TSTP Solution File: REL027+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL027+3 : 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 01:19:18 EST 2010
% Result : Theorem 3.34s
% Output : CNFRefutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 12
% Syntax : Number of formulae : 121 ( 116 unt; 0 def)
% Number of atoms : 126 ( 123 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 10 ~; 0 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 167 ( 10 sgn 44 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/tmp/tmpNtWhj6/sel_REL027+3.p_1',converse_multiplicativity) ).
fof(4,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmpNtWhj6/sel_REL027+3.p_1',converse_idempotence) ).
fof(5,axiom,
! [X1] : composition(X1,one) = X1,
file('/tmp/tmpNtWhj6/sel_REL027+3.p_1',composition_identity) ).
fof(6,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpNtWhj6/sel_REL027+3.p_1',converse_additivity) ).
fof(7,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpNtWhj6/sel_REL027+3.p_1',maddux1_join_commutativity) ).
fof(10,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/tmp/tmpNtWhj6/sel_REL027+3.p_1',def_top) ).
fof(11,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmpNtWhj6/sel_REL027+3.p_1',maddux4_definiton_of_meet) ).
fof(12,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/tmp/tmpNtWhj6/sel_REL027+3.p_1',composition_distributivity) ).
fof(13,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmpNtWhj6/sel_REL027+3.p_1',maddux2_join_associativity) ).
fof(14,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/tmp/tmpNtWhj6/sel_REL027+3.p_1',maddux3_a_kind_of_de_Morgan) ).
fof(15,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/tmp/tmpNtWhj6/sel_REL027+3.p_1',converse_cancellativity) ).
fof(16,conjecture,
! [X1] :
( join(X1,one) = one
=> meet(complement(composition(X1,top)),one) = meet(complement(X1),one) ),
file('/tmp/tmpNtWhj6/sel_REL027+3.p_1',goals) ).
fof(17,negated_conjecture,
~ ! [X1] :
( join(X1,one) = one
=> meet(complement(composition(X1,top)),one) = meet(complement(X1),one) ),
inference(assume_negation,[status(cth)],[16]) ).
fof(22,plain,
! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(23,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[4]) ).
cnf(25,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[24]) ).
fof(26,plain,
! [X2] : composition(X2,one) = X2,
inference(variable_rename,[status(thm)],[5]) ).
cnf(27,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[26]) ).
fof(28,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[6]) ).
cnf(29,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[28]) ).
fof(30,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[7]) ).
cnf(31,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[30]) ).
fof(36,plain,
! [X2] : top = join(X2,complement(X2)),
inference(variable_rename,[status(thm)],[10]) ).
cnf(37,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[36]) ).
fof(38,plain,
! [X3,X4] : meet(X3,X4) = complement(join(complement(X3),complement(X4))),
inference(variable_rename,[status(thm)],[11]) ).
cnf(39,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[38]) ).
fof(40,plain,
! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
inference(variable_rename,[status(thm)],[12]) ).
cnf(41,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[40]) ).
fof(42,plain,
! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
inference(variable_rename,[status(thm)],[13]) ).
cnf(43,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[42]) ).
fof(44,plain,
! [X3,X4] : X3 = join(complement(join(complement(X3),complement(X4))),complement(join(complement(X3),X4))),
inference(variable_rename,[status(thm)],[14]) ).
cnf(45,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[44]) ).
fof(46,plain,
! [X3,X4] : join(composition(converse(X3),complement(composition(X3,X4))),complement(X4)) = complement(X4),
inference(variable_rename,[status(thm)],[15]) ).
cnf(47,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[46]) ).
fof(48,negated_conjecture,
? [X1] :
( join(X1,one) = one
& meet(complement(composition(X1,top)),one) != meet(complement(X1),one) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(49,negated_conjecture,
? [X2] :
( join(X2,one) = one
& meet(complement(composition(X2,top)),one) != meet(complement(X2),one) ),
inference(variable_rename,[status(thm)],[48]) ).
fof(50,negated_conjecture,
( join(esk1_0,one) = one
& meet(complement(composition(esk1_0,top)),one) != meet(complement(esk1_0),one) ),
inference(skolemize,[status(esa)],[49]) ).
