TSTP Solution File: REL027+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL027+2 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 01:18:53 EST 2010
% Result : Theorem 186.75s
% Output : CNFRefutation 186.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 13
% Syntax : Number of formulae : 138 ( 120 unt; 0 def)
% Number of atoms : 161 ( 156 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 30 ~; 16 |; 5 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 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 : 197 ( 11 sgn 50 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/tmp/tmpnFtilz/sel_REL027+2.p_4',converse_multiplicativity) ).
fof(2,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmpnFtilz/sel_REL027+2.p_4',converse_idempotence) ).
fof(3,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/tmp/tmpnFtilz/sel_REL027+2.p_4',composition_distributivity) ).
fof(4,axiom,
! [X1] : composition(X1,one) = X1,
file('/tmp/tmpnFtilz/sel_REL027+2.p_4',composition_identity) ).
fof(5,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpnFtilz/sel_REL027+2.p_4',converse_additivity) ).
fof(6,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpnFtilz/sel_REL027+2.p_4',maddux1_join_commutativity) ).
fof(7,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/tmp/tmpnFtilz/sel_REL027+2.p_4',composition_associativity) ).
fof(8,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/tmp/tmpnFtilz/sel_REL027+2.p_4',def_top) ).
fof(9,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmpnFtilz/sel_REL027+2.p_4',maddux4_definiton_of_meet) ).
fof(10,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/tmp/tmpnFtilz/sel_REL027+2.p_4',converse_cancellativity) ).
fof(11,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmpnFtilz/sel_REL027+2.p_4',maddux2_join_associativity) ).
fof(12,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/tmp/tmpnFtilz/sel_REL027+2.p_4',maddux3_a_kind_of_de_Morgan) ).
fof(13,conjecture,
! [X1] :
( join(X1,one) = one
=> ( join(meet(complement(composition(X1,top)),one),meet(complement(X1),one)) = meet(complement(X1),one)
& join(meet(complement(X1),one),meet(complement(composition(X1,top)),one)) = meet(complement(composition(X1,top)),one) ) ),
file('/tmp/tmpnFtilz/sel_REL027+2.p_4',goals) ).
fof(14,negated_conjecture,
~ ! [X1] :
( join(X1,one) = one
=> ( join(meet(complement(composition(X1,top)),one),meet(complement(X1),one)) = meet(complement(X1),one)
& join(meet(complement(X1),one),meet(complement(composition(X1,top)),one)) = meet(complement(composition(X1,top)),one) ) ),
inference(assume_negation,[status(cth)],[13]) ).
fof(15,plain,
! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
inference(variable_rename,[status(thm)],[1]) ).
cnf(16,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[15]) ).
fof(17,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(18,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[17]) ).
fof(19,plain,
! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(20,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[19]) ).
fof(21,plain,
! [X2] : composition(X2,one) = X2,
inference(variable_rename,[status(thm)],[4]) ).
cnf(22,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[5]) ).
cnf(24,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[23]) ).
fof(25,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[6]) ).
cnf(26,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[25]) ).
fof(27,plain,
! [X4,X5,X6] : composition(X4,composition(X5,X6)) = composition(composition(X4,X5),X6),
inference(variable_rename,[status(thm)],[7]) ).
cnf(28,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X2] : top = join(X2,complement(X2)),
inference(variable_rename,[status(thm)],[8]) ).
cnf(30,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X3,X4] : meet(X3,X4) = complement(join(complement(X3),complement(X4))),
inference(variable_rename,[status(thm)],[9]) ).
cnf(32,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[31]) ).
fof(33,plain,
! [X3,X4] : join(composition(converse(X3),complement(composition(X3,X4))),complement(X4)) = complement(X4),
inference(variable_rename,[status(thm)],[10]) ).
cnf(34,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[33]) ).
fof(35,plain,
! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
inference(variable_rename,[status(thm)],[11]) ).
cnf(36,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X3,X4] : X3 = join(complement(join(complement(X3),complement(X4))),complement(join(complement(X3),X4))),
inference(variable_rename,[status(thm)],[12]) ).
