TSTP Solution File: REL004+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL004+2 : 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 00:59:23 EST 2010
% Result : Theorem 5.36s
% Output : CNFRefutation 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 11
% Syntax : Number of formulae : 169 ( 169 unt; 0 def)
% Number of atoms : 169 ( 166 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 : 12 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 365 ( 43 sgn 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
file('/tmp/tmpLDC67-/sel_REL004+2.p_1',modular_law_1) ).
fof(3,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/tmp/tmpLDC67-/sel_REL004+2.p_1',converse_multiplicativity) ).
fof(4,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmpLDC67-/sel_REL004+2.p_1',converse_idempotence) ).
fof(5,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/tmp/tmpLDC67-/sel_REL004+2.p_1',composition_distributivity) ).
fof(6,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpLDC67-/sel_REL004+2.p_1',converse_additivity) ).
fof(7,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpLDC67-/sel_REL004+2.p_1',maddux1_join_commutativity) ).
fof(10,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/tmp/tmpLDC67-/sel_REL004+2.p_1',converse_cancellativity) ).
fof(11,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmpLDC67-/sel_REL004+2.p_1',maddux4_definiton_of_meet) ).
fof(12,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmpLDC67-/sel_REL004+2.p_1',maddux2_join_associativity) ).
fof(13,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/tmp/tmpLDC67-/sel_REL004+2.p_1',maddux3_a_kind_of_de_Morgan) ).
fof(14,conjecture,
! [X1] : converse(complement(X1)) = complement(converse(X1)),
file('/tmp/tmpLDC67-/sel_REL004+2.p_1',goals) ).
fof(15,negated_conjecture,
~ ! [X1] : converse(complement(X1)) = complement(converse(X1)),
inference(assume_negation,[status(cth)],[14]) ).
fof(18,plain,
! [X4,X5,X6] : join(meet(composition(X4,X5),X6),meet(composition(X4,meet(X5,composition(converse(X4),X6))),X6)) = meet(composition(X4,meet(X5,composition(converse(X4),X6))),X6),
inference(variable_rename,[status(thm)],[2]) ).
cnf(19,plain,
join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
inference(split_conjunct,[status(thm)],[18]) ).
fof(20,plain,
! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(21,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[20]) ).
fof(22,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[4]) ).
cnf(23,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,plain,
! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
inference(variable_rename,[status(thm)],[5]) ).
cnf(25,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[24]) ).
fof(26,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[6]) ).
cnf(27,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[26]) ).
fof(28,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[7]) ).
cnf(29,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[28]) ).
fof(34,plain,
! [X3,X4] : join(composition(converse(X3),complement(composition(X3,X4))),complement(X4)) = complement(X4),
inference(variable_rename,[status(thm)],[10]) ).
cnf(35,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[34]) ).
fof(36,plain,
! [X3,X4] : meet(X3,X4) = complement(join(complement(X3),complement(X4))),
inference(variable_rename,[status(thm)],[11]) ).
cnf(37,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[36]) ).
fof(38,plain,
! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
inference(variable_rename,[status(thm)],[12]) ).
cnf(39,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[38]) ).
fof(40,plain,
! [X3,X4] : X3 = join(complement(join(complement(X3),complement(X4))),complement(join(complement(X3),X4))),
inference(variable_rename,[status(thm)],[13]) ).
cnf(41,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[40]) ).
fof(42,negated_conjecture,
? [X1] : converse(complement(X1)) != complement(converse(X1)),
inference(fof_nnf,[status(thm)],[15]) ).
fof(43,negated_conjecture,
? [X2] : converse(complement(X2)) != complement(converse(X2)),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,negated_conjecture,
converse(complement(esk1_0)) != complement(converse(esk1_0)),
inference(skolemize,[status(esa)],[43]) ).
cnf(45,negated_conjecture,
converse(complement(esk1_0)) != complement(converse(esk1_0)),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(46,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3)))) = complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[19,37,theory(equality)]),37,theory(equality)]),37,theory(equality)]),37,theory(equality)]),37,theory(equality)]),
[unfolding] ).
