TSTP Solution File: SEU245+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU245+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 06:12:35 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 46 ( 7 unt; 0 def)
% Number of atoms : 194 ( 25 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 237 ( 89 ~; 101 |; 40 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 79 ( 5 sgn 38 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1] :
( relation(X1)
=> ! [X2] : relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
file('/tmp/tmp3XCZTP/sel_SEU245+1.p_1',d6_wellord1) ).
fof(6,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
file('/tmp/tmp3XCZTP/sel_SEU245+1.p_1',t16_wellord1) ).
fof(17,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/tmp/tmp3XCZTP/sel_SEU245+1.p_1',d3_xboole_0) ).
fof(27,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(35,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] : relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(36,plain,
! [X3] :
( ~ relation(X3)
| ! [X4] : relation_restriction(X3,X4) = set_intersection2(X3,cartesian_product2(X4,X4)) ),
inference(variable_rename,[status(thm)],[35]) ).
fof(37,plain,
! [X3,X4] :
( relation_restriction(X3,X4) = set_intersection2(X3,cartesian_product2(X4,X4))
| ~ relation(X3) ),
inference(shift_quantors,[status(thm)],[36]) ).
cnf(38,plain,
( relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(46,negated_conjecture,
? [X1,X2,X3] :
( relation(X3)
& ( ~ in(X1,relation_restriction(X3,X2))
| ~ in(X1,X3)
| ~ in(X1,cartesian_product2(X2,X2)) )
& ( in(X1,relation_restriction(X3,X2))
| ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(47,negated_conjecture,
? [X4,X5,X6] :
( relation(X6)
& ( ~ in(X4,relation_restriction(X6,X5))
| ~ in(X4,X6)
| ~ in(X4,cartesian_product2(X5,X5)) )
& ( in(X4,relation_restriction(X6,X5))
| ( in(X4,X6)
& in(X4,cartesian_product2(X5,X5)) ) ) ),
inference(variable_rename,[status(thm)],[46]) ).
fof(48,negated_conjecture,
( relation(esk5_0)
& ( ~ in(esk3_0,relation_restriction(esk5_0,esk4_0))
| ~ in(esk3_0,esk5_0)
| ~ in(esk3_0,cartesian_product2(esk4_0,esk4_0)) )
& ( in(esk3_0,relation_restriction(esk5_0,esk4_0))
| ( in(esk3_0,esk5_0)
& in(esk3_0,cartesian_product2(esk4_0,esk4_0)) ) ) ),
inference(skolemize,[status(esa)],[47]) ).
fof(49,negated_conjecture,
( relation(esk5_0)
& ( ~ in(esk3_0,relation_restriction(esk5_0,esk4_0))
| ~ in(esk3_0,esk5_0)
| ~ in(esk3_0,cartesian_product2(esk4_0,esk4_0)) )
& ( in(esk3_0,esk5_0)
| in(esk3_0,relation_restriction(esk5_0,esk4_0)) )
& ( in(esk3_0,cartesian_product2(esk4_0,esk4_0))
| in(esk3_0,relation_restriction(esk5_0,esk4_0)) ) ),
inference(distribute,[status(thm)],[48]) ).
cnf(50,negated_conjecture,
( in(esk3_0,relation_restriction(esk5_0,esk4_0))
| in(esk3_0,cartesian_product2(esk4_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(51,negated_conjecture,
( in(esk3_0,relation_restriction(esk5_0,esk4_0))
| in(esk3_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(52,negated_conjecture,
( ~ in(esk3_0,cartesian_product2(esk4_0,esk4_0))
| ~ in(esk3_0,esk5_0)
| ~ in(esk3_0,relation_restriction(esk5_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(53,negated_conjecture,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[49]) ).
fof(81,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)],[17]) ).
fof(82,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)],[81]) ).
fof(83,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(esk7_3(X5,X6,X7),X7)
| ~ in(esk7_3(X5,X6,X7),X5)
| ~ in(esk7_3(X5,X6,X7),X6) )
& ( in(esk7_3(X5,X6,X7),X7)
| ( in(esk7_3(X5,X6,X7),X5)
& in(esk7_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(skolemize,[status(esa)],[82]) ).
fof(84,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(esk7_3(X5,X6,X7),X7)
| ~ in(esk7_3(X5,X6,X7),X5)
| ~ in(esk7_3(X5,X6,X7),X6) )
& ( in(esk7_3(X5,X6,X7),X7)
| ( in(esk7_3(X5,X6,X7),X5)
& in(esk7_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[83]) ).
fof(85,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(esk7_3(X5,X6,X7),X7)
| ~ in(esk7_3(X5,X6,X7),X5)
| ~ in(esk7_3(X5,X6,X7),X6)
| X7 = set_intersection2(X5,X6) )
& ( in(esk7_3(X5,X6,X7),X5)
| in(esk7_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) )
& ( in(esk7_3(X5,X6,X7),X6)
| in(esk7_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) ) ),
inference(distribute,[status(thm)],[84]) ).