cnf(38,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,negated_conjecture,
? [X1] :
( join(X1,one) = one
& ( join(meet(complement(composition(X1,top)),one),meet(complement(X1),one)) != meet(complement(X1),one)
| join(meet(complement(X1),one),meet(complement(composition(X1,top)),one)) != meet(complement(composition(X1,top)),one) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(40,negated_conjecture,
? [X2] :
( join(X2,one) = one
& ( join(meet(complement(composition(X2,top)),one),meet(complement(X2),one)) != meet(complement(X2),one)
| join(meet(complement(X2),one),meet(complement(composition(X2,top)),one)) != meet(complement(composition(X2,top)),one) ) ),
inference(variable_rename,[status(thm)],[39]) ).
fof(41,negated_conjecture,
( join(esk1_0,one) = one
& ( join(meet(complement(composition(esk1_0,top)),one),meet(complement(esk1_0),one)) != meet(complement(esk1_0),one)
| join(meet(complement(esk1_0),one),meet(complement(composition(esk1_0,top)),one)) != meet(complement(composition(esk1_0,top)),one) ) ),
inference(skolemize,[status(esa)],[40]) ).
cnf(42,negated_conjecture,
( join(meet(complement(esk1_0),one),meet(complement(composition(esk1_0,top)),one)) != meet(complement(composition(esk1_0,top)),one)
| join(meet(complement(composition(esk1_0,top)),one),meet(complement(esk1_0),one)) != meet(complement(esk1_0),one) ),
inference(split_conjunct,[status(thm)],[41]) ).
cnf(43,negated_conjecture,
join(esk1_0,one) = one,
inference(split_conjunct,[status(thm)],[41]) ).
cnf(44,negated_conjecture,
( join(complement(join(complement(complement(composition(esk1_0,top))),complement(one))),complement(join(complement(complement(esk1_0)),complement(one)))) != complement(join(complement(complement(esk1_0)),complement(one)))
| join(complement(join(complement(complement(esk1_0)),complement(one))),complement(join(complement(complement(composition(esk1_0,top))),complement(one)))) != complement(join(complement(complement(composition(esk1_0,top))),complement(one))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[42,32,theory(equality)]),32,theory(equality)]),32,theory(equality)]),32,theory(equality)]),32,theory(equality)]),32,theory(equality)]),
[unfolding] ).
cnf(45,negated_conjecture,
join(one,esk1_0) = one,
inference(rw,[status(thm)],[43,26,theory(equality)]) ).
cnf(52,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[30,36,theory(equality)]) ).
cnf(53,plain,
join(top,X2) = join(X1,join(complement(X1),X2)),
inference(spm,[status(thm)],[36,30,theory(equality)]) ).
cnf(55,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[26,36,theory(equality)]) ).
cnf(57,plain,
join(join(X2,X1),X3) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[36,26,theory(equality)]) ).
cnf(61,plain,
join(X2,join(X1,X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[57,36,theory(equality)]) ).
cnf(63,plain,
composition(X1,converse(X2)) = converse(composition(X2,converse(X1))),
inference(spm,[status(thm)],[16,18,theory(equality)]) ).
cnf(64,plain,
composition(converse(X1),X2) = converse(composition(converse(X2),X1)),
inference(spm,[status(thm)],[16,18,theory(equality)]) ).
cnf(66,plain,
join(X1,converse(X2)) = converse(join(converse(X1),X2)),
inference(spm,[status(thm)],[24,18,theory(equality)]) ).
cnf(88,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(rw,[status(thm)],[34,26,theory(equality)]) ).
cnf(91,plain,
join(complement(X1),composition(converse(composition(X2,X3)),complement(composition(X2,composition(X3,X1))))) = complement(X1),
inference(spm,[status(thm)],[88,28,theory(equality)]) ).
cnf(95,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[38,26,theory(equality)]) ).
cnf(99,plain,
join(complement(complement(X1)),complement(join(complement(X1),complement(composition(converse(X2),complement(composition(X2,X1))))))) = X1,
inference(spm,[status(thm)],[95,88,theory(equality)]) ).