cnf(50,plain,
composition(converse(X1),X2) = converse(composition(converse(X2),X1)),
inference(spm,[status(thm)],[21,23,theory(equality)]) ).
cnf(51,plain,
join(X1,converse(X2)) = converse(join(converse(X1),X2)),
inference(spm,[status(thm)],[27,23,theory(equality)]) ).
cnf(57,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(rw,[status(thm)],[35,29,theory(equality)]) ).
cnf(61,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[41,29,theory(equality)]) ).
cnf(63,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)],[61,61,theory(equality)]) ).
cnf(64,plain,
join(complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2)))),complement(X1)) = join(complement(X1),X2),
inference(spm,[status(thm)],[61,61,theory(equality)]) ).
cnf(65,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[61,29,theory(equality)]) ).
cnf(66,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[61,29,theory(equality)]) ).
cnf(69,plain,
join(complement(X1),complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2))))) = join(complement(X1),X2),
inference(rw,[status(thm)],[64,29,theory(equality)]) ).
cnf(77,plain,
join(X1,X3) = join(complement(join(complement(X1),X2)),join(complement(join(complement(X1),complement(X2))),X3)),
inference(spm,[status(thm)],[39,61,theory(equality)]) ).
cnf(79,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[29,39,theory(equality)]) ).
cnf(81,plain,
join(join(X2,X1),X3) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[39,29,theory(equality)]) ).
cnf(85,plain,
join(X2,join(X1,X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[81,39,theory(equality)]) ).
cnf(87,plain,
join(converse(composition(X2,X1)),composition(X3,converse(X2))) = composition(join(converse(X1),X3),converse(X2)),
inference(spm,[status(thm)],[25,21,theory(equality)]) ).
cnf(96,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3))))))))) = complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3))),
inference(rw,[status(thm)],[46,29,theory(equality)]) ).
cnf(97,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3))))))))) = complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))))),
inference(rw,[status(thm)],[96,29,theory(equality)]) ).
cnf(105,plain,
join(complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))))),X4) = join(complement(join(complement(composition(X1,X2)),complement(X3))),join(complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))))),X4)),
inference(spm,[status(thm)],[39,97,theory(equality)]) ).
cnf(186,plain,
join(converse(X1),composition(converse(X3),X2)) = converse(join(X1,composition(converse(X2),X3))),
inference(spm,[status(thm)],[27,50,theory(equality)]) ).
cnf(292,plain,
join(complement(join(X3,join(complement(X1),X2))),complement(join(complement(X1),complement(join(X2,X3))))) = X1,
inference(spm,[status(thm)],[61,79,theory(equality)]) ).
cnf(293,plain,
join(complement(join(X2,join(X3,complement(X1)))),complement(join(complement(X1),complement(join(X2,X3))))) = X1,
inference(spm,[status(thm)],[61,79,theory(equality)]) ).
cnf(373,plain,
join(X1,complement(X2)) = join(complement(X2),join(X1,composition(converse(X3),complement(composition(X3,X2))))),
inference(spm,[status(thm)],[85,57,theory(equality)]) ).
cnf(377,plain,
join(X1,X2) = join(complement(join(complement(X2),X3)),join(X1,complement(join(complement(X2),complement(X3))))),
inference(spm,[status(thm)],[85,61,theory(equality)]) ).
cnf(942,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)],[69,79,theory(equality)]),29,theory(equality)]) ).
cnf(1130,plain,
join(complement(join(X1,complement(X2))),complement(join(complement(X1),complement(X2)))) = X2,
inference(spm,[status(thm)],[65,29,theory(equality)]) ).
cnf(1577,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = join(X1,composition(converse(X3),complement(composition(X3,join(complement(X1),complement(X2)))))),
inference(spm,[status(thm)],[77,57,theory(equality)]) ).
cnf(1581,plain,
join(complement(join(complement(X1),X2)),X1) = join(X1,complement(join(complement(X1),complement(complement(X2))))),
inference(spm,[status(thm)],[77,61,theory(equality)]) ).
cnf(1649,plain,
X1 = join(X1,composition(converse(X3),complement(composition(X3,join(complement(X1),complement(X2)))))),
inference(rw,[status(thm)],[1577,61,theory(equality)]) ).
