TSTP Solution File: SEU140+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU140+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 04:50:51 EST 2010
% Result : Theorem 2.98s
% Output : CNFRefutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 26 unt; 0 def)
% Number of atoms : 122 ( 32 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 104 ( 44 ~; 39 |; 14 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 104 ( 6 sgn 55 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',t36_xboole_1) ).
fof(5,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',t1_xboole_1) ).
fof(7,conjecture,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',t63_xboole_1) ).
fof(12,axiom,
! [X1,X2] : subset(X1,X1),
file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',reflexivity_r1_tarski) ).
fof(15,axiom,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',t3_xboole_1) ).
fof(23,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',t37_xboole_1) ).
fof(31,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',d7_xboole_0) ).
fof(34,axiom,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',t48_xboole_1) ).
fof(41,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',commutativity_k3_xboole_0) ).
fof(50,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',t19_xboole_1) ).
fof(57,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
inference(assume_negation,[status(cth)],[7]) ).
fof(68,plain,
! [X3,X4] : subset(set_difference(X3,X4),X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(69,plain,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[68]) ).
fof(77,plain,
! [X1,X2,X3] :
( ~ subset(X1,X2)
| ~ subset(X2,X3)
| subset(X1,X3) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(78,plain,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X5,X6)
| subset(X4,X6) ),
inference(variable_rename,[status(thm)],[77]) ).
cnf(79,plain,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[78]) ).
fof(83,negated_conjecture,
? [X1,X2,X3] :
( subset(X1,X2)
& disjoint(X2,X3)
& ~ disjoint(X1,X3) ),
inference(fof_nnf,[status(thm)],[57]) ).
fof(84,negated_conjecture,
? [X4,X5,X6] :
( subset(X4,X5)
& disjoint(X5,X6)
& ~ disjoint(X4,X6) ),
inference(variable_rename,[status(thm)],[83]) ).
fof(85,negated_conjecture,
( subset(esk2_0,esk3_0)
& disjoint(esk3_0,esk4_0)
& ~ disjoint(esk2_0,esk4_0) ),
inference(skolemize,[status(esa)],[84]) ).
cnf(86,negated_conjecture,
~ disjoint(esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[85]) ).
cnf(87,negated_conjecture,
disjoint(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[85]) ).
cnf(88,negated_conjecture,
subset(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[85]) ).
fof(100,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[12]) ).
cnf(101,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[100]) ).
fof(106,plain,
! [X1] :
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(107,plain,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[106]) ).
cnf(108,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[107]) ).
fof(134,plain,
! [X1,X2] :
( ( set_difference(X1,X2) != empty_set
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| set_difference(X1,X2) = empty_set ) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(135,plain,
! [X3,X4] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| set_difference(X3,X4) = empty_set ) ),
inference(variable_rename,[status(thm)],[134]) ).
cnf(136,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(137,plain,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[135]) ).
fof(165,plain,
! [X1,X2] :
( ( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set )
& ( set_intersection2(X1,X2) != empty_set
| disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(166,plain,
! [X3,X4] :
( ( ~ disjoint(X3,X4)
| set_intersection2(X3,X4) = empty_set )
& ( set_intersection2(X3,X4) != empty_set
| disjoint(X3,X4) ) ),
inference(variable_rename,[status(thm)],[165]) ).
cnf(167,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[166]) ).
cnf(168,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[166]) ).
fof(183,plain,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[34]) ).
cnf(184,plain,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[183]) ).
fof(208,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[41]) ).
cnf(209,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[208]) ).
fof(229,plain,
! [X1,X2,X3] :
( ~ subset(X1,X2)
| ~ subset(X1,X3)
| subset(X1,set_intersection2(X2,X3)) ),
inference(fof_nnf,[status(thm)],[50]) ).
fof(230,plain,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X4,X6)
| subset(X4,set_intersection2(X5,X6)) ),
inference(variable_rename,[status(thm)],[229]) ).
cnf(231,plain,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[230]) ).
cnf(266,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[209,184,theory(equality)]),184,theory(equality)]),
[unfolding] ).
cnf(272,plain,
( set_difference(X1,set_difference(X1,X2)) = empty_set
| ~ disjoint(X1,X2) ),
inference(rw,[status(thm)],[168,184,theory(equality)]),
[unfolding] ).
cnf(273,plain,
( disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) != empty_set ),
inference(rw,[status(thm)],[167,184,theory(equality)]),
[unfolding] ).
cnf(277,plain,
( subset(X1,set_difference(X2,set_difference(X2,X3)))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[231,184,theory(equality)]),
[unfolding] ).
cnf(302,negated_conjecture,
( subset(X1,esk3_0)
| ~ subset(X1,esk2_0) ),
inference(spm,[status(thm)],[79,88,theory(equality)]) ).
cnf(329,plain,
( subset(X1,X2)
| ~ subset(X1,X3)
| set_difference(X3,X2) != empty_set ),
inference(spm,[status(thm)],[79,137,theory(equality)]) ).
cnf(395,negated_conjecture,
set_difference(esk3_0,set_difference(esk3_0,esk4_0)) = empty_set,
inference(spm,[status(thm)],[272,87,theory(equality)]) ).
cnf(971,negated_conjecture,
( set_difference(X1,esk3_0) = empty_set
| ~ subset(X1,esk2_0) ),
inference(spm,[status(thm)],[136,302,theory(equality)]) ).
cnf(1435,negated_conjecture,
( subset(X1,empty_set)
| ~ subset(X1,esk4_0)
| ~ subset(X1,esk3_0) ),
inference(spm,[status(thm)],[277,395,theory(equality)]) ).
cnf(1481,plain,
( subset(set_difference(esk4_0,X1),empty_set)
| ~ subset(set_difference(esk4_0,X1),esk3_0) ),
inference(spm,[status(thm)],[1435,69,theory(equality)]) ).
cnf(1826,plain,
set_difference(set_difference(esk2_0,X1),esk3_0) = empty_set,
inference(spm,[status(thm)],[971,69,theory(equality)]) ).
cnf(1889,plain,
( subset(X1,esk3_0)
| ~ subset(X1,set_difference(esk2_0,X2)) ),
inference(spm,[status(thm)],[329,1826,theory(equality)]) ).
cnf(3388,plain,
subset(set_difference(esk2_0,X1),esk3_0),
inference(spm,[status(thm)],[1889,101,theory(equality)]) ).
cnf(3421,plain,
subset(set_difference(X1,set_difference(X1,esk2_0)),esk3_0),
inference(spm,[status(thm)],[3388,266,theory(equality)]) ).
cnf(58287,plain,
subset(set_difference(esk4_0,set_difference(esk4_0,esk2_0)),empty_set),
inference(spm,[status(thm)],[1481,3421,theory(equality)]) ).
cnf(58336,plain,
subset(set_difference(esk2_0,set_difference(esk2_0,esk4_0)),empty_set),
inference(rw,[status(thm)],[58287,266,theory(equality)]) ).
cnf(58532,plain,
empty_set = set_difference(esk2_0,set_difference(esk2_0,esk4_0)),
inference(spm,[status(thm)],[108,58336,theory(equality)]) ).
cnf(58767,plain,
disjoint(esk2_0,esk4_0),
inference(spm,[status(thm)],[273,58532,theory(equality)]) ).
cnf(59105,plain,
$false,
inference(sr,[status(thm)],[58767,86,theory(equality)]) ).
cnf(59106,plain,
$false,
59105,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU140+2.p
% --creating new selector for []
% -running prover on /tmp/tmpMGnc_S/sel_SEU140+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU140+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU140+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU140+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
%
%------------------------------------------------------------------------------