%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU008+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 04:06:14 EST 2010
% Result : Theorem 0.50s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 16 unt; 0 def)
% Number of atoms : 279 ( 78 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 362 ( 138 ~; 154 |; 58 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 104 ( 4 sgn 68 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(22,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/tmp/tmpWIjOGr/sel_SEU008+1.p_1',t34_funct_1) ).
fof(27,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/tmp/tmpWIjOGr/sel_SEU008+1.p_1',t23_funct_1) ).
fof(29,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/tmp/tmpWIjOGr/sel_SEU008+1.p_1',commutativity_k3_xboole_0) ).
fof(33,axiom,
! [X1] : relation(identity_relation(X1)),
file('/tmp/tmpWIjOGr/sel_SEU008+1.p_1',dt_k6_relat_1) ).
fof(34,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/tmp/tmpWIjOGr/sel_SEU008+1.p_1',fc2_funct_1) ).
fof(36,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,set_intersection2(relation_dom(X3),X1))
=> apply(X3,X2) = apply(relation_composition(identity_relation(X1),X3),X2) ) ),
file('/tmp/tmpWIjOGr/sel_SEU008+1.p_1',t38_funct_1) ).
fof(39,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/tmp/tmpWIjOGr/sel_SEU008+1.p_1',d3_xboole_0) ).
fof(42,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,set_intersection2(relation_dom(X3),X1))
=> apply(X3,X2) = apply(relation_composition(identity_relation(X1),X3),X2) ) ),
inference(assume_negation,[status(cth)],[36]) ).
fof(116,plain,
! [X1,X2] :
( ~ relation(X2)
| ~ function(X2)
| ( ( X2 != identity_relation(X1)
| ( relation_dom(X2) = X1
& ! [X3] :
( ~ in(X3,X1)
| apply(X2,X3) = X3 ) ) )
& ( relation_dom(X2) != X1
| ? [X3] :
( in(X3,X1)
& apply(X2,X3) != X3 )
| X2 = identity_relation(X1) ) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(117,plain,
! [X4,X5] :
( ~ relation(X5)
| ~ function(X5)
| ( ( X5 != identity_relation(X4)
| ( relation_dom(X5) = X4
& ! [X6] :
( ~ in(X6,X4)
| apply(X5,X6) = X6 ) ) )
& ( relation_dom(X5) != X4
| ? [X7] :
( in(X7,X4)
& apply(X5,X7) != X7 )
| X5 = identity_relation(X4) ) ) ),
inference(variable_rename,[status(thm)],[116]) ).
fof(118,plain,
! [X4,X5] :
( ~ relation(X5)
| ~ function(X5)
| ( ( X5 != identity_relation(X4)
| ( relation_dom(X5) = X4
& ! [X6] :
( ~ in(X6,X4)
| apply(X5,X6) = X6 ) ) )
& ( relation_dom(X5) != X4
| ( in(esk6_2(X4,X5),X4)
& apply(X5,esk6_2(X4,X5)) != esk6_2(X4,X5) )
| X5 = identity_relation(X4) ) ) ),
inference(skolemize,[status(esa)],[117]) ).
fof(119,plain,
! [X4,X5,X6] :
( ( ( ( ( ~ in(X6,X4)
| apply(X5,X6) = X6 )
& relation_dom(X5) = X4 )
| X5 != identity_relation(X4) )
& ( relation_dom(X5) != X4
| ( in(esk6_2(X4,X5),X4)
& apply(X5,esk6_2(X4,X5)) != esk6_2(X4,X5) )
| X5 = identity_relation(X4) ) )
| ~ relation(X5)
| ~ function(X5) ),
inference(shift_quantors,[status(thm)],[118]) ).
fof(120,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| apply(X5,X6) = X6
| X5 != identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( relation_dom(X5) = X4
| X5 != identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk6_2(X4,X5),X4)
| relation_dom(X5) != X4
| X5 = identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( apply(X5,esk6_2(X4,X5)) != esk6_2(X4,X5)
| relation_dom(X5) != X4
| X5 = identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[119]) ).
cnf(123,plain,
( relation_dom(X1) = X2
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2) ),
inference(split_conjunct,[status(thm)],[120]) ).
cnf(124,plain,
( apply(X1,X3) = X3
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[120]) ).
