TSTP Solution File: REL007+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL007+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 01:00:57 EST 2010
% Result : Theorem 0.63s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% 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 : 12 ( 7 ~; 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/tmpgkzTKR/sel_REL007+1.p_1',converse_idempotence) ).
fof(4,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpgkzTKR/sel_REL007+1.p_1',converse_additivity) ).
fof(5,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpgkzTKR/sel_REL007+1.p_1',maddux1_join_commutativity) ).
fof(7,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/tmp/tmpgkzTKR/sel_REL007+1.p_1',def_zero) ).
fof(9,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmpgkzTKR/sel_REL007+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/tmpgkzTKR/sel_REL007+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/tmpgkzTKR/sel_REL007+1.p_1',maddux3_a_kind_of_de_Morgan) ).
fof(12,conjecture,
! [X1,X2] :
( meet(X1,converse(X2)) = zero
=> meet(converse(X1),X2) = zero ),
file('/tmp/tmpgkzTKR/sel_REL007+1.p_1',goals) ).
fof(13,negated_conjecture,
~ ! [X1,X2] :
( meet(X1,converse(X2)) = zero
=> meet(converse(X1),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(X1,converse(X2)) = zero
& meet(converse(X1),X2) != zero ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(37,negated_conjecture,
? [X3,X4] :
( meet(X3,converse(X4)) = zero
& meet(converse(X3),X4) != zero ),
inference(variable_rename,[status(thm)],[36]) ).
fof(38,negated_conjecture,
( meet(esk1_0,converse(esk2_0)) = zero
& meet(converse(esk1_0),esk2_0) != zero ),
inference(skolemize,[status(esa)],[37]) ).
cnf(39,negated_conjecture,
meet(converse(esk1_0),esk2_0) != zero,
inference(split_conjunct,[status(thm)],[38]) ).
cnf(40,negated_conjecture,
meet(esk1_0,converse(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(esk1_0),complement(converse(esk2_0)))) = zero,
inference(rw,[status(thm)],[40,31,theory(equality)]),
[unfolding] ).
cnf(43,negated_conjecture,
complement(join(complement(converse(esk1_0)),complement(esk2_0))) != zero,
inference(rw,[status(thm)],[39,31,theory(equality)]),
[unfolding] ).
cnf(44,negated_conjecture,
complement(join(zero,complement(zero))) = zero,
inference(spm,[status(thm)],[41,42,theory(equality)]) ).
cnf(46,negated_conjecture,
complement(join(complement(esk2_0),complement(converse(esk1_0)))) != zero,
inference(rw,[status(thm)],[43,23,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(86,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[35,23,theory(equality)]) ).
cnf(90,negated_conjecture,
join(complement(join(complement(esk1_0),converse(esk2_0))),zero) = esk1_0,
inference(spm,[status(thm)],[86,42,theory(equality)]) ).
cnf(92,plain,
join(zero,complement(join(complement(X1),complement(complement(complement(X1)))))) = X1,
inference(spm,[status(thm)],[86,41,theory(equality)]) ).
cnf(94,plain,
join(complement(join(complement(X1),complement(X1))),zero) = X1,
inference(spm,[status(thm)],[86,41,theory(equality)]) ).
cnf(98,plain,
join(complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2)))),complement(X1)) = join(complement(X1),X2),
inference(spm,[status(thm)],[86,86,theory(equality)]) ).
cnf(99,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[86,23,theory(equality)]) ).
cnf(100,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[86,23,theory(equality)]) ).
cnf(101,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[86,23,theory(equality)]) ).
cnf(104,negated_conjecture,
join(zero,complement(join(complement(esk1_0),converse(esk2_0)))) = esk1_0,
inference(rw,[status(thm)],[90,23,theory(equality)]) ).
cnf(106,plain,
join(zero,complement(join(complement(X1),complement(X1)))) = X1,
inference(rw,[status(thm)],[94,23,theory(equality)]) ).