cnf(51,negated_conjecture,
meet(complement(composition(esk1_0,top)),one) != meet(complement(esk1_0),one),
inference(split_conjunct,[status(thm)],[50]) ).
cnf(52,negated_conjecture,
join(esk1_0,one) = one,
inference(split_conjunct,[status(thm)],[50]) ).
cnf(56,negated_conjecture,
complement(join(complement(complement(composition(esk1_0,top))),complement(one))) != complement(join(complement(complement(esk1_0)),complement(one))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[51,39,theory(equality)]),39,theory(equality)]),
[unfolding] ).
cnf(57,negated_conjecture,
join(one,esk1_0) = one,
inference(rw,[status(thm)],[52,31,theory(equality)]) ).
cnf(64,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[37,43,theory(equality)]) ).
cnf(65,plain,
join(top,X2) = join(X1,join(complement(X1),X2)),
inference(spm,[status(thm)],[43,37,theory(equality)]) ).
cnf(67,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[31,43,theory(equality)]) ).
cnf(69,plain,
join(join(X2,X1),X3) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[43,31,theory(equality)]) ).
cnf(73,plain,
join(X2,join(X1,X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[69,43,theory(equality)]) ).
cnf(75,plain,
composition(X1,converse(X2)) = converse(composition(X2,converse(X1))),
inference(spm,[status(thm)],[23,25,theory(equality)]) ).
cnf(76,plain,
composition(converse(X1),X2) = converse(composition(converse(X2),X1)),
inference(spm,[status(thm)],[23,25,theory(equality)]) ).
cnf(78,plain,
join(X1,converse(X2)) = converse(join(converse(X1),X2)),
inference(spm,[status(thm)],[29,25,theory(equality)]) ).
cnf(100,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(rw,[status(thm)],[47,31,theory(equality)]) ).
cnf(107,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[45,31,theory(equality)]) ).
cnf(112,plain,
join(complement(X1),complement(join(complement(join(complement(X1),X2)),complement(complement(join(complement(X1),complement(X2))))))) = join(complement(X1),X2),
inference(spm,[status(thm)],[107,107,theory(equality)]) ).
cnf(114,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[107,31,theory(equality)]) ).
cnf(120,negated_conjecture,
complement(join(complement(one),complement(complement(composition(esk1_0,top))))) != complement(join(complement(complement(esk1_0)),complement(one))),
inference(rw,[status(thm)],[56,31,theory(equality)]) ).
cnf(121,negated_conjecture,
complement(join(complement(one),complement(complement(composition(esk1_0,top))))) != complement(join(complement(one),complement(complement(esk1_0)))),
inference(rw,[status(thm)],[120,31,theory(equality)]) ).
cnf(340,plain,
join(X1,top) = join(top,complement(complement(X1))),
inference(spm,[status(thm)],[65,37,theory(equality)]) ).
cnf(845,plain,
converse(converse(X1)) = composition(converse(one),X1),
inference(spm,[status(thm)],[76,27,theory(equality)]) ).
cnf(863,plain,
X1 = composition(converse(one),X1),
inference(rw,[status(thm)],[845,25,theory(equality)]) ).
cnf(881,plain,
one = converse(one),
inference(spm,[status(thm)],[27,863,theory(equality)]) ).
cnf(927,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[863,881,theory(equality)]) ).
cnf(939,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[41,927,theory(equality)]) ).
cnf(941,plain,
join(complement(X1),composition(converse(one),complement(X1))) = complement(X1),
inference(spm,[status(thm)],[100,927,theory(equality)]) ).
cnf(952,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[941,881,theory(equality)]),927,theory(equality)]) ).
cnf(965,plain,
join(complement(complement(X1)),complement(join(complement(X1),complement(complement(X1))))) = X1,
inference(spm,[status(thm)],[107,952,theory(equality)]) ).
cnf(976,plain,
join(complement(X1),join(complement(X1),complement(complement(X1)))) = top,
inference(spm,[status(thm)],[64,952,theory(equality)]) ).
cnf(985,plain,
join(complement(top),complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[965,37,theory(equality)]),31,theory(equality)]) ).