cnf(89,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[85]) ).
cnf(90,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[85]) ).
cnf(91,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[85]) ).
cnf(135,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[90,theory(equality)]) ).
cnf(141,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[91,theory(equality)]) ).
cnf(158,plain,
( in(X1,X2)
| relation_restriction(X3,X4) != X2
| ~ in(X1,cartesian_product2(X4,X4))
| ~ in(X1,X3)
| ~ relation(X3) ),
inference(spm,[status(thm)],[89,38,theory(equality)]) ).
cnf(215,plain,
( in(X1,cartesian_product2(X2,X2))
| ~ in(X1,relation_restriction(X3,X2))
| ~ relation(X3) ),
inference(spm,[status(thm)],[135,38,theory(equality)]) ).
cnf(275,plain,
( in(X1,X2)
| ~ in(X1,relation_restriction(X2,X3))
| ~ relation(X2) ),
inference(spm,[status(thm)],[141,38,theory(equality)]) ).
cnf(292,negated_conjecture,
( in(esk3_0,esk5_0)
| ~ relation(esk5_0) ),
inference(spm,[status(thm)],[275,51,theory(equality)]) ).
cnf(302,negated_conjecture,
( in(esk3_0,esk5_0)
| $false ),
inference(rw,[status(thm)],[292,53,theory(equality)]) ).
cnf(303,negated_conjecture,
in(esk3_0,esk5_0),
inference(cn,[status(thm)],[302,theory(equality)]) ).
cnf(310,negated_conjecture,
( ~ in(esk3_0,relation_restriction(esk5_0,esk4_0))
| ~ in(esk3_0,cartesian_product2(esk4_0,esk4_0))
| $false ),
inference(rw,[status(thm)],[52,303,theory(equality)]) ).
cnf(311,negated_conjecture,
( ~ in(esk3_0,relation_restriction(esk5_0,esk4_0))
| ~ in(esk3_0,cartesian_product2(esk4_0,esk4_0)) ),
inference(cn,[status(thm)],[310,theory(equality)]) ).
cnf(531,negated_conjecture,
( in(esk3_0,X1)
| in(esk3_0,relation_restriction(esk5_0,esk4_0))
| relation_restriction(X2,esk4_0) != X1
| ~ in(esk3_0,X2)
| ~ relation(X2) ),
inference(spm,[status(thm)],[158,50,theory(equality)]) ).
cnf(647,negated_conjecture,
( in(esk3_0,relation_restriction(esk5_0,esk4_0))
| in(esk3_0,relation_restriction(X1,esk4_0))
| ~ in(esk3_0,X1)
| ~ relation(X1) ),
inference(er,[status(thm)],[531,theory(equality)]) ).
cnf(663,negated_conjecture,
( in(esk3_0,relation_restriction(esk5_0,esk4_0))
| ~ relation(esk5_0) ),
inference(spm,[status(thm)],[647,303,theory(equality)]) ).
cnf(667,negated_conjecture,
( in(esk3_0,relation_restriction(esk5_0,esk4_0))
| $false ),
inference(rw,[status(thm)],[663,53,theory(equality)]) ).
cnf(668,negated_conjecture,
in(esk3_0,relation_restriction(esk5_0,esk4_0)),
inference(cn,[status(thm)],[667,theory(equality)]) ).
cnf(674,negated_conjecture,
( in(esk3_0,cartesian_product2(esk4_0,esk4_0))
| ~ relation(esk5_0) ),
inference(spm,[status(thm)],[215,668,theory(equality)]) ).
cnf(679,negated_conjecture,
( $false
| ~ in(esk3_0,cartesian_product2(esk4_0,esk4_0)) ),
inference(rw,[status(thm)],[311,668,theory(equality)]) ).
cnf(680,negated_conjecture,
~ in(esk3_0,cartesian_product2(esk4_0,esk4_0)),
inference(cn,[status(thm)],[679,theory(equality)]) ).
cnf(689,negated_conjecture,
( in(esk3_0,cartesian_product2(esk4_0,esk4_0))
| $false ),
inference(rw,[status(thm)],[674,53,theory(equality)]) ).
cnf(690,negated_conjecture,
in(esk3_0,cartesian_product2(esk4_0,esk4_0)),
inference(cn,[status(thm)],[689,theory(equality)]) ).
cnf(724,negated_conjecture,
$false,
inference(sr,[status(thm)],[690,680,theory(equality)]) ).
cnf(725,negated_conjecture,
$false,
724,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU245+1.p
% --creating new selector for []
% -running prover on /tmp/tmp3XCZTP/sel_SEU245+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU245+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU245+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU245+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
%
%------------------------------------------------------------------------------