ).
cnf(283831,negated_conjecture,
( apply(esk7_0,esk5_0) != esk6_0
| $false
| ~ in(esk5_0,relation_dom(esk7_0)) ),
inference(rw,[status(thm)],[3306,283688,theory(equality)]) ).
cnf(283832,negated_conjecture,
( apply(esk7_0,esk5_0) != esk6_0
| ~ in(esk5_0,relation_dom(esk7_0)) ),
inference(cn,[status(thm)],[283831,theory(equality)]) ).
cnf(283841,negated_conjecture,
( in(esk5_0,relation_dom(esk7_0))
| $false ),
inference(rw,[status(thm)],[283709,317,theory(equality)]) ).
cnf(283842,negated_conjecture,
in(esk5_0,relation_dom(esk7_0)),
inference(cn,[status(thm)],[283841,theory(equality)]) ).
cnf(284141,negated_conjecture,
( apply(esk7_0,esk5_0) != esk6_0
| $false ),
inference(rw,[status(thm)],[283832,283842,theory(equality)]) ).
cnf(284142,negated_conjecture,
apply(esk7_0,esk5_0) != esk6_0,
inference(cn,[status(thm)],[284141,theory(equality)]) ).
cnf(295340,negated_conjecture,
( apply(esk7_0,esk5_0) = esk6_0
| ~ function(esk7_0)
| ~ relation(esk7_0) ),
inference(spm,[status(thm)],[3445,283688,theory(equality)]) ).
cnf(295504,negated_conjecture,
( apply(esk7_0,esk5_0) = esk6_0
| $false
| ~ relation(esk7_0) ),
inference(rw,[status(thm)],[295340,316,theory(equality)]) ).
cnf(295505,negated_conjecture,
( apply(esk7_0,esk5_0) = esk6_0
| $false
| $false ),
inference(rw,[status(thm)],[295504,317,theory(equality)]) ).
cnf(295506,negated_conjecture,
apply(esk7_0,esk5_0) = esk6_0,
inference(cn,[status(thm)],[295505,theory(equality)]) ).
cnf(295507,negated_conjecture,
$false,
inference(sr,[status(thm)],[295506,284142,theory(equality)]) ).
cnf(295508,negated_conjecture,
$false,
295507,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU212+2.p
% --creating new selector for []
% -running prover on /tmp/tmpY_w6-T/sel_SEU212+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU212+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU212+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU212+2.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
%
%------------------------------------------------------------------------------