TSTP Solution File: REL006+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL006+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 01:00:49 EST 2010
% Result : Theorem 0.66s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 8
% Syntax : Number of formulae : 113 ( 108 unt; 0 def)
% Number of atoms : 118 ( 115 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 0 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 118 ( 5 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmp4cs1A3/sel_REL006+1.p_1',converse_idempotence) ).
fof(4,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmp4cs1A3/sel_REL006+1.p_1',converse_additivity) ).
fof(5,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmp4cs1A3/sel_REL006+1.p_1',maddux1_join_commutativity) ).
fof(7,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/tmp/tmp4cs1A3/sel_REL006+1.p_1',def_zero) ).
fof(9,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmp4cs1A3/sel_REL006+1.p_1',maddux4_definiton_of_meet) ).
fof(10,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmp4cs1A3/sel_REL006+1.p_1',maddux2_join_associativity) ).
fof(11,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/tmp/tmp4cs1A3/sel_REL006+1.p_1',maddux3_a_kind_of_de_Morgan) ).
fof(12,conjecture,
! [X1,X2] :
( meet(converse(X1),X2) = zero
=> meet(X1,converse(X2)) = zero ),
file('/tmp/tmp4cs1A3/sel_REL006+1.p_1',goals) ).
fof(13,negated_conjecture,
~ ! [X1,X2] :
( meet(converse(X1),X2) = zero
=> meet(X1,converse(X2)) = zero ),
inference(assume_negation,[status(cth)],[12]) ).
fof(16,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(17,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[16]) ).
fof(20,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(21,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[20]) ).
fof(22,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(23,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[22]) ).
fof(26,plain,
! [X2] : zero = meet(X2,complement(X2)),
inference(variable_rename,[status(thm)],[7]) ).
cnf(27,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[26]) ).
fof(30,plain,
! [X3,X4] : meet(X3,X4) = complement(join(complement(X3),complement(X4))),
inference(variable_rename,[status(thm)],[9]) ).
cnf(31,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[30]) ).
fof(32,plain,
! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
inference(variable_rename,[status(thm)],[10]) ).
cnf(33,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[32]) ).
fof(34,plain,
! [X3,X4] : X3 = join(complement(join(complement(X3),complement(X4))),complement(join(complement(X3),X4))),
inference(variable_rename,[status(thm)],[11]) ).
cnf(35,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[34]) ).
fof(36,negated_conjecture,
? [X1,X2] :
( meet(converse(X1),X2) = zero
& meet(X1,converse(X2)) != zero ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(37,negated_conjecture,
? [X3,X4] :
( meet(converse(X3),X4) = zero
& meet(X3,converse(X4)) != zero ),
inference(variable_rename,[status(thm)],[36]) ).
fof(38,negated_conjecture,
( meet(converse(esk1_0),esk2_0) = zero
& meet(esk1_0,converse(esk2_0)) != zero ),
inference(skolemize,[status(esa)],[37]) ).
cnf(39,negated_conjecture,
meet(esk1_0,converse(esk2_0)) != zero,
inference(split_conjunct,[status(thm)],[38]) ).
cnf(40,negated_conjecture,
meet(converse(esk1_0),esk2_0) = zero,
inference(split_conjunct,[status(thm)],[38]) ).
cnf(41,plain,
complement(join(complement(X1),complement(complement(X1)))) = zero,
inference(rw,[status(thm)],[27,31,theory(equality)]),
[unfolding] ).
cnf(42,negated_conjecture,
complement(join(complement(converse(esk1_0)),complement(esk2_0))) = zero,
inference(rw,[status(thm)],[40,31,theory(equality)]),
[unfolding] ).
cnf(43,negated_conjecture,
complement(join(complement(esk1_0),complement(converse(esk2_0)))) != zero,
inference(rw,[status(thm)],[39,31,theory(equality)]),
[unfolding] ).
cnf(45,plain,
complement(join(zero,complement(zero))) = zero,
inference(spm,[status(thm)],[41,41,theory(equality)]) ).
cnf(46,negated_conjecture,
complement(join(complement(esk2_0),complement(converse(esk1_0)))) = zero,
inference(rw,[status(thm)],[42,23,theory(equality)]) ).
cnf(49,plain,
join(X1,converse(X2)) = converse(join(converse(X1),X2)),
inference(spm,[status(thm)],[21,17,theory(equality)]) ).
cnf(50,plain,
join(converse(X1),X2) = converse(join(X1,converse(X2))),
inference(spm,[status(thm)],[21,17,theory(equality)]) ).
