TSTP Solution File: REL004+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL004+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 00:59:11 EST 2010
% Result : Theorem 23.95s
% Output : CNFRefutation 23.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 6
% Syntax : Number of formulae : 96 ( 96 unt; 0 def)
% Number of atoms : 96 ( 93 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 174 ( 7 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmpfoqSNE/sel_REL004+1.p_1',converse_idempotence) ).
fof(4,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpfoqSNE/sel_REL004+1.p_1',converse_additivity) ).
fof(5,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpfoqSNE/sel_REL004+1.p_1',maddux1_join_commutativity) ).
fof(8,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmpfoqSNE/sel_REL004+1.p_1',maddux2_join_associativity) ).
fof(9,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/tmp/tmpfoqSNE/sel_REL004+1.p_1',maddux3_a_kind_of_de_Morgan) ).
fof(10,conjecture,
! [X1] : converse(complement(X1)) = complement(converse(X1)),
file('/tmp/tmpfoqSNE/sel_REL004+1.p_1',goals) ).
fof(11,negated_conjecture,
~ ! [X1] : converse(complement(X1)) = complement(converse(X1)),
inference(assume_negation,[status(cth)],[10]) ).
fof(14,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(15,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[14]) ).
fof(18,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(19,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[18]) ).
fof(20,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(21,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[20]) ).
fof(26,plain,
! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
inference(variable_rename,[status(thm)],[8]) ).
cnf(27,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[26]) ).
fof(28,plain,
! [X3,X4] : X3 = join(complement(join(complement(X3),complement(X4))),complement(join(complement(X3),X4))),
inference(variable_rename,[status(thm)],[9]) ).
cnf(29,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[28]) ).
fof(30,negated_conjecture,
? [X1] : converse(complement(X1)) != complement(converse(X1)),
inference(fof_nnf,[status(thm)],[11]) ).
fof(31,negated_conjecture,
? [X2] : converse(complement(X2)) != complement(converse(X2)),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,negated_conjecture,
converse(complement(esk1_0)) != complement(converse(esk1_0)),
inference(skolemize,[status(esa)],[31]) ).
cnf(33,negated_conjecture,
converse(complement(esk1_0)) != complement(converse(esk1_0)),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(36,plain,
join(X1,converse(X2)) = converse(join(converse(X1),X2)),
inference(spm,[status(thm)],[19,15,theory(equality)]) ).
cnf(48,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[21,27,theory(equality)]) ).
cnf(50,plain,
join(join(X2,X1),X3) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[27,21,theory(equality)]) ).
cnf(54,plain,
join(X2,join(X1,X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[50,27,theory(equality)]) ).
cnf(71,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[29,21,theory(equality)]) ).
cnf(75,plain,
join(complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2)))),complement(X1)) = join(complement(X1),X2),
inference(spm,[status(thm)],[71,71,theory(equality)]) ).
cnf(76,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[71,21,theory(equality)]) ).
cnf(77,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[71,21,theory(equality)]) ).
cnf(80,plain,
join(complement(X1),complement(join(complement(X1),join(complement(X2),complement(join(complement(X1),X2)))))) = join(complement(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[75,21,theory(equality)]),27,theory(equality)]),21,theory(equality)]) ).
cnf(369,plain,
join(X1,X2) = join(complement(join(complement(X2),X3)),join(X1,complement(join(complement(X2),complement(X3))))),
inference(spm,[status(thm)],[54,71,theory(equality)]) ).
cnf(1824,plain,
join(complement(join(complement(join(X1,complement(X2))),join(complement(X2),complement(X1)))),complement(X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[71,76,theory(equality)]) ).
cnf(1830,plain,
join(complement(join(X1,complement(X2))),complement(join(complement(X1),complement(X2)))) = X2,
inference(spm,[status(thm)],[76,21,theory(equality)]) ).
cnf(1835,plain,
join(X1,X3) = join(complement(join(X2,complement(X3))),join(X1,complement(join(complement(X3),complement(X2))))),
inference(spm,[status(thm)],[54,76,theory(equality)]) ).