cnf(107,plain,
join(complement(X1),complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2))))) = join(complement(X1),X2),
inference(rw,[status(thm)],[98,23,theory(equality)]) ).
cnf(110,negated_conjecture,
join(complement(join(zero,X1)),complement(join(zero,complement(X1)))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[86,44,theory(equality)]) ).
cnf(216,plain,
join(zero,complement(join(zero,zero))) = join(complement(X1),complement(complement(X1))),
inference(spm,[status(thm)],[106,41,theory(equality)]) ).
cnf(218,negated_conjecture,
join(zero,complement(join(zero,zero))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[106,44,theory(equality)]) ).
cnf(705,negated_conjecture,
join(zero,complement(join(zero,complement(complement(zero))))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[92,44,theory(equality)]) ).
cnf(753,negated_conjecture,
join(join(zero,complement(zero)),X1) = join(zero,join(complement(join(zero,complement(complement(zero)))),X1)),
inference(spm,[status(thm)],[33,705,theory(equality)]) ).
cnf(760,negated_conjecture,
join(zero,join(complement(zero),X1)) = join(zero,join(complement(join(zero,complement(complement(zero)))),X1)),
inference(rw,[status(thm)],[753,33,theory(equality)]) ).
cnf(1220,negated_conjecture,
join(complement(join(zero,join(zero,complement(zero)))),complement(join(zero,zero))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[110,44,theory(equality)]) ).
cnf(1259,negated_conjecture,
join(complement(join(zero,zero)),complement(join(zero,join(zero,complement(zero))))) = join(zero,complement(zero)),
inference(rw,[status(thm)],[1220,23,theory(equality)]) ).
cnf(1593,plain,
join(zero,complement(zero)) = join(complement(X1),complement(complement(X1))),
inference(rw,[status(thm)],[216,218,theory(equality)]) ).
cnf(1837,negated_conjecture,
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)],[86,1259,theory(equality)]) ).
cnf(1852,negated_conjecture,
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)],[1837,67,theory(equality)]),61,theory(equality)]),23,theory(equality)]),218,theory(equality)]),67,theory(equality)]),44,theory(equality)]),23,theory(equality)]) ).
cnf(3761,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)],[107,61,theory(equality)]),23,theory(equality)]) ).
cnf(4002,negated_conjecture,
join(zero,complement(zero)) = join(zero,join(complement(zero),complement(join(complement(complement(zero)),complement(zero))))),
inference(spm,[status(thm)],[760,99,theory(equality)]) ).
cnf(4066,negated_conjecture,
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)],[4002,23,theory(equality)]),1593,theory(equality)]),44,theory(equality)]),23,theory(equality)]) ).
cnf(4089,negated_conjecture,
join(join(zero,complement(zero)),X1) = join(zero,join(join(zero,complement(zero)),X1)),
inference(spm,[status(thm)],[33,4066,theory(equality)]) ).
cnf(4104,negated_conjecture,
join(zero,join(complement(zero),X1)) = join(zero,join(join(zero,complement(zero)),X1)),
inference(rw,[status(thm)],[4089,33,theory(equality)]) ).
cnf(4105,negated_conjecture,
join(zero,join(complement(zero),X1)) = join(zero,join(zero,join(complement(zero),X1))),
inference(rw,[status(thm)],[4104,33,theory(equality)]) ).
cnf(4201,negated_conjecture,
join(zero,complement(join(zero,join(complement(zero),complement(zero))))) = join(zero,zero),
inference(rw,[status(thm)],[1852,4105,theory(equality)]) ).
cnf(4291,plain,
join(complement(join(complement(complement(X1)),X1)),complement(join(zero,complement(zero)))) = complement(X1),
inference(spm,[status(thm)],[100,1593,theory(equality)]) ).
cnf(4350,plain,
join(zero,complement(join(X1,complement(complement(X1))))) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[4291,23,theory(equality)]),44,theory(equality)]),23,theory(equality)]) ).