cnf(102,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[95,26,theory(equality)]) ).
cnf(108,negated_conjecture,
( join(complement(join(complement(one),complement(complement(esk1_0)))),complement(join(complement(one),complement(complement(composition(esk1_0,top)))))) != complement(join(complement(complement(esk1_0)),complement(one)))
| join(complement(join(complement(complement(esk1_0)),complement(one))),complement(join(complement(complement(composition(esk1_0,top))),complement(one)))) != complement(join(complement(complement(composition(esk1_0,top))),complement(one))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[44,26,theory(equality)]),26,theory(equality)]),26,theory(equality)]) ).
cnf(109,negated_conjecture,
( join(complement(join(complement(one),complement(complement(esk1_0)))),complement(join(complement(one),complement(complement(composition(esk1_0,top)))))) != complement(join(complement(one),complement(complement(esk1_0))))
| join(complement(join(complement(complement(esk1_0)),complement(one))),complement(join(complement(complement(composition(esk1_0,top))),complement(one)))) != complement(join(complement(complement(composition(esk1_0,top))),complement(one))) ),
inference(rw,[status(thm)],[108,26,theory(equality)]) ).
cnf(110,negated_conjecture,
( join(complement(join(complement(one),complement(complement(esk1_0)))),complement(join(complement(one),complement(complement(composition(esk1_0,top)))))) != complement(join(complement(one),complement(complement(esk1_0))))
| join(complement(join(complement(one),complement(complement(esk1_0)))),complement(join(complement(one),complement(complement(composition(esk1_0,top)))))) != complement(join(complement(complement(composition(esk1_0,top))),complement(one))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[109,26,theory(equality)]),26,theory(equality)]) ).
cnf(111,negated_conjecture,
( join(complement(join(complement(one),complement(complement(esk1_0)))),complement(join(complement(one),complement(complement(composition(esk1_0,top)))))) != complement(join(complement(one),complement(complement(esk1_0))))
| join(complement(join(complement(one),complement(complement(esk1_0)))),complement(join(complement(one),complement(complement(composition(esk1_0,top)))))) != complement(join(complement(one),complement(complement(composition(esk1_0,top))))) ),
inference(rw,[status(thm)],[110,26,theory(equality)]) ).
cnf(142,plain,
join(complement(top),complement(join(complement(X1),complement(join(X2,complement(join(complement(X1),X2))))))) = X1,
inference(spm,[status(thm)],[95,52,theory(equality)]) ).
cnf(150,plain,
join(X1,join(X2,complement(join(X2,X1)))) = top,
inference(spm,[status(thm)],[52,26,theory(equality)]) ).
cnf(207,plain,
join(X1,top) = join(top,complement(complement(X1))),
inference(spm,[status(thm)],[53,30,theory(equality)]) ).
cnf(221,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[53,26,theory(equality)]) ).
cnf(346,plain,
join(X1,join(X2,X3)) = join(X3,join(X2,X1)),
inference(spm,[status(thm)],[55,26,theory(equality)]) ).
cnf(765,plain,
converse(converse(X1)) = composition(converse(one),X1),
inference(spm,[status(thm)],[64,22,theory(equality)]) ).
cnf(779,plain,
X1 = composition(converse(one),X1),
inference(rw,[status(thm)],[765,18,theory(equality)]) ).
cnf(829,plain,
one = converse(one),
inference(spm,[status(thm)],[22,779,theory(equality)]) ).
cnf(860,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[779,829,theory(equality)]) ).
cnf(870,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[20,860,theory(equality)]) ).
cnf(872,plain,
join(complement(X1),composition(converse(one),complement(X1))) = complement(X1),
inference(spm,[status(thm)],[88,860,theory(equality)]) ).
cnf(877,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[872,829,theory(equality)]),860,theory(equality)]) ).
cnf(881,plain,
join(complement(complement(X1)),complement(join(complement(X1),complement(complement(X1))))) = X1,
inference(spm,[status(thm)],[95,877,theory(equality)]) ).
cnf(