cnf(61,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[23,33,theory(equality)]) ).
cnf(63,plain,
join(join(X2,X1),X3) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[33,23,theory(equality)]) ).
cnf(67,plain,
join(X2,join(X1,X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[63,33,theory(equality)]) ).
cnf(85,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[35,23,theory(equality)]) ).
cnf(87,plain,
join(zero,complement(join(complement(X1),complement(complement(complement(X1)))))) = X1,
inference(spm,[status(thm)],[85,41,theory(equality)]) ).
cnf(89,plain,
join(complement(join(complement(X1),complement(X1))),zero) = X1,
inference(spm,[status(thm)],[85,41,theory(equality)]) ).
cnf(93,plain,
join(complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2)))),complement(X1)) = join(complement(X1),X2),
inference(spm,[status(thm)],[85,85,theory(equality)]) ).
cnf(94,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[85,23,theory(equality)]) ).
cnf(95,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[85,23,theory(equality)]) ).
cnf(96,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[85,23,theory(equality)]) ).
cnf(99,plain,
join(zero,complement(join(complement(X1),complement(X1)))) = X1,
inference(rw,[status(thm)],[89,23,theory(equality)]) ).
cnf(100,plain,
join(complement(X1),complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2))))) = join(complement(X1),X2),
inference(rw,[status(thm)],[93,23,theory(equality)]) ).
cnf(103,plain,
join(complement(join(zero,X1)),complement(join(zero,complement(X1)))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[85,45,theory(equality)]) ).
cnf(176,negated_conjecture,
join(complement(join(complement(esk2_0),converse(esk1_0))),zero) = esk2_0,
inference(spm,[status(thm)],[85,46,theory(equality)]) ).
cnf(179,negated_conjecture,
join(zero,complement(join(complement(esk2_0),converse(esk1_0)))) = esk2_0,
inference(rw,[status(thm)],[176,23,theory(equality)]) ).
cnf(216,plain,
join(zero,complement(join(zero,zero))) = join(complement(X1),complement(complement(X1))),
inference(spm,[status(thm)],[99,41,theory(equality)]) ).
cnf(218,plain,
join(zero,complement(join(zero,zero))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[99,45,theory(equality)]) ).
cnf(706,plain,
join(zero,complement(join(zero,complement(complement(zero))))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[87,45,theory(equality)]) ).
cnf(716,plain,
join(join(zero,complement(zero)),X1) = join(zero,join(complement(join(zero,complement(complement(zero)))),X1)),
inference(spm,[status(thm)],[33,706,theory(equality)]) ).
cnf(723,plain,
join(zero,join(complement(zero),X1)) = join(zero,join(complement(join(zero,complement(complement(zero)))),X1)),
inference(rw,[status(thm)],[716,33,theory(equality)]) ).
cnf(1221,plain,
join(complement(join(zero,join(zero,complement(zero)))),complement(join(zero,zero))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[103,45,theory(equality)]) ).
cnf(1260,plain,
join(complement(join(zero,zero)),complement(join(zero,join(zero,complement(zero))))) = join(zero,complement(zero)),
inference(rw,[status(thm)],[1221,23,theory(equality)]) ).
cnf(1412,plain,
join(zero,complement(zero)) = join(complement(X1),complement(complement(X1))),
inference(rw,[status(thm)],[216,218,theory(equality)]) ).
cnf(1838,plain,
join(complement(join(complement(join(zero,zero)),join(zero,join(zero,complement(zero))))),complement(join(zero,complement(zero)))) = join(zero,zero),
inference(spm,[status(thm)],[85,1260,theory(equality)]) ).
cnf(1853,plain,
join(zero,complement(join(zero,join(zero,join(complement(zero),complement(zero)))))) = join(zero,zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1838,67,theory(equality)]),61,theory(equality)]),23,theory(equality)]),218,theory(equality)]),67,theory(equality)]),45,theory(equality)]),23,theory(equality)]) ).
cnf(3762,plain,
join(complement(X1),complement(join(complement(X2),join(complement(X1),complement(join(complement(X1),X2)))))) = join(complement(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[100,61,theory(equality)]),23,theory(equality)]) ).
cnf(4003,plain,
join(zero,complement(zero)) = join(zero,join(complement(zero),complement(join(complement(complement(zero)),complement(zero))))),
inference(spm,[status(thm)],[723,94,theory(equality)]) ).
cnf(4067,plain,
join(zero,complement(zero)) = join(zero,join(zero,complement(zero))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[4003,23,theory(equality)]),1412,theory(equality)]),45,theory(equality)]),23,theory(equality)]) ).