cnf(1839,plain,
join(complement(X2),complement(join(complement(X1),join(complement(X2),complement(join(X1,complement(X2))))))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1824,48,theory(equality)]),21,theory(equality)]),21,theory(equality)]) ).
cnf(1869,plain,
join(X1,X2) = join(complement(join(complement(X2),X3)),join(X1,complement(join(complement(X3),complement(X2))))),
inference(spm,[status(thm)],[54,77,theory(equality)]) ).
cnf(21576,plain,
join(complement(join(complement(X1),X2)),X2) = join(complement(join(complement(X2),X1)),X1),
inference(spm,[status(thm)],[369,77,theory(equality)]) ).
cnf(21580,plain,
join(complement(join(complement(X1),X2)),X2) = join(complement(join(X1,complement(X2))),X1),
inference(spm,[status(thm)],[369,1830,theory(equality)]) ).
cnf(21711,plain,
join(X2,complement(join(complement(X1),X2))) = join(complement(join(complement(X2),X1)),X1),
inference(rw,[status(thm)],[21576,21,theory(equality)]) ).
cnf(21712,plain,
join(X2,complement(join(complement(X1),X2))) = join(X1,complement(join(complement(X2),X1))),
inference(rw,[status(thm)],[21711,21,theory(equality)]) ).
cnf(21714,plain,
join(X2,complement(join(complement(X1),X2))) = join(complement(join(X1,complement(X2))),X1),
inference(rw,[status(thm)],[21580,21,theory(equality)]) ).
cnf(21715,plain,
join(X2,complement(join(complement(X1),X2))) = join(X1,complement(join(X1,complement(X2)))),
inference(rw,[status(thm)],[21714,21,theory(equality)]) ).
cnf(22590,plain,
join(complement(join(complement(X1),X2)),join(X1,complement(join(complement(complement(X2)),X1)))) = join(complement(X2),X1),
inference(spm,[status(thm)],[369,21712,theory(equality)]) ).
cnf(22882,plain,
join(X1,join(complement(join(complement(X1),X2)),complement(join(complement(complement(X2)),X1)))) = join(complement(X2),X1),
inference(rw,[status(thm)],[22590,54,theory(equality)]) ).
cnf(348223,plain,
join(complement(X1),X1) = join(complement(complement(X1)),complement(X1)),
inference(spm,[status(thm)],[22882,1830,theory(equality)]) ).
cnf(348915,plain,
join(X1,complement(X1)) = join(complement(complement(X1)),complement(X1)),
inference(rw,[status(thm)],[348223,21,theory(equality)]) ).
cnf(348916,plain,
join(X1,complement(X1)) = join(complement(X1),complement(complement(X1))),
inference(rw,[status(thm)],[348915,21,theory(equality)]) ).
cnf(349756,plain,
join(complement(join(complement(complement(X1)),X1)),complement(join(X1,complement(X1)))) = complement(X1),
inference(spm,[status(thm)],[77,348916,theory(equality)]) ).
cnf(349931,plain,
join(complement(join(X1,complement(X1))),complement(join(X1,complement(complement(X1))))) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[349756,21,theory(equality)]),21,theory(equality)]) ).
cnf(360552,plain,
complement(complement(X1)) = X1,
inference(spm,[status(thm)],[71,349931,theory(equality)]) ).
cnf(362105,plain,
join(complement(join(X1,X2)),complement(join(X1,complement(X2)))) = complement(X1),
inference(spm,[status(thm)],[71,360552,theory(equality)]) ).
cnf(362108,plain,
join(complement(join(X1,X2)),complement(join(X2,complement(X1)))) = complement(X2),
inference(spm,[status(thm)],[76,360552,theory(equality)]) ).
cnf(362110,plain,
join(complement(join(X1,X2)),complement(join(complement(X2),X1))) = complement(X1),
inference(spm,[status(thm)],[77,360552,theory(equality)]) ).
