TSTP Solution File: REL005+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL005+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 00:59:58 EST 2010
% Result : Theorem 24.62s
% Output : CNFRefutation 24.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 7
% Syntax : Number of formulae : 103 ( 103 unt; 0 def)
% Number of atoms : 103 ( 100 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 188 ( 7 sgn 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmpZjIHYf/sel_REL005+1.p_1',converse_idempotence) ).
fof(4,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpZjIHYf/sel_REL005+1.p_1',converse_additivity) ).
fof(5,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpZjIHYf/sel_REL005+1.p_1',maddux1_join_commutativity) ).
fof(8,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmpZjIHYf/sel_REL005+1.p_1',maddux4_definiton_of_meet) ).
fof(9,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmpZjIHYf/sel_REL005+1.p_1',maddux2_join_associativity) ).
fof(10,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/tmp/tmpZjIHYf/sel_REL005+1.p_1',maddux3_a_kind_of_de_Morgan) ).
fof(11,conjecture,
! [X1,X2] : converse(meet(X1,X2)) = meet(converse(X1),converse(X2)),
file('/tmp/tmpZjIHYf/sel_REL005+1.p_1',goals) ).
fof(12,negated_conjecture,
~ ! [X1,X2] : converse(meet(X1,X2)) = meet(converse(X1),converse(X2)),
inference(assume_negation,[status(cth)],[11]) ).
fof(15,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(16,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[15]) ).
fof(19,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(20,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[19]) ).
fof(21,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(22,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[21]) ).
fof(27,plain,
! [X3,X4] : meet(X3,X4) = complement(join(complement(X3),complement(X4))),
inference(variable_rename,[status(thm)],[8]) ).
cnf(28,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
inference(variable_rename,[status(thm)],[9]) ).
cnf(30,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X3,X4] : X3 = join(complement(join(complement(X3),complement(X4))),complement(join(complement(X3),X4))),
inference(variable_rename,[status(thm)],[10]) ).
cnf(32,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[31]) ).
fof(33,negated_conjecture,
? [X1,X2] : converse(meet(X1,X2)) != meet(converse(X1),converse(X2)),
inference(fof_nnf,[status(thm)],[12]) ).
fof(34,negated_conjecture,
? [X3,X4] : converse(meet(X3,X4)) != meet(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[33]) ).
fof(35,negated_conjecture,
converse(meet(esk1_0,esk2_0)) != meet(converse(esk1_0),converse(esk2_0)),
inference(skolemize,[status(esa)],[34]) ).
cnf(36,negated_conjecture,
converse(meet(esk1_0,esk2_0)) != meet(converse(esk1_0),converse(esk2_0)),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(37,negated_conjecture,
complement(join(complement(converse(esk1_0)),complement(converse(esk2_0)))) != converse(complement(join(complement(esk1_0),complement(esk2_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[36,28,theory(equality)]),28,theory(equality)]),
[unfolding] ).
cnf(40,plain,
join(X1,converse(X2)) = converse(join(converse(X1),X2)),
inference(spm,[status(thm)],[20,16,theory(equality)]) ).
cnf(52,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[22,30,theory(equality)]) ).
cnf(54,plain,
join(join(X2,X1),X3) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[30,22,theory(equality)]) ).
cnf(58,plain,
join(X2,join(X1,X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[54,30,theory(equality)]) ).
cnf(75,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[32,22,theory(equality)]) ).
cnf(79,plain,
join(complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2)))),complement(X1)) = join(complement(X1),X2),
inference(spm,[status(thm)],[75,75,theory(equality)]) ).
cnf(80,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[75,22,theory(equality)]) ).
cnf(81,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[75,22,theory(equality)]) ).
cnf(84,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)],[79,22,theory(equality)]),30,theory(equality)]),22,theory(equality)]) ).
cnf(373,plain,
join(X1,X2) = join(complement(join(complement(X2),X3)),join(X1,complement(join(complement(X2),complement(X3))))),
inference(spm,[status(thm)],[58,75,theory(equality)]) ).
cnf(1828,plain,
join(complement(join(complement(join(X1,complement(X2))),join(complement(X2),complement(X1)))),complement(X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[75,80,theory(equality)]) ).