cnf(1653,plain,
join(X1,complement(join(complement(X1),X2))) = join(X1,complement(join(complement(X1),complement(complement(X2))))),
inference(rw,[status(thm)],[1581,29,theory(equality)]) ).
cnf(1980,plain,
converse(composition(join(converse(X2),converse(X3)),converse(X1))) = join(converse(converse(composition(X1,X2))),composition(converse(converse(X1)),X3)),
inference(spm,[status(thm)],[186,87,theory(equality)]) ).
cnf(2018,plain,
composition(X1,join(X2,X3)) = join(converse(converse(composition(X1,X2))),composition(converse(converse(X1)),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1980,27,theory(equality)]),21,theory(equality)]),23,theory(equality)]) ).
cnf(2019,plain,
composition(X1,join(X2,X3)) = join(composition(X1,X2),composition(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2018,23,theory(equality)]),23,theory(equality)]) ).
cnf(4405,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),X3) = X3,
inference(spm,[status(thm)],[105,61,theory(equality)]) ).
cnf(4440,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),join(X3,X4)) = join(X3,X4),
inference(spm,[status(thm)],[105,77,theory(equality)]) ).
cnf(4490,plain,
join(X3,complement(join(complement(composition(X1,X2)),complement(X3)))) = X3,
inference(rw,[status(thm)],[4405,29,theory(equality)]) ).
cnf(4523,plain,
join(X3,join(complement(join(complement(composition(X1,X2)),complement(X3))),X4)) = join(X3,X4),
inference(rw,[status(thm)],[4440,85,theory(equality)]) ).
cnf(4598,plain,
join(X1,complement(join(complement(X1),complement(composition(X2,X3))))) = X1,
inference(spm,[status(thm)],[4490,29,theory(equality)]) ).
cnf(4602,plain,
join(X1,X2) = join(X2,join(X1,complement(join(complement(composition(X3,X4)),complement(X2))))),
inference(spm,[status(thm)],[85,4490,theory(equality)]) ).
cnf(5818,plain,
join(X1,composition(converse(X2),complement(composition(X2,join(complement(X1),X3))))) = X1,
inference(spm,[status(thm)],[1649,63,theory(equality)]) ).
cnf(6480,plain,
join(X1,composition(converse(X2),complement(composition(X2,join(X3,complement(X1)))))) = X1,
inference(spm,[status(thm)],[5818,29,theory(equality)]) ).
cnf(9679,plain,
join(X1,X1) = join(X1,complement(join(complement(X1),complement(complement(composition(X2,X3)))))),
inference(spm,[status(thm)],[4523,65,theory(equality)]) ).
cnf(9782,plain,
join(X1,X1) = join(X1,complement(join(complement(X1),composition(X2,X3)))),
inference(rw,[status(thm)],[9679,1653,theory(equality)]) ).
cnf(9852,plain,
join(X1,complement(complement(X1))) = join(X1,X1),
inference(spm,[status(thm)],[9782,57,theory(equality)]) ).
cnf(9999,plain,
join(complement(join(complement(X1),complement(X1))),complement(join(complement(X1),complement(complement(complement(complement(X1))))))) = X1,
inference(spm,[status(thm)],[61,9852,theory(equality)]) ).
cnf(10015,plain,
join(complement(join(complement(complement(complement(X1))),X1)),complement(join(complement(X1),complement(X1)))) = complement(complement(X1)),
inference(spm,[status(thm)],[66,9852,theory(equality)]) ).
cnf(10075,plain,
join(complement(join(complement(X1),complement(X1))),complement(join(X1,complement(complement(complement(X1)))))) = complement(complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[10015,29,theory(equality)]),29,theory(equality)]) ).
cnf(32268,plain,
join(complement(join(complement(X1),X1)),complement(complement(X1))) = join(X1,complement(join(X1,complement(complement(complement(X1)))))),
inference(spm,[status(thm)],[77,10075,theory(equality)]) ).
cnf(32301,plain,
join(complement(complement(X1)),complement(join(X1,complement(X1)))) = join(X1,complement(join(X1,complement(complement(complement(X1)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[32268,29,theory(equality)]),29,theory(equality)]) ).