cnf(362114,plain,
join(complement(join(X1,X2)),complement(join(complement(X1),X2))) = complement(X2),
inference(spm,[status(thm)],[1830,360552,theory(equality)]) ).
cnf(362119,plain,
join(X1,complement(join(X1,join(complement(X2),complement(join(X1,X2)))))) = join(X1,X2),
inference(spm,[status(thm)],[80,360552,theory(equality)]) ).
cnf(362160,plain,
join(complement(join(X1,X2)),join(X3,complement(join(X1,complement(X2))))) = join(X3,complement(X1)),
inference(spm,[status(thm)],[369,360552,theory(equality)]) ).
cnf(362260,plain,
join(X1,complement(join(complement(X2),join(X1,complement(join(X2,X1)))))) = join(X2,X1),
inference(spm,[status(thm)],[1839,360552,theory(equality)]) ).
cnf(365395,plain,
join(complement(converse(join(X1,X2))),complement(join(complement(converse(X2)),converse(X1)))) = complement(converse(X1)),
inference(spm,[status(thm)],[362110,19,theory(equality)]) ).
cnf(386600,plain,
join(complement(join(X1,X2)),join(X2,complement(join(complement(X1),X2)))) = join(X1,complement(X1)),
inference(spm,[status(thm)],[362160,21715,theory(equality)]) ).
cnf(387072,plain,
join(X2,complement(X2)) = join(X1,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[386600,54,theory(equality)]),362114,theory(equality)]) ).
cnf(387138,plain,
join(X3,complement(X3)) = join(X1,join(X2,complement(join(X1,X2)))),
inference(spm,[status(thm)],[27,387072,theory(equality)]) ).
cnf(387141,plain,
converse(join(X2,complement(X2))) = join(X1,converse(complement(converse(X1)))),
inference(spm,[status(thm)],[36,387072,theory(equality)]) ).
cnf(387581,plain,
join(complement(join(X2,complement(X2))),complement(join(X1,complement(complement(X1))))) = complement(X1),
inference(spm,[status(thm)],[362105,387072,theory(equality)]) ).
cnf(387582,plain,
join(complement(join(X1,X1)),complement(join(X2,complement(X2)))) = complement(X1),
inference(spm,[status(thm)],[362105,387072,theory(equality)]) ).
cnf(387845,plain,
join(complement(join(X2,complement(X2))),complement(join(X1,X1))) = complement(X1),
inference(rw,[status(thm)],[387581,360552,theory(equality)]) ).
cnf(397651,plain,
join(X1,complement(X1)) = join(join(X2,X2),complement(X2)),
inference(spm,[status(thm)],[387138,387582,theory(equality)]) ).
cnf(398222,plain,
join(X1,complement(X1)) = join(X2,join(X2,complement(X2))),
inference(rw,[status(thm)],[397651,27,theory(equality)]) ).
cnf(400227,plain,
join(X1,complement(X1)) = join(X2,join(X3,complement(X3))),
inference(spm,[status(thm)],[398222,387072,theory(equality)]) ).
cnf(402856,plain,
join(X3,complement(X3)) = join(join(X2,complement(X2)),X1),
inference(spm,[status(thm)],[21,400227,theory(equality)]) ).
cnf(403200,plain,
join(X3,complement(X3)) = join(X2,join(complement(X2),X1)),
inference(rw,[status(thm)],[402856,27,theory(equality)]) ).
cnf(405480,plain,
join(X1,complement(join(X2,complement(X2)))) = join(X1,X1),
inference(spm,[status(thm)],[362119,403200,theory(equality)]) ).
cnf(411645,plain,
join(complement(join(X1,complement(X1))),complement(join(complement(X2),join(complement(join(X1,complement(X1))),complement(join(X2,X2)))))) = join(X2,X2),
inference(spm,[status(thm)],[362260,405480,theory(equality)]) ).
cnf(412793,plain,
X2 = join(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[411645,387845,theory(equality)]),387845,theory(equality)]),360552,theory(equality)]) ).