cnf(1834,plain,
join(complement(join(X1,complement(X2))),complement(join(complement(X1),complement(X2)))) = X2,
inference(spm,[status(thm)],[80,22,theory(equality)]) ).
cnf(1839,plain,
join(X1,X3) = join(complement(join(X2,complement(X3))),join(X1,complement(join(complement(X3),complement(X2))))),
inference(spm,[status(thm)],[58,80,theory(equality)]) ).
cnf(1843,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)],[1828,52,theory(equality)]),22,theory(equality)]),22,theory(equality)]) ).
cnf(1873,plain,
join(X1,X2) = join(complement(join(complement(X2),X3)),join(X1,complement(join(complement(X3),complement(X2))))),
inference(spm,[status(thm)],[58,81,theory(equality)]) ).
cnf(21602,plain,
join(complement(join(complement(X1),X2)),X2) = join(complement(join(complement(X2),X1)),X1),
inference(spm,[status(thm)],[373,81,theory(equality)]) ).
cnf(21606,plain,
join(complement(join(complement(X1),X2)),X2) = join(complement(join(X1,complement(X2))),X1),
inference(spm,[status(thm)],[373,1834,theory(equality)]) ).
cnf(21737,plain,
join(X2,complement(join(complement(X1),X2))) = join(complement(join(complement(X2),X1)),X1),
inference(rw,[status(thm)],[21602,22,theory(equality)]) ).
cnf(21738,plain,
join(X2,complement(join(complement(X1),X2))) = join(X1,complement(join(complement(X2),X1))),
inference(rw,[status(thm)],[21737,22,theory(equality)]) ).
cnf(21740,plain,
join(X2,complement(join(complement(X1),X2))) = join(complement(join(X1,complement(X2))),X1),
inference(rw,[status(thm)],[21606,22,theory(equality)]) ).
cnf(21741,plain,
join(X2,complement(join(complement(X1),X2))) = join(X1,complement(join(X1,complement(X2)))),
inference(rw,[status(thm)],[21740,22,theory(equality)]) ).
cnf(22616,plain,
join(complement(join(complement(X1),X2)),join(X1,complement(join(complement(complement(X2)),X1)))) = join(complement(X2),X1),
inference(spm,[status(thm)],[373,21738,theory(equality)]) ).
cnf(22912,plain,
join(X1,join(complement(join(complement(X1),X2)),complement(join(complement(complement(X2)),X1)))) = join(complement(X2),X1),
inference(rw,[status(thm)],[22616,58,theory(equality)]) ).
cnf(344684,plain,
join(complement(X1),X1) = join(complement(complement(X1)),complement(X1)),
inference(spm,[status(thm)],[22912,1834,theory(equality)]) ).
cnf(345376,plain,
join(X1,complement(X1)) = join(complement(complement(X1)),complement(X1)),
inference(rw,[status(thm)],[344684,22,theory(equality)]) ).
cnf(345377,plain,
join(X1,complement(X1)) = join(complement(X1),complement(complement(X1))),
inference(rw,[status(thm)],[345376,22,theory(equality)]) ).
cnf(346217,plain,
join(complement(join(complement(complement(X1)),X1)),complement(join(X1,complement(X1)))) = complement(X1),
inference(spm,[status(thm)],[81,345377,theory(equality)]) ).
cnf(346392,plain,
join(complement(join(X1,complement(X1))),complement(join(X1,complement(complement(X1))))) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[346217,22,theory(equality)]),22,theory(equality)]) ).
cnf(356935,plain,
complement(complement(X1)) = X1,
inference(spm,[status(thm)],[75,346392,theory(equality)]) ).
cnf(357297,plain,
join(complement(join(X1,X2)),complement(join(X1,complement(X2)))) = complement(X1),
inference(spm,[status(thm)],[75,356935,theory(equality)]) ).
cnf(357300,plain,
join(complement(join(X1,X2)),complement(join(X2,complement(X1)))) = complement(X2),
inference(spm,[status(thm)],[80,356935,theory(equality)]) ).