cnf(46162,plain,
join(X1,composition(X2,X3)) = join(complement(join(complement(composition(X2,X3)),X1)),X1),
inference(spm,[status(thm)],[4602,61,theory(equality)]) ).
cnf(46336,plain,
join(X1,composition(X2,X3)) = join(X1,complement(join(complement(composition(X2,X3)),X1))),
inference(rw,[status(thm)],[46162,29,theory(equality)]) ).
cnf(57820,plain,
join(complement(join(complement(X1),complement(X1))),join(complement(X1),complement(join(complement(X1),complement(complement(complement(complement(X1)))))))) = join(complement(complement(complement(X1))),X1),
inference(spm,[status(thm)],[377,32301,theory(equality)]) ).
cnf(58116,plain,
join(X1,complement(X1)) = join(complement(complement(complement(X1))),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[57820,85,theory(equality)]),9999,theory(equality)]),29,theory(equality)]) ).
cnf(58117,plain,
join(X1,complement(X1)) = join(X1,complement(complement(complement(X1)))),
inference(rw,[status(thm)],[58116,29,theory(equality)]) ).
cnf(58325,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[10075,58117,theory(equality)]),29,theory(equality)]),1130,theory(equality)]) ).
cnf(58423,plain,
join(complement(join(X1,X2)),complement(join(X1,complement(X2)))) = complement(X1),
inference(spm,[status(thm)],[61,58325,theory(equality)]) ).
cnf(58435,plain,
join(complement(join(X1,X2)),complement(join(X2,complement(X1)))) = complement(X2),
inference(spm,[status(thm)],[65,58325,theory(equality)]) ).
cnf(58437,plain,
join(complement(join(X1,X2)),complement(join(complement(X2),X1))) = complement(X1),
inference(spm,[status(thm)],[66,58325,theory(equality)]) ).
cnf(58454,plain,
join(complement(X1),complement(join(complement(composition(X2,X3)),X1))) = complement(X1),
inference(spm,[status(thm)],[4490,58325,theory(equality)]) ).
cnf(58455,plain,
join(complement(X1),complement(join(X1,complement(composition(X2,X3))))) = complement(X1),
inference(spm,[status(thm)],[4598,58325,theory(equality)]) ).
cnf(58906,plain,
join(complement(converse(join(X1,X2))),complement(join(converse(X1),complement(converse(X2))))) = complement(converse(X1)),
inference(spm,[status(thm)],[58423,27,theory(equality)]) ).
cnf(59419,plain,
join(complement(converse(join(X1,X2))),complement(join(converse(X2),complement(converse(X1))))) = complement(converse(X2)),
inference(spm,[status(thm)],[58435,27,theory(equality)]) ).
cnf(60019,plain,
join(complement(join(complement(join(complement(composition(X1,X2)),complement(complement(X3)))),X3)),complement(complement(X3))) = complement(complement(join(complement(composition(X1,X2)),complement(complement(X3))))),
inference(spm,[status(thm)],[58437,4490,theory(equality)]) ).
cnf(60365,plain,
join(X3,complement(join(X3,composition(X1,X2)))) = complement(complement(join(complement(composition(X1,X2)),complement(complement(X3))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[60019,29,theory(equality)]),58325,theory(equality)]),46336,theory(equality)]),58325,theory(equality)]),29,theory(equality)]) ).
cnf(60366,plain,
join(X3,complement(join(X3,composition(X1,X2)))) = join(complement(composition(X1,X2)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[60365,58325,theory(equality)]),58325,theory(equality)]) ).
cnf(61532,plain,
join(complement(join(X1,join(complement(X1),complement(composition(X2,X3))))),complement(complement(X1))) = X1,
inference(spm,[status(thm)],[292,58454,theory(equality)]) ).
cnf(61728,plain,
join(X1,complement(join(X1,join(complement(X1),complement(composition(X2,X3)))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[61532,58325,theory(equality)]),29,theory(equality)]) ).
cnf(65211,plain,
join(complement(join(complement(composition(X1,X2)),composition(X3,X4))),complement(join(complement(composition(X3,X4)),complement(composition(X1,X2))))) = join(complement(join(complement(composition(X1,X2)),composition(X3,X4))),composition(X1,X2)),
inference(spm,[status(thm)],[46336,60366,theory(equality)]) ).