cnf(1001,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[976,37,theory(equality)]),31,theory(equality)]) ).
cnf(1017,plain,
top = join(X1,top),
inference(rw,[status(thm)],[340,1001,theory(equality)]) ).
cnf(1039,plain,
join(complement(top),complement(join(complement(X1),complement(top)))) = X1,
inference(spm,[status(thm)],[107,1017,theory(equality)]) ).
cnf(1044,plain,
top = join(top,X1),
inference(spm,[status(thm)],[31,1017,theory(equality)]) ).
cnf(1227,plain,
converse(top) = join(X1,converse(complement(converse(X1)))),
inference(spm,[status(thm)],[78,37,theory(equality)]) ).
cnf(1246,plain,
converse(top) = join(X1,converse(top)),
inference(spm,[status(thm)],[78,1017,theory(equality)]) ).
cnf(1275,plain,
join(complement(top),complement(join(complement(top),complement(X1)))) = X1,
inference(spm,[status(thm)],[1039,31,theory(equality)]) ).
cnf(1293,plain,
converse(top) = top,
inference(spm,[status(thm)],[1044,1246,theory(equality)]) ).
cnf(1544,plain,
join(complement(top),complement(X1)) = complement(X1),
inference(spm,[status(thm)],[1275,985,theory(equality)]) ).
cnf(1582,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1275,1544,theory(equality)]),1544,theory(equality)]) ).
cnf(1583,plain,
complement(join(complement(X1),complement(top))) = X1,
inference(rw,[status(thm)],[1039,1544,theory(equality)]) ).
cnf(1606,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[952,1582,theory(equality)]) ).
cnf(1608,plain,
join(complement(top),X1) = X1,
inference(spm,[status(thm)],[1544,1582,theory(equality)]) ).
cnf(1609,negated_conjecture,
complement(join(complement(one),composition(esk1_0,top))) != complement(join(complement(one),complement(complement(esk1_0)))),
inference(rw,[status(thm)],[121,1582,theory(equality)]) ).
cnf(1610,negated_conjecture,
complement(join(complement(one),composition(esk1_0,top))) != complement(join(esk1_0,complement(one))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1609,1582,theory(equality)]),31,theory(equality)]) ).
cnf(1617,plain,
join(X1,complement(join(complement(X1),complement(complement(top))))) = X1,
inference(spm,[status(thm)],[107,1583,theory(equality)]) ).
cnf(1642,plain,
join(X1,complement(top)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1617,1582,theory(equality)]),31,theory(equality)]),1044,theory(equality)]) ).
cnf(1657,plain,
join(X1,X2) = join(X1,join(X1,X2)),
inference(spm,[status(thm)],[43,1606,theory(equality)]) ).
cnf(1678,plain,
join(X1,X2) = join(X2,join(X1,X2)),
inference(spm,[status(thm)],[67,1606,theory(equality)]) ).
cnf(2063,plain,
join(complement(join(complement(X1),X2)),X1) = X1,
inference(spm,[status(thm)],[1657,107,theory(equality)]) ).
cnf(2115,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[2063,31,theory(equality)]) ).
cnf(2337,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[1227,1293,theory(equality)]) ).
cnf(2514,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(spm,[status(thm)],[2115,1582,theory(equality)]) ).
cnf(2523,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[2115,1678,theory(equality)]) ).
cnf(2828,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[2523,1582,theory(equality)]) ).
cnf(5152,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)],[112,1582,theory(equality)]),73,theory(equality)]),31,theory(equality)]) ).
cnf(5533,plain,
join(complement(X1),complement(join(complement(X1),complement(X2)))) = join(complement(X1),X2),
inference(rw,[status(thm)],[5152,2828,theory(equality)]) ).
cnf(5934,plain,
join(complement(join(join(X1,complement(complement(X2))),complement(X2))),complement(complement(X2))) = X2,
inference(spm,[status(thm)],[114,2523,theory(equality)]) ).
cnf(5994,plain,
complement(complement(X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5934,43,theory(equality)]),31,theory(equality)]),37,theory(equality)]),1017,theory(equality)]),1608,theory(equality)]) ).