cnf(412927,plain,
join(X1,X2) = join(X1,join(X1,X2)),
inference(spm,[status(thm)],[27,412793,theory(equality)]) ).
cnf(414406,plain,
join(complement(join(X1,complement(X2))),complement(join(complement(X2),complement(X1)))) = join(complement(join(X1,complement(X2))),X2),
inference(spm,[status(thm)],[1835,412927,theory(equality)]) ).
cnf(414413,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = join(complement(join(complement(X1),X2)),X1),
inference(spm,[status(thm)],[1869,412927,theory(equality)]) ).
cnf(415066,plain,
X2 = join(complement(join(X1,complement(X2))),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[414406,362108,theory(equality)]),360552,theory(equality)]) ).
cnf(415067,plain,
X2 = join(X2,complement(join(X1,complement(X2)))),
inference(rw,[status(thm)],[415066,21,theory(equality)]) ).
cnf(415075,plain,
X1 = join(complement(join(complement(X1),X2)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[414413,362110,theory(equality)]),360552,theory(equality)]) ).
cnf(415076,plain,
X1 = join(X1,complement(join(complement(X1),X2))),
inference(rw,[status(thm)],[415075,21,theory(equality)]) ).
cnf(418303,plain,
join(complement(join(X1,X2)),X2) = join(X2,complement(X1)),
inference(spm,[status(thm)],[362160,415067,theory(equality)]) ).
cnf(418606,plain,
join(X2,complement(join(X1,X2))) = join(X2,complement(X1)),
inference(rw,[status(thm)],[418303,21,theory(equality)]) ).
cnf(419079,plain,
join(X1,complement(converse(join(X2,complement(X2))))) = X1,
inference(spm,[status(thm)],[415076,387141,theory(equality)]) ).
cnf(429161,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[418606,21,theory(equality)]) ).
cnf(433669,plain,
join(X1,complement(converse(join(X2,complement(X2))))) = join(X1,complement(converse(complement(converse(X1))))),
inference(spm,[status(thm)],[429161,387141,theory(equality)]) ).
cnf(434054,plain,
X1 = join(X1,complement(converse(complement(converse(X1))))),
inference(rw,[status(thm)],[433669,419079,theory(equality)]) ).
cnf(434072,plain,
converse(converse(X1)) = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(spm,[status(thm)],[36,434054,theory(equality)]) ).
cnf(434392,plain,
X1 = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(rw,[status(thm)],[434072,15,theory(equality)]) ).
cnf(434393,plain,
X1 = join(X1,converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[434392,15,theory(equality)]) ).
cnf(435048,plain,
join(complement(converse(join(complement(converse(complement(complement(converse(X1))))),X1))),complement(complement(converse(X1)))) = complement(converse(complement(converse(complement(complement(converse(X1))))))),
inference(spm,[status(thm)],[365395,434393,theory(equality)]) ).
cnf(435396,plain,
converse(X1) = complement(converse(complement(converse(complement(complement(converse(X1))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[435048,360552,theory(equality)]),15,theory(equality)]),21,theory(equality)]),360552,theory(equality)]),21,theory(equality)]),419079,theory(equality)]) ).
cnf(435397,plain,
converse(X1) = complement(converse(complement(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[435396,360552,theory(equality)]),15,theory(equality)]) ).
cnf(435584,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[360552,435397,theory(equality)]) ).
cnf(436082,negated_conjecture,
$false,
inference(rw,[status(thm)],[33,435584,theory(equality)]) ).
cnf(436083,negated_conjecture,
$false,
inference(cn,[status(thm)],[436082,theory(equality)]) ).
cnf(436084,negated_conjecture,
$false,
436083,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL004+1.p
% --creating new selector for [REL001+0.ax]
% -running prover on /tmp/tmpfoqSNE/sel_REL004+1.p_1 with time limit 29
% -prover status Theorem
% Problem REL004+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL004+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL004+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
%
%------------------------------------------------------------------------------