cnf(357302,plain,
join(complement(join(X1,X2)),complement(join(complement(X2),X1))) = complement(X1),
inference(spm,[status(thm)],[81,356935,theory(equality)]) ).
cnf(357306,plain,
join(complement(join(X1,X2)),complement(join(complement(X1),X2))) = complement(X2),
inference(spm,[status(thm)],[1834,356935,theory(equality)]) ).
cnf(357311,plain,
join(X1,complement(join(X1,join(complement(X2),complement(join(X1,X2)))))) = join(X1,X2),
inference(spm,[status(thm)],[84,356935,theory(equality)]) ).
cnf(357352,plain,
join(complement(join(X1,X2)),join(X3,complement(join(X1,complement(X2))))) = join(X3,complement(X1)),
inference(spm,[status(thm)],[373,356935,theory(equality)]) ).
cnf(357452,plain,
join(X1,complement(join(complement(X2),join(X1,complement(join(X2,X1)))))) = join(X2,X1),
inference(spm,[status(thm)],[1843,356935,theory(equality)]) ).
cnf(360246,plain,
join(complement(converse(join(X1,X2))),complement(join(complement(converse(X2)),converse(X1)))) = complement(converse(X1)),
inference(spm,[status(thm)],[357302,20,theory(equality)]) ).
cnf(381473,plain,
join(complement(join(X1,X2)),join(X2,complement(join(complement(X1),X2)))) = join(X1,complement(X1)),
inference(spm,[status(thm)],[357352,21741,theory(equality)]) ).
cnf(381949,plain,
join(X2,complement(X2)) = join(X1,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[381473,58,theory(equality)]),357306,theory(equality)]) ).
cnf(383697,plain,
join(X3,complement(X3)) = join(X1,join(X2,complement(join(X1,X2)))),
inference(spm,[status(thm)],[30,381949,theory(equality)]) ).
cnf(383700,plain,
converse(join(X2,complement(X2))) = join(X1,converse(complement(converse(X1)))),
inference(spm,[status(thm)],[40,381949,theory(equality)]) ).
cnf(384140,plain,
join(complement(join(X2,complement(X2))),complement(join(X1,complement(complement(X1))))) = complement(X1),
inference(spm,[status(thm)],[357297,381949,theory(equality)]) ).
cnf(384141,plain,
join(complement(join(X1,X1)),complement(join(X2,complement(X2)))) = complement(X1),
inference(spm,[status(thm)],[357297,381949,theory(equality)]) ).
cnf(384426,plain,
join(complement(join(X2,complement(X2))),complement(join(X1,X1))) = complement(X1),
inference(rw,[status(thm)],[384140,356935,theory(equality)]) ).
cnf(392646,plain,
join(X1,complement(X1)) = join(join(X2,X2),complement(X2)),
inference(spm,[status(thm)],[383697,384141,theory(equality)]) ).
cnf(393228,plain,
join(X1,complement(X1)) = join(X2,join(X2,complement(X2))),
inference(rw,[status(thm)],[392646,30,theory(equality)]) ).
cnf(396926,plain,
join(X1,complement(X1)) = join(X2,join(X3,complement(X3))),
inference(spm,[status(thm)],[393228,381949,theory(equality)]) ).
cnf(399419,plain,
join(X3,complement(X3)) = join(join(X2,complement(X2)),X1),
inference(spm,[status(thm)],[22,396926,theory(equality)]) ).
cnf(399782,plain,
join(X3,complement(X3)) = join(X2,join(complement(X2),X1)),
inference(rw,[status(thm)],[399419,30,theory(equality)]) ).
cnf(402101,plain,
join(X1,complement(join(X2,complement(X2)))) = join(X1,X1),
inference(spm,[status(thm)],[357311,399782,theory(equality)]) ).
cnf(406756,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)],[357452,402101,theory(equality)]) ).
cnf(407907,plain,
X2 = join(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[406756,384426,theory(equality)]),384426,theory(equality)]),356935,theory(equality)]) ).
cnf(408040,plain,
join(X1,X2) = join(X1,join(X1,X2)),
inference(spm,[status(thm)],[30,407907,theory(equality)]) ).