fof(141,plain,
! [X1,X2] :
( ~ relation(X2)
| ~ function(X2)
| ! [X3] :
( ~ relation(X3)
| ~ function(X3)
| ~ in(X1,relation_dom(X2))
| apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(142,plain,
! [X4,X5] :
( ~ relation(X5)
| ~ function(X5)
| ! [X6] :
( ~ relation(X6)
| ~ function(X6)
| ~ in(X4,relation_dom(X5))
| apply(relation_composition(X5,X6),X4) = apply(X6,apply(X5,X4)) ) ),
inference(variable_rename,[status(thm)],[141]) ).
fof(143,plain,
! [X4,X5,X6] :
( ~ relation(X6)
| ~ function(X6)
| ~ in(X4,relation_dom(X5))
| apply(relation_composition(X5,X6),X4) = apply(X6,apply(X5,X4))
| ~ relation(X5)
| ~ function(X5) ),
inference(shift_quantors,[status(thm)],[142]) ).
cnf(144,plain,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X3,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[143]) ).
fof(149,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[29]) ).
cnf(150,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[149]) ).
fof(159,plain,
! [X2] : relation(identity_relation(X2)),
inference(variable_rename,[status(thm)],[33]) ).
cnf(160,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[159]) ).
fof(161,plain,
! [X2] :
( relation(identity_relation(X2))
& function(identity_relation(X2)) ),
inference(variable_rename,[status(thm)],[34]) ).
cnf(162,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[161]) ).
fof(168,negated_conjecture,
? [X1,X2,X3] :
( relation(X3)
& function(X3)
& in(X2,set_intersection2(relation_dom(X3),X1))
& apply(X3,X2) != apply(relation_composition(identity_relation(X1),X3),X2) ),
inference(fof_nnf,[status(thm)],[42]) ).
fof(169,negated_conjecture,
? [X4,X5,X6] :
( relation(X6)
& function(X6)
& in(X5,set_intersection2(relation_dom(X6),X4))
& apply(X6,X5) != apply(relation_composition(identity_relation(X4),X6),X5) ),
inference(variable_rename,[status(thm)],[168]) ).
fof(170,negated_conjecture,
( relation(esk12_0)
& function(esk12_0)
& in(esk11_0,set_intersection2(relation_dom(esk12_0),esk10_0))
& apply(esk12_0,esk11_0) != apply(relation_composition(identity_relation(esk10_0),esk12_0),esk11_0) ),
inference(skolemize,[status(esa)],[169]) ).
cnf(171,negated_conjecture,
apply(esk12_0,esk11_0) != apply(relation_composition(identity_relation(esk10_0),esk12_0),esk11_0),
inference(split_conjunct,[status(thm)],[170]) ).
cnf(172,negated_conjecture,
in(esk11_0,set_intersection2(relation_dom(esk12_0),esk10_0)),
inference(split_conjunct,[status(thm)],[170]) ).
cnf(173,negated_conjecture,
function(esk12_0),
inference(split_conjunct,[status(thm)],[170]) ).
cnf(174,negated_conjecture,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[170]) ).
fof(181,plain,
! [X1,X2,X3] :
( ( X3 != set_intersection2(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| ( in(X4,X1)
& in(X4,X2) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X2)
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ~ in(X4,X1)
| ~ in(X4,X2) )
& ( in(X4,X3)
| ( in(X4,X1)
& in(X4,X2) ) ) )
| X3 = set_intersection2(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(182,plain,
! [X5,X6,X7] :
( ( X7 != set_intersection2(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& in(X8,X6) ) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ~ in(X9,X5)
| ~ in(X9,X6) )
& ( in(X9,X7)
| ( in(X9,X5)
& in(X9,X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(variable_rename,[status(thm)],[181]) ).
fof(183,plain,
! [X5,X6,X7] :
( ( X7 != set_intersection2(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& in(X8,X6) ) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk13_3(X5,X6,X7),X7)
| ~ in(esk13_3(X5,X6,X7),X5)
| ~ in(esk13_3(X5,X6,X7),X6) )
& ( in(esk13_3(X5,X6,X7),X7)
| ( in(esk13_3(X5,X6,X7),X5)
& in(esk13_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(skolemize,[status(esa)],[182]) ).
fof(184,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| ( in(X8,X5)
& in(X8,X6) ) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7) ) )
| X7 != set_intersection2(X5,X6) )
& ( ( ( ~ in(esk13_3(X5,X6,X7),X7)
| ~ in(esk13_3(X5,X6,X7),X5)
| ~ in(esk13_3(X5,X6,X7),X6) )
& ( in(esk13_3(X5,X6,X7),X7)
| ( in(esk13_3(X5,X6,X7),X5)
& in(esk13_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[183]) ).