cnf(4402,negated_conjecture,
join(zero,complement(join(join(zero,complement(zero)),complement(zero)))) = zero,
inference(spm,[status(thm)],[4350,44,theory(equality)]) ).
cnf(4415,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[92,4350,theory(equality)]) ).
cnf(4416,negated_conjecture,
join(zero,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[4402,33,theory(equality)]),4201,theory(equality)]) ).
cnf(4424,negated_conjecture,
join(zero,X1) = join(zero,join(zero,X1)),
inference(spm,[status(thm)],[33,4416,theory(equality)]) ).
cnf(4619,negated_conjecture,
join(zero,X1) = X1,
inference(spm,[status(thm)],[4424,106,theory(equality)]) ).
cnf(4708,plain,
complement(join(complement(X1),complement(X1))) = X1,
inference(rw,[status(thm)],[106,4619,theory(equality)]) ).
cnf(4709,negated_conjecture,
complement(join(complement(esk1_0),converse(esk2_0))) = esk1_0,
inference(rw,[status(thm)],[104,4619,theory(equality)]) ).
cnf(5009,negated_conjecture,
complement(esk1_0) = join(complement(esk1_0),converse(esk2_0)),
inference(spm,[status(thm)],[4415,4709,theory(equality)]) ).
cnf(5024,negated_conjecture,
join(complement(esk1_0),X1) = join(complement(esk1_0),join(converse(esk2_0),X1)),
inference(spm,[status(thm)],[33,5009,theory(equality)]) ).
cnf(5328,plain,
complement(join(X1,X1)) = complement(X1),
inference(spm,[status(thm)],[4708,4415,theory(equality)]) ).
cnf(5359,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = join(X1,X1),
inference(spm,[status(thm)],[86,5328,theory(equality)]) ).
cnf(5393,plain,
X1 = join(X1,X1),
inference(rw,[status(thm)],[5359,86,theory(equality)]) ).
cnf(5419,plain,
join(X1,X2) = join(X1,join(X1,X2)),
inference(spm,[status(thm)],[33,5393,theory(equality)]) ).
cnf(5423,plain,
join(complement(join(complement(X1),X1)),complement(complement(X1))) = X1,
inference(spm,[status(thm)],[86,5393,theory(equality)]) ).
cnf(5472,plain,
join(X1,complement(join(X1,complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5423,23,theory(equality)]),4415,theory(equality)]),23,theory(equality)]) ).
cnf(5661,plain,
join(complement(join(X1,complement(X2))),X2) = X2,
inference(spm,[status(thm)],[5419,101,theory(equality)]) ).
cnf(5671,plain,
join(X1,X2) = join(X2,join(X1,X1)),
inference(spm,[status(thm)],[61,5419,theory(equality)]) ).
cnf(5750,plain,
join(X1,X2) = join(X2,X1),
inference(rw,[status(thm)],[5671,5393,theory(equality)]) ).
cnf(6603,plain,
join(complement(X1),complement(join(complement(complement(complement(X1))),complement(X1)))) = join(complement(X1),complement(complement(X1))),
inference(spm,[status(thm)],[3761,5472,theory(equality)]) ).
cnf(6639,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)],[6603,23,theory(equality)]),4415,theory(equality)]),5393,theory(equality)]),4415,theory(equality)]),23,theory(equality)]) ).
cnf(6640,plain,
join(X1,complement(X1)) = complement(zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[6639,1593,theory(equality)]),4619,theory(equality)]) ).
cnf(6661,plain,
converse(complement(zero)) = join(X1,converse(complement(converse(X1)))),
inference(spm,[status(thm)],[49,6640,theory(equality)]) ).
cnf(6679,plain,
join(X1,complement(zero)) = complement(zero),
inference(spm,[status(thm)],[5419,6640,theory(equality)]) ).
cnf(6716,plain,
converse(complement(zero)) = join(X1,converse(complement(zero))),
inference(spm,[status(thm)],[49,6679,theory(equality)]) ).