cnf(410295,plain,
join(complement(join(X1,complement(X2))),complement(join(complement(X2),complement(X1)))) = join(complement(join(X1,complement(X2))),X2),
inference(spm,[status(thm)],[1839,408040,theory(equality)]) ).
cnf(410302,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = join(complement(join(complement(X1),X2)),X1),
inference(spm,[status(thm)],[1873,408040,theory(equality)]) ).
cnf(410958,plain,
X2 = join(complement(join(X1,complement(X2))),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[410295,357300,theory(equality)]),356935,theory(equality)]) ).
cnf(410959,plain,
X2 = join(X2,complement(join(X1,complement(X2)))),
inference(rw,[status(thm)],[410958,22,theory(equality)]) ).
cnf(410967,plain,
X1 = join(complement(join(complement(X1),X2)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[410302,357302,theory(equality)]),356935,theory(equality)]) ).
cnf(410968,plain,
X1 = join(X1,complement(join(complement(X1),X2))),
inference(rw,[status(thm)],[410967,22,theory(equality)]) ).
cnf(414457,plain,
join(complement(join(X1,X2)),X2) = join(X2,complement(X1)),
inference(spm,[status(thm)],[357352,410959,theory(equality)]) ).
cnf(414762,plain,
join(X2,complement(join(X1,X2))) = join(X2,complement(X1)),
inference(rw,[status(thm)],[414457,22,theory(equality)]) ).
cnf(415240,plain,
join(X1,complement(converse(join(X2,complement(X2))))) = X1,
inference(spm,[status(thm)],[410968,383700,theory(equality)]) ).
cnf(424334,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[414762,22,theory(equality)]) ).
cnf(428845,plain,
join(X1,complement(converse(join(X2,complement(X2))))) = join(X1,complement(converse(complement(converse(X1))))),
inference(spm,[status(thm)],[424334,383700,theory(equality)]) ).
cnf(429230,plain,
X1 = join(X1,complement(converse(complement(converse(X1))))),
inference(rw,[status(thm)],[428845,415240,theory(equality)]) ).
cnf(429248,plain,
converse(converse(X1)) = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(spm,[status(thm)],[40,429230,theory(equality)]) ).
cnf(429568,plain,
X1 = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(rw,[status(thm)],[429248,16,theory(equality)]) ).
cnf(429569,plain,
X1 = join(X1,converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[429568,16,theory(equality)]) ).
cnf(430224,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)],[360246,429569,theory(equality)]) ).
cnf(430573,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)],[430224,356935,theory(equality)]),16,theory(equality)]),22,theory(equality)]),356935,theory(equality)]),22,theory(equality)]),415240,theory(equality)]) ).
cnf(430574,plain,
converse(X1) = complement(converse(complement(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[430573,356935,theory(equality)]),16,theory(equality)]) ).
cnf(430761,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[356935,430574,theory(equality)]) ).
cnf(430967,plain,
join(complement(converse(X1)),converse(X2)) = converse(join(complement(X1),X2)),
inference(spm,[status(thm)],[20,430761,theory(equality)]) ).
cnf(431527,negated_conjecture,
complement(join(complement(converse(esk1_0)),complement(converse(esk2_0)))) != complement(converse(join(complement(esk1_0),complement(esk2_0)))),
inference(rw,[status(thm)],[37,430761,theory(equality)]) ).
cnf(437861,plain,
join(complement(converse(X1)),complement(converse(X2))) = converse(join(complement(X1),complement(X2))),
inference(spm,[status(thm)],[430967,430761,theory(equality)]) ).
cnf(453531,negated_conjecture,
$false,
inference(rw,[status(thm)],[431527,437861,theory(equality)]) ).
cnf(453532,negated_conjecture,
$false,
inference(cn,[status(thm)],[453531,theory(equality)]) ).
cnf(453533,negated_conjecture,
$false,
453532,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL005+1.p
% --creating new selector for [REL001+0.ax]
% -running prover on /tmp/tmpZjIHYf/sel_REL005+1.p_1 with time limit 29
% -prover status Theorem
% Problem REL005+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL005+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL005+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
%
%------------------------------------------------------------------------------