cnf(65373,plain,
composition(X1,X2) = join(complement(join(complement(composition(X1,X2)),composition(X3,X4))),composition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[65211,58437,theory(equality)]),58325,theory(equality)]) ).
cnf(65374,plain,
composition(X1,X2) = composition(X1,join(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[65373,29,theory(equality)]),9782,theory(equality)]),2019,theory(equality)]) ).
cnf(65444,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(join(X2,X2),X3)),
inference(spm,[status(thm)],[2019,65374,theory(equality)]) ).
cnf(65445,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,join(X3,X3))),
inference(spm,[status(thm)],[2019,65374,theory(equality)]) ).
cnf(65671,plain,
composition(X1,join(X2,X3)) = composition(X1,join(join(X2,X2),X3)),
inference(rw,[status(thm)],[65444,2019,theory(equality)]) ).
cnf(65672,plain,
composition(X1,join(X2,X3)) = composition(X1,join(X2,join(X2,X3))),
inference(rw,[status(thm)],[65671,39,theory(equality)]) ).
cnf(65673,plain,
composition(X1,join(X2,X3)) = composition(X1,join(X2,join(X3,X3))),
inference(rw,[status(thm)],[65445,2019,theory(equality)]) ).
cnf(68699,plain,
composition(X1,join(complement(join(complement(X2),X3)),X2)) = composition(X1,join(complement(join(complement(X2),X3)),complement(join(complement(X2),complement(X3))))),
inference(spm,[status(thm)],[65672,377,theory(equality)]) ).
cnf(68998,plain,
composition(X1,join(complement(join(complement(X2),X3)),X2)) = composition(X1,X2),
inference(rw,[status(thm)],[68699,61,theory(equality)]) ).
cnf(69247,plain,
composition(X1,join(join(X3,X3),X2)) = composition(X1,join(X2,X3)),
inference(spm,[status(thm)],[65673,29,theory(equality)]) ).
cnf(69406,plain,
composition(X1,join(X3,X2)) = composition(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[69247,39,theory(equality)]),65672,theory(equality)]) ).
cnf(70095,plain,
composition(X1,join(X2,complement(join(complement(X2),X3)))) = composition(X1,X2),
inference(rw,[status(thm)],[68998,69406,theory(equality)]) ).
cnf(70200,plain,
join(join(complement(X1),X2),composition(converse(X3),complement(composition(X3,X1)))) = join(complement(X1),X2),
inference(spm,[status(thm)],[6480,70095,theory(equality)]) ).
cnf(70525,plain,
join(X2,complement(X1)) = join(complement(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[70200,39,theory(equality)]),373,theory(equality)]) ).
cnf(70723,plain,
join(complement(join(complement(X1),X2)),join(X3,complement(join(complement(X1),complement(X2))))) = join(X1,X3),
inference(spm,[status(thm)],[77,70525,theory(equality)]) ).
cnf(71166,plain,
join(X3,X1) = join(X1,X3),
inference(rw,[status(thm)],[70723,377,theory(equality)]) ).
cnf(87489,plain,
join(complement(X1),complement(join(complement(join(complement(complement(X1)),complement(composition(X2,X3)))),complement(X1)))) = join(complement(X1),join(complement(complement(X1)),complement(composition(X2,X3)))),
inference(spm,[status(thm)],[942,61728,theory(equality)]) ).
cnf(87669,plain,
join(X1,complement(X1)) = join(complement(X1),join(complement(complement(X1)),complement(composition(X2,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[87489,58325,theory(equality)]),29,theory(equality)]),58455,theory(equality)]),58325,theory(equality)]),29,theory(equality)]) ).
cnf(87670,plain,
join(X1,complement(X1)) = join(X1,join(complement(X1),complement(composition(X2,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[87669,58325,theory(equality)]),85,theory(equality)]) ).
cnf(87929,plain,
join(complement(join(X1,complement(X1))),complement(join(X1,complement(join(complement(X1),complement(composition(X2,X3))))))) = complement(X1),
inference(spm,[status(thm)],[58423,87670,theory(equality)]) ).