cnf(6741,plain,
complement(zero) = join(complement(zero),X1),
inference(spm,[status(thm)],[5750,6679,theory(equality)]) ).
cnf(7017,plain,
converse(complement(zero)) = complement(zero),
inference(spm,[status(thm)],[6741,6716,theory(equality)]) ).
cnf(7430,plain,
join(X2,complement(join(X1,complement(X2)))) = X2,
inference(rw,[status(thm)],[5661,5750,theory(equality)]) ).
cnf(7991,plain,
join(X1,converse(complement(converse(X1)))) = complement(zero),
inference(rw,[status(thm)],[6661,7017,theory(equality)]) ).
cnf(8445,negated_conjecture,
join(complement(esk1_0),complement(zero)) = join(complement(esk1_0),converse(complement(converse(converse(esk2_0))))),
inference(spm,[status(thm)],[5024,7991,theory(equality)]) ).
cnf(8480,negated_conjecture,
complement(zero) = join(complement(esk1_0),converse(complement(converse(converse(esk2_0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[8445,5750,theory(equality)]),6741,theory(equality)]) ).
cnf(8481,negated_conjecture,
complement(zero) = join(complement(esk1_0),converse(complement(esk2_0))),
inference(rw,[status(thm)],[8480,17,theory(equality)]) ).
cnf(8490,negated_conjecture,
join(complement(complement(zero)),complement(join(complement(esk1_0),complement(converse(complement(esk2_0)))))) = esk1_0,
inference(spm,[status(thm)],[86,8481,theory(equality)]) ).
cnf(8511,negated_conjecture,
complement(join(complement(esk1_0),complement(converse(complement(esk2_0))))) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[8490,4415,theory(equality)]),4619,theory(equality)]) ).
cnf(8617,negated_conjecture,
join(converse(complement(esk2_0)),esk1_0) = converse(complement(esk2_0)),
inference(spm,[status(thm)],[7430,8511,theory(equality)]) ).
cnf(8640,negated_conjecture,
join(esk1_0,converse(complement(esk2_0))) = converse(complement(esk2_0)),
inference(rw,[status(thm)],[8617,5750,theory(equality)]) ).
cnf(8642,negated_conjecture,
converse(converse(complement(esk2_0))) = join(converse(esk1_0),complement(esk2_0)),
inference(spm,[status(thm)],[50,8640,theory(equality)]) ).
cnf(8657,negated_conjecture,
complement(esk2_0) = join(converse(esk1_0),complement(esk2_0)),
inference(rw,[status(thm)],[8642,17,theory(equality)]) ).
cnf(8658,negated_conjecture,
complement(esk2_0) = join(complement(esk2_0),converse(esk1_0)),
inference(rw,[status(thm)],[8657,5750,theory(equality)]) ).
cnf(8673,negated_conjecture,
join(complement(esk2_0),X1) = join(complement(esk2_0),join(converse(esk1_0),X1)),
inference(spm,[status(thm)],[33,8658,theory(equality)]) ).
cnf(12109,negated_conjecture,
join(complement(esk2_0),complement(zero)) = join(complement(esk2_0),complement(converse(esk1_0))),
inference(spm,[status(thm)],[8673,6640,theory(equality)]) ).
cnf(12162,negated_conjecture,
complement(zero) = join(complement(esk2_0),complement(converse(esk1_0))),
inference(rw,[status(thm)],[12109,6679,theory(equality)]) ).
cnf(12229,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[46,12162,theory(equality)]),4415,theory(equality)]) ).
cnf(12230,negated_conjecture,
$false,
inference(cn,[status(thm)],[12229,theory(equality)]) ).
cnf(12231,negated_conjecture,
$false,
12230,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL007+1.p
% --creating new selector for [REL001+0.ax]
% -running prover on /tmp/tmpgkzTKR/sel_REL007+1.p_1 with time limit 29
% -prover status Theorem
% Problem REL007+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL007+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL007+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
%
%------------------------------------------------------------------------------