cnf(4090,plain,
join(join(zero,complement(zero)),X1) = join(zero,join(join(zero,complement(zero)),X1)),
inference(spm,[status(thm)],[33,4067,theory(equality)]) ).
cnf(4105,plain,
join(zero,join(complement(zero),X1)) = join(zero,join(join(zero,complement(zero)),X1)),
inference(rw,[status(thm)],[4090,33,theory(equality)]) ).
cnf(4106,plain,
join(zero,join(complement(zero),X1)) = join(zero,join(zero,join(complement(zero),X1))),
inference(rw,[status(thm)],[4105,33,theory(equality)]) ).
cnf(4202,plain,
join(zero,complement(join(zero,join(complement(zero),complement(zero))))) = join(zero,zero),
inference(rw,[status(thm)],[1853,4106,theory(equality)]) ).
cnf(4292,plain,
join(complement(join(complement(complement(X1)),X1)),complement(join(zero,complement(zero)))) = complement(X1),
inference(spm,[status(thm)],[95,1412,theory(equality)]) ).
cnf(4351,plain,
join(zero,complement(join(X1,complement(complement(X1))))) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[4292,23,theory(equality)]),45,theory(equality)]),23,theory(equality)]) ).
cnf(4403,plain,
join(zero,complement(join(join(zero,complement(zero)),complement(zero)))) = zero,
inference(spm,[status(thm)],[4351,45,theory(equality)]) ).
cnf(4416,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[87,4351,theory(equality)]) ).
cnf(4417,plain,
join(zero,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[4403,33,theory(equality)]),4202,theory(equality)]) ).
cnf(4425,plain,
join(zero,X1) = join(zero,join(zero,X1)),
inference(spm,[status(thm)],[33,4417,theory(equality)]) ).
cnf(4620,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[4425,99,theory(equality)]) ).
cnf(4709,plain,
complement(join(complement(X1),complement(X1))) = X1,
inference(rw,[status(thm)],[99,4620,theory(equality)]) ).
cnf(4710,negated_conjecture,
complement(join(complement(esk2_0),converse(esk1_0))) = esk2_0,
inference(rw,[status(thm)],[179,4620,theory(equality)]) ).
cnf(5010,negated_conjecture,
complement(esk2_0) = join(complement(esk2_0),converse(esk1_0)),
inference(spm,[status(thm)],[4416,4710,theory(equality)]) ).
cnf(5025,negated_conjecture,
join(complement(esk2_0),X1) = join(complement(esk2_0),join(converse(esk1_0),X1)),
inference(spm,[status(thm)],[33,5010,theory(equality)]) ).
cnf(5329,plain,
complement(join(X1,X1)) = complement(X1),
inference(spm,[status(thm)],[4709,4416,theory(equality)]) ).
cnf(5360,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = join(X1,X1),
inference(spm,[status(thm)],[85,5329,theory(equality)]) ).
cnf(5394,plain,
X1 = join(X1,X1),
inference(rw,[status(thm)],[5360,85,theory(equality)]) ).
cnf(5420,plain,
join(X1,X2) = join(X1,join(X1,X2)),
inference(spm,[status(thm)],[33,5394,theory(equality)]) ).
cnf(5424,plain,
join(complement(join(complement(X1),X1)),complement(complement(X1))) = X1,
inference(spm,[status(thm)],[85,5394,theory(equality)]) ).
cnf(5473,plain,
join(X1,complement(join(X1,complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5424,23,theory(equality)]),4416,theory(equality)]),23,theory(equality)]) ).
cnf(5662,plain,
join(complement(join(X1,complement(X2))),X2) = X2,
inference(spm,[status(thm)],[5420,96,theory(equality)]) ).
cnf(5672,plain,
join(X1,X2) = join(X2,join(X1,X1)),
inference(spm,[status(thm)],[61,5420,theory(equality)]) ).
cnf(5751,plain,
join(X1,X2) = join(X2,X1),
inference(rw,[status(thm)],[5672,5394,theory(equality)]) ).
cnf(6604,plain,
join(complement(X1),complement(join(complement(complement(complement(X1))),complement(X1)))) = join(complement(X1),complement(complement(X1))),
inference(spm,[status(thm)],[3762,5473,theory(equality)]) ).
cnf(6640,plain,
join(X1,complement(X1)) = join(complement(X1),complement(complement(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[6604,23,theory(equality)]),4416,theory(equality)]),5394,theory(equality)]),4416,theory(equality)]),23,theory(equality)]) ).