cnf(6046,plain,
join(X1,complement(join(X1,complement(X2)))) = join(X1,X2),
inference(spm,[status(thm)],[5533,5994,theory(equality)]) ).
cnf(31413,plain,
join(complement(join(X1,X2)),complement(join(complement(join(X1,complement(X2))),complement(X1)))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[114,6046,theory(equality)]) ).
cnf(31626,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[31413,31,theory(equality)]),2514,theory(equality)]),1582,theory(equality)]),31,theory(equality)]) ).
cnf(32585,plain,
join(X1,complement(top)) = join(X1,complement(converse(complement(converse(X1))))),
inference(spm,[status(thm)],[31626,2337,theory(equality)]) ).
cnf(32882,plain,
X1 = join(X1,complement(converse(complement(converse(X1))))),
inference(rw,[status(thm)],[32585,1642,theory(equality)]) ).
cnf(33829,plain,
converse(converse(X1)) = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(spm,[status(thm)],[78,32882,theory(equality)]) ).
cnf(33963,plain,
X1 = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(rw,[status(thm)],[33829,25,theory(equality)]) ).
cnf(33964,plain,
X1 = join(X1,converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[33963,25,theory(equality)]) ).
cnf(35858,plain,
join(complement(converse(complement(converse(complement(X1))))),complement(X1)) = complement(converse(complement(converse(complement(X1))))),
inference(spm,[status(thm)],[2828,33964,theory(equality)]) ).
cnf(35939,plain,
complement(X1) = complement(converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[35858,31,theory(equality)]),32882,theory(equality)]) ).
cnf(36259,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = converse(complement(converse(complement(X1)))),
inference(spm,[status(thm)],[107,35939,theory(equality)]) ).
cnf(36409,plain,
X1 = converse(complement(converse(complement(X1)))),
inference(rw,[status(thm)],[36259,107,theory(equality)]) ).
cnf(36536,plain,
converse(X1) = complement(converse(complement(X1))),
inference(spm,[status(thm)],[25,36409,theory(equality)]) ).
cnf(36661,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[5994,36536,theory(equality)]) ).
cnf(69158,plain,
join(X1,composition(complement(one),X1)) = composition(top,X1),
inference(spm,[status(thm)],[939,37,theory(equality)]) ).
cnf(69171,negated_conjecture,
join(X1,composition(esk1_0,X1)) = composition(one,X1),
inference(spm,[status(thm)],[939,57,theory(equality)]) ).
cnf(69526,negated_conjecture,
join(X1,composition(esk1_0,X1)) = X1,
inference(rw,[status(thm)],[69171,927,theory(equality)]) ).
cnf(69917,negated_conjecture,
join(X1,X2) = join(X2,join(X1,composition(esk1_0,X2))),
inference(spm,[status(thm)],[73,69526,theory(equality)]) ).
cnf(73623,plain,
converse(composition(top,converse(X1))) = join(X1,converse(composition(complement(one),converse(X1)))),
inference(spm,[status(thm)],[78,69158,theory(equality)]) ).
cnf(73736,plain,
composition(X1,top) = join(X1,converse(composition(complement(one),converse(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[73623,75,theory(equality)]),1293,theory(equality)]) ).
cnf(73737,plain,
composition(X1,top) = join(X1,composition(X1,complement(one))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[73736,75,theory(equality)]),36661,theory(equality)]),881,theory(equality)]) ).
cnf(92328,negated_conjecture,
join(complement(one),composition(esk1_0,top)) = join(esk1_0,complement(one)),
inference(spm,[status(thm)],[69917,73737,theory(equality)]) ).
cnf(92621,negated_conjecture,
$false,
inference(rw,[status(thm)],[1610,92328,theory(equality)]) ).
cnf(92622,negated_conjecture,
$false,
inference(cn,[status(thm)],[92621,theory(equality)]) ).
cnf(92623,negated_conjecture,
$false,
92622,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL027+3.p
% --creating new selector for [REL001+0.ax, REL001+1.ax]
% -running prover on /tmp/tmpNtWhj6/sel_REL027+3.p_1 with time limit 29
% -prover status Theorem
% Problem REL027+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL027+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL027+3.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
%
%------------------------------------------------------------------------------