cnf(87989,plain,
join(X1,complement(join(X1,complement(X1)))) = X1,
inference(rw,[status(thm)],[61728,87670,theory(equality)]) ).
cnf(88038,plain,
join(complement(X1),complement(join(X1,complement(X1)))) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[87929,4598,theory(equality)]),29,theory(equality)]) ).
cnf(88102,plain,
join(complement(X1),complement(join(complement(complement(complement(X1))),complement(X1)))) = join(complement(X1),complement(complement(X1))),
inference(spm,[status(thm)],[942,87989,theory(equality)]) ).
cnf(88256,plain,
join(complement(X1),complement(join(complement(X1),complement(X1)))) = join(complement(X1),complement(complement(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[88102,29,theory(equality)]),9852,theory(equality)]) ).
cnf(88257,plain,
join(complement(X1),complement(join(complement(X1),complement(X1)))) = join(X1,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[88256,58325,theory(equality)]),29,theory(equality)]) ).
cnf(88524,plain,
join(complement(join(complement(X1),complement(X1))),complement(complement(X1))) = join(complement(complement(X1)),X1),
inference(spm,[status(thm)],[377,88038,theory(equality)]) ).
cnf(88654,plain,
join(X1,complement(join(complement(X1),complement(X1)))) = join(complement(complement(X1)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[88524,29,theory(equality)]),58325,theory(equality)]) ).
cnf(88655,plain,
join(X1,complement(join(complement(X1),complement(X1)))) = join(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[88654,29,theory(equality)]),58325,theory(equality)]) ).
cnf(90146,plain,
join(complement(join(X1,complement(X1))),complement(join(complement(join(complement(X1),complement(X1))),complement(complement(X1))))) = complement(complement(join(complement(X1),complement(X1)))),
inference(spm,[status(thm)],[58435,88257,theory(equality)]) ).
cnf(90315,plain,
complement(X1) = complement(complement(join(complement(X1),complement(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[90146,29,theory(equality)]),58325,theory(equality)]),88655,theory(equality)]),29,theory(equality)]),58423,theory(equality)]) ).
cnf(90316,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(rw,[status(thm)],[90315,58325,theory(equality)]) ).
cnf(90512,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[90316,58325,theory(equality)]) ).
cnf(90894,plain,
join(X1,X2) = join(X1,join(X1,X2)),
inference(spm,[status(thm)],[39,90512,theory(equality)]) ).
cnf(91136,plain,
join(X1,X2) = join(X2,join(X1,X2)),
inference(spm,[status(thm)],[79,90512,theory(equality)]) ).
cnf(91734,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = join(complement(join(complement(X1),X2)),X1),
inference(spm,[status(thm)],[377,90894,theory(equality)]) ).
cnf(92003,plain,
X1 = join(complement(join(complement(X1),X2)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[91734,58423,theory(equality)]),58325,theory(equality)]) ).
cnf(92004,plain,
X1 = join(X1,complement(join(complement(X1),X2))),
inference(rw,[status(thm)],[92003,29,theory(equality)]) ).
cnf(92752,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[92004,4602,theory(equality)]) ).
cnf(93316,plain,
join(complement(join(complement(X1),X2)),X2) = join(X2,X1),
inference(spm,[status(thm)],[377,92752,theory(equality)]) ).
cnf(93546,plain,
join(X2,complement(join(complement(X1),X2))) = join(X2,X1),
inference(rw,[status(thm)],[93316,29,theory(equality)]) ).
cnf(95944,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[93546,58325,theory(equality)]) ).
cnf(96605,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[95944,71166,theory(equality)]) ).
cnf(97253,plain,
join(X1,complement(X1)) = join(X1,complement(complement(join(complement(X1),X2)))),
inference(spm,[status(thm)],[96605,92004,theory(equality)]) ).
cnf(97431,plain,
join(X1,complement(X1)) = join(X1,join(complement(X1),X2)),
inference(rw,[status(thm)],[97253,58325,theory(equality)]) ).