cnf(6641,plain,
join(X1,complement(X1)) = complement(zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[6640,1412,theory(equality)]),4620,theory(equality)]) ).
cnf(6662,plain,
converse(complement(zero)) = join(X1,converse(complement(converse(X1)))),
inference(spm,[status(thm)],[49,6641,theory(equality)]) ).
cnf(6680,plain,
join(X1,complement(zero)) = complement(zero),
inference(spm,[status(thm)],[5420,6641,theory(equality)]) ).
cnf(6717,plain,
converse(complement(zero)) = join(X1,converse(complement(zero))),
inference(spm,[status(thm)],[49,6680,theory(equality)]) ).
cnf(6742,plain,
complement(zero) = join(complement(zero),X1),
inference(spm,[status(thm)],[5751,6680,theory(equality)]) ).
cnf(7018,plain,
converse(complement(zero)) = complement(zero),
inference(spm,[status(thm)],[6742,6717,theory(equality)]) ).
cnf(7431,plain,
join(X2,complement(join(X1,complement(X2)))) = X2,
inference(rw,[status(thm)],[5662,5751,theory(equality)]) ).
cnf(7992,plain,
join(X1,converse(complement(converse(X1)))) = complement(zero),
inference(rw,[status(thm)],[6662,7018,theory(equality)]) ).
cnf(8446,negated_conjecture,
join(complement(esk2_0),complement(zero)) = join(complement(esk2_0),converse(complement(converse(converse(esk1_0))))),
inference(spm,[status(thm)],[5025,7992,theory(equality)]) ).
cnf(8481,negated_conjecture,
complement(zero) = join(complement(esk2_0),converse(complement(converse(converse(esk1_0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[8446,5751,theory(equality)]),6742,theory(equality)]) ).
cnf(8482,negated_conjecture,
complement(zero) = join(complement(esk2_0),converse(complement(esk1_0))),
inference(rw,[status(thm)],[8481,17,theory(equality)]) ).
cnf(8491,negated_conjecture,
join(complement(complement(zero)),complement(join(complement(esk2_0),complement(converse(complement(esk1_0)))))) = esk2_0,
inference(spm,[status(thm)],[85,8482,theory(equality)]) ).
cnf(8512,negated_conjecture,
complement(join(complement(esk2_0),complement(converse(complement(esk1_0))))) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[8491,4416,theory(equality)]),4620,theory(equality)]) ).
cnf(8618,negated_conjecture,
join(converse(complement(esk1_0)),esk2_0) = converse(complement(esk1_0)),
inference(spm,[status(thm)],[7431,8512,theory(equality)]) ).
cnf(8641,negated_conjecture,
join(esk2_0,converse(complement(esk1_0))) = converse(complement(esk1_0)),
inference(rw,[status(thm)],[8618,5751,theory(equality)]) ).
cnf(8643,negated_conjecture,
converse(converse(complement(esk1_0))) = join(converse(esk2_0),complement(esk1_0)),
inference(spm,[status(thm)],[50,8641,theory(equality)]) ).
cnf(8658,negated_conjecture,
complement(esk1_0) = join(converse(esk2_0),complement(esk1_0)),
inference(rw,[status(thm)],[8643,17,theory(equality)]) ).
cnf(8659,negated_conjecture,
complement(esk1_0) = join(complement(esk1_0),converse(esk2_0)),
inference(rw,[status(thm)],[8658,5751,theory(equality)]) ).
cnf(8674,negated_conjecture,
join(complement(esk1_0),X1) = join(complement(esk1_0),join(converse(esk2_0),X1)),
inference(spm,[status(thm)],[33,8659,theory(equality)]) ).
cnf(12110,negated_conjecture,
join(complement(esk1_0),complement(zero)) = join(complement(esk1_0),complement(converse(esk2_0))),
inference(spm,[status(thm)],[8674,6641,theory(equality)]) ).
cnf(12163,negated_conjecture,
complement(zero) = join(complement(esk1_0),complement(converse(esk2_0))),
inference(rw,[status(thm)],[12110,6680,theory(equality)]) ).
cnf(12230,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[43,12163,theory(equality)]),4416,theory(equality)]) ).
cnf(12231,negated_conjecture,
$false,
inference(cn,[status(thm)],[12230,theory(equality)]) ).
cnf(12232,negated_conjecture,
$false,
12231,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL006+1.p
% --creating new selector for [REL001+0.ax]
% -running prover on /tmp/tmp4cs1A3/sel_REL006+1.p_1 with time limit 29
% -prover status Theorem
% Problem REL006+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL006+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL006+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
%
%------------------------------------------------------------------------------