TSTP Solution File: SET974+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET974+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 03:56:35 EST 2010
% Result : Theorem 0.28s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 7 unt; 0 def)
% Number of atoms : 86 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 95 ( 41 ~; 28 |; 24 &)
% ( 0 <=>; 2 =>; 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 : 10 ( 10 usr; 4 con; 0-5 aty)
% Number of variables : 102 ( 11 sgn 53 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,conjecture,
! [X1,X2,X3,X4] :
( ( disjoint(X1,X2)
| disjoint(X3,X4) )
=> disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
file('/tmp/tmpsBIjTG/sel_SET974+1.p_1',t127_zfmisc_1) ).
fof(11,axiom,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/tmp/tmpsBIjTG/sel_SET974+1.p_1',t4_xboole_0) ).
fof(12,axiom,
! [X1,X2,X3,X4,X5] :
~ ( in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5)))
& ! [X6,X7] :
~ ( X1 = ordered_pair(X6,X7)
& in(X6,set_intersection2(X2,X4))
& in(X7,set_intersection2(X3,X5)) ) ),
file('/tmp/tmpsBIjTG/sel_SET974+1.p_1',t104_zfmisc_1) ).
fof(13,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( disjoint(X1,X2)
| disjoint(X3,X4) )
=> disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
inference(assume_negation,[status(cth)],[3]) ).
fof(17,plain,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(22,negated_conjecture,
? [X1,X2,X3,X4] :
( ( disjoint(X1,X2)
| disjoint(X3,X4) )
& ~ disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(23,negated_conjecture,
? [X5,X6,X7,X8] :
( ( disjoint(X5,X6)
| disjoint(X7,X8) )
& ~ disjoint(cartesian_product2(X5,X7),cartesian_product2(X6,X8)) ),
inference(variable_rename,[status(thm)],[22]) ).
fof(24,negated_conjecture,
( ( disjoint(esk1_0,esk2_0)
| disjoint(esk3_0,esk4_0) )
& ~ disjoint(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk2_0,esk4_0)) ),
inference(skolemize,[status(esa)],[23]) ).
cnf(25,negated_conjecture,
~ disjoint(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk2_0,esk4_0)),
inference(split_conjunct,[status(thm)],[24]) ).
cnf(26,negated_conjecture,
( disjoint(esk3_0,esk4_0)
| disjoint(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(45,plain,
! [X1,X2] :
( ( disjoint(X1,X2)
| ? [X3] : in(X3,set_intersection2(X1,X2)) )
& ( ! [X3] : ~ in(X3,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(46,plain,
! [X4,X5] :
( ( disjoint(X4,X5)
| ? [X6] : in(X6,set_intersection2(X4,X5)) )
& ( ! [X7] : ~ in(X7,set_intersection2(X4,X5))
| ~ disjoint(X4,X5) ) ),
inference(variable_rename,[status(thm)],[45]) ).
fof(47,plain,
! [X4,X5] :
( ( disjoint(X4,X5)
| in(esk7_2(X4,X5),set_intersection2(X4,X5)) )
& ( ! [X7] : ~ in(X7,set_intersection2(X4,X5))
| ~ disjoint(X4,X5) ) ),
inference(skolemize,[status(esa)],[46]) ).
fof(48,plain,
! [X4,X5,X7] :
( ( ~ in(X7,set_intersection2(X4,X5))
| ~ disjoint(X4,X5) )
& ( disjoint(X4,X5)
| in(esk7_2(X4,X5),set_intersection2(X4,X5)) ) ),
inference(shift_quantors,[status(thm)],[47]) ).
cnf(49,plain,
( in(esk7_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(50,plain,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(51,plain,
! [X1,X2,X3,X4,X5] :
( ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5)))
| ? [X6,X7] :
( X1 = ordered_pair(X6,X7)
& in(X6,set_intersection2(X2,X4))
& in(X7,set_intersection2(X3,X5)) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(52,plain,
! [X8,X9,X10,X11,X12] :
( ~ in(X8,set_intersection2(cartesian_product2(X9,X10),cartesian_product2(X11,X12)))
| ? [X13,X14] :
( X8 = ordered_pair(X13,X14)
& in(X13,set_intersection2(X9,X11))
& in(X14,set_intersection2(X10,X12)) ) ),
inference(variable_rename,[status(thm)],[51]) ).
fof(53,plain,
! [X8,X9,X10,X11,X12] :
( ~ in(X8,set_intersection2(cartesian_product2(X9,X10),cartesian_product2(X11,X12)))
| ( X8 = ordered_pair(esk8_5(X8,X9,X10,X11,X12),esk9_5(X8,X9,X10,X11,X12))
& in(esk8_5(X8,X9,X10,X11,X12),set_intersection2(X9,X11))
& in(esk9_5(X8,X9,X10,X11,X12),set_intersection2(X10,X12)) ) ),
inference(skolemize,[status(esa)],[52]) ).
fof(54,plain,
! [X8,X9,X10,X11,X12] :
( ( X8 = ordered_pair(esk8_5(X8,X9,X10,X11,X12),esk9_5(X8,X9,X10,X11,X12))
| ~ in(X8,set_intersection2(cartesian_product2(X9,X10),cartesian_product2(X11,X12))) )
& ( in(esk8_5(X8,X9,X10,X11,X12),set_intersection2(X9,X11))
| ~ in(X8,set_intersection2(cartesian_product2(X9,X10),cartesian_product2(X11,X12))) )
& ( in(esk9_5(X8,X9,X10,X11,X12),set_intersection2(X10,X12))
| ~ in(X8,set_intersection2(cartesian_product2(X9,X10),cartesian_product2(X11,X12))) ) ),
inference(distribute,[status(thm)],[53]) ).
cnf(55,plain,
( in(esk9_5(X1,X2,X3,X4,X5),set_intersection2(X3,X5))
| ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))) ),
inference(split_conjunct,[status(thm)],[54]) ).
cnf(56,plain,
( in(esk8_5(X1,X2,X3,X4,X5),set_intersection2(X2,X4))
| ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))) ),
inference(split_conjunct,[status(thm)],[54]) ).
cnf(81,plain,
( ~ disjoint(X2,X4)
| ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))) ),
inference(spm,[status(thm)],[50,56,theory(equality)]) ).
cnf(86,plain,
( ~ disjoint(X3,X5)
| ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))) ),
inference(spm,[status(thm)],[50,55,theory(equality)]) ).
cnf(166,plain,
( disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ disjoint(X1,X3) ),
inference(spm,[status(thm)],[81,49,theory(equality)]) ).
cnf(173,negated_conjecture,
~ disjoint(esk1_0,esk2_0),
inference(spm,[status(thm)],[25,166,theory(equality)]) ).
cnf(177,negated_conjecture,
disjoint(esk3_0,esk4_0),
inference(sr,[status(thm)],[26,173,theory(equality)]) ).
cnf(197,plain,
( disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ disjoint(X2,X4) ),
inference(spm,[status(thm)],[86,49,theory(equality)]) ).
cnf(204,negated_conjecture,
~ disjoint(esk3_0,esk4_0),
inference(spm,[status(thm)],[25,197,theory(equality)]) ).
cnf(206,negated_conjecture,
$false,
inference(rw,[status(thm)],[204,177,theory(equality)]) ).
cnf(207,negated_conjecture,
$false,
inference(cn,[status(thm)],[206,theory(equality)]) ).
cnf(208,negated_conjecture,
$false,
207,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET974+1.p
% --creating new selector for []
% -running prover on /tmp/tmpsBIjTG/sel_SET974+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET974+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET974+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET974+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
%
%------------------------------------------------------------------------------