cnf(97547,plain,
join(complement(join(X1,complement(X1))),complement(join(complement(X2),complement(join(X1,complement(X1)))))) = X2,
inference(spm,[status(thm)],[293,97431,theory(equality)]) ).
cnf(97777,plain,
join(complement(join(X1,complement(X1))),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[97547,95944,theory(equality)]),58325,theory(equality)]) ).
cnf(97895,plain,
join(complement(X2),join(complement(join(complement(join(X1,complement(X1))),complement(X2))),X3)) = join(join(X1,complement(X1)),X3),
inference(spm,[status(thm)],[77,97777,theory(equality)]) ).
cnf(98135,plain,
join(X2,complement(X2)) = join(join(X1,complement(X1)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[97895,97777,theory(equality)]),58325,theory(equality)]),85,theory(equality)]),97431,theory(equality)]) ).
cnf(98136,plain,
join(X2,complement(X2)) = join(X1,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[98135,39,theory(equality)]),97431,theory(equality)]) ).
cnf(99053,plain,
converse(join(X2,complement(X2))) = join(X1,converse(complement(converse(X1)))),
inference(spm,[status(thm)],[51,98136,theory(equality)]) ).
cnf(105364,plain,
join(X1,complement(converse(join(X2,complement(X2))))) = X1,
inference(spm,[status(thm)],[92004,99053,theory(equality)]) ).
cnf(106052,plain,
join(complement(converse(join(X1,complement(X1)))),X2) = X2,
inference(spm,[status(thm)],[91136,105364,theory(equality)]) ).
cnf(106453,plain,
complement(join(converse(X1),complement(converse(complement(X1))))) = complement(converse(X1)),
inference(spm,[status(thm)],[58906,106052,theory(equality)]) ).
cnf(107073,plain,
join(complement(join(X1,join(complement(converse(X2)),X3))),complement(join(complement(converse(X2)),complement(join(X3,X1))))) = join(converse(X2),complement(converse(complement(X2)))),
inference(spm,[status(thm)],[292,106453,theory(equality)]) ).
cnf(107231,plain,
converse(X2) = join(converse(X2),complement(converse(complement(X2)))),
inference(rw,[status(thm)],[107073,292,theory(equality)]) ).
cnf(107303,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(spm,[status(thm)],[107231,23,theory(equality)]) ).
cnf(107560,plain,
join(complement(converse(X1)),complement(join(converse(complement(converse(complement(converse(X1))))),complement(converse(X1))))) = complement(converse(complement(converse(complement(converse(X1)))))),
inference(spm,[status(thm)],[59419,107303,theory(equality)]) ).
cnf(107756,plain,
complement(converse(X1)) = complement(converse(complement(converse(complement(converse(X1)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[107560,71166,theory(equality)]),96605,theory(equality)]),107303,theory(equality)]) ).
cnf(108075,plain,
complement(converse(complement(converse(complement(X1))))) = complement(X1),
inference(spm,[status(thm)],[107756,23,theory(equality)]) ).
cnf(108640,plain,
join(complement(join(X1,join(complement(X2),X3))),complement(join(complement(X2),complement(join(X3,X1))))) = converse(complement(converse(complement(X2)))),
inference(spm,[status(thm)],[292,108075,theory(equality)]) ).
cnf(108853,plain,
X2 = converse(complement(converse(complement(X2)))),
inference(rw,[status(thm)],[108640,292,theory(equality)]) ).
cnf(108941,plain,
converse(X1) = complement(converse(complement(X1))),
inference(spm,[status(thm)],[23,108853,theory(equality)]) ).
cnf(109632,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[58325,108941,theory(equality)]) ).
cnf(110124,negated_conjecture,
$false,
inference(rw,[status(thm)],[45,109632,theory(equality)]) ).
cnf(110125,negated_conjecture,
$false,
inference(cn,[status(thm)],[110124,theory(equality)]) ).
cnf(110126,negated_conjecture,
$false,
110125,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL004+2.p
% --creating new selector for [REL001+0.ax, REL001+1.ax]
% -running prover on /tmp/tmpLDC67-/sel_REL004+2.p_1 with time limit 29
% -prover status Theorem
% Problem REL004+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL004+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL004+2.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
%
%------------------------------------------------------------------------------