fof(185,plain,
! [X5,X6,X7,X8] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( in(X8,X6)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(esk13_3(X5,X6,X7),X7)
| ~ in(esk13_3(X5,X6,X7),X5)
| ~ in(esk13_3(X5,X6,X7),X6)
| X7 = set_intersection2(X5,X6) )
& ( in(esk13_3(X5,X6,X7),X5)
| in(esk13_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) )
& ( in(esk13_3(X5,X6,X7),X6)
| in(esk13_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) ) ),
inference(distribute,[status(thm)],[184]) ).
cnf(191,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[185]) ).
cnf(229,negated_conjecture,
in(esk11_0,set_intersection2(esk10_0,relation_dom(esk12_0))),
inference(rw,[status(thm)],[172,150,theory(equality)]) ).
cnf(237,plain,
( relation_dom(identity_relation(X1)) = X1
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1)) ),
inference(er,[status(thm)],[123,theory(equality)]) ).
cnf(238,plain,
( relation_dom(identity_relation(X1)) = X1
| $false
| ~ relation(identity_relation(X1)) ),
inference(rw,[status(thm)],[237,162,theory(equality)]) ).
cnf(239,plain,
( relation_dom(identity_relation(X1)) = X1
| $false
| $false ),
inference(rw,[status(thm)],[238,160,theory(equality)]) ).
cnf(240,plain,
relation_dom(identity_relation(X1)) = X1,
inference(cn,[status(thm)],[239,theory(equality)]) ).
cnf(248,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[191,theory(equality)]) ).
cnf(448,negated_conjecture,
in(esk11_0,esk10_0),
inference(spm,[status(thm)],[248,229,theory(equality)]) ).
cnf(460,negated_conjecture,
( apply(X1,esk11_0) = esk11_0
| identity_relation(esk10_0) != X1
| ~ function(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[124,448,theory(equality)]) ).
cnf(789,negated_conjecture,
( apply(X1,esk11_0) = apply(relation_composition(X2,X1),esk11_0)
| ~ function(X1)
| ~ function(X2)
| ~ in(esk11_0,relation_dom(X2))
| ~ relation(X1)
| ~ relation(X2)
| identity_relation(esk10_0) != X2 ),
inference(spm,[status(thm)],[144,460,theory(equality)]) ).
cnf(5719,negated_conjecture,
( ~ function(esk12_0)
| ~ function(identity_relation(esk10_0))
| ~ in(esk11_0,relation_dom(identity_relation(esk10_0)))
| ~ relation(esk12_0)
| ~ relation(identity_relation(esk10_0)) ),
inference(spm,[status(thm)],[171,789,theory(equality)]) ).
cnf(5737,negated_conjecture,
( $false
| ~ function(identity_relation(esk10_0))
| ~ in(esk11_0,relation_dom(identity_relation(esk10_0)))
| ~ relation(esk12_0)
| ~ relation(identity_relation(esk10_0)) ),
inference(rw,[status(thm)],[5719,173,theory(equality)]) ).
cnf(5738,negated_conjecture,
( $false
| $false
| ~ in(esk11_0,relation_dom(identity_relation(esk10_0)))
| ~ relation(esk12_0)
| ~ relation(identity_relation(esk10_0)) ),
inference(rw,[status(thm)],[5737,162,theory(equality)]) ).
cnf(5739,negated_conjecture,
( $false
| $false
| $false
| ~ relation(esk12_0)
| ~ relation(identity_relation(esk10_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[5738,240,theory(equality)]),448,theory(equality)]) ).
cnf(5740,negated_conjecture,
( $false
| $false
| $false
| $false
| ~ relation(identity_relation(esk10_0)) ),
inference(rw,[status(thm)],[5739,174,theory(equality)]) ).
cnf(5741,negated_conjecture,
( $false
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[5740,160,theory(equality)]) ).
cnf(5742,negated_conjecture,
$false,
inference(cn,[status(thm)],[5741,theory(equality)]) ).
cnf(5743,negated_conjecture,
$false,
5742,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU008+1.p
% --creating new selector for []
% -running prover on /tmp/tmpWIjOGr/sel_SEU008+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU008+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU008+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU008+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
%
%------------------------------------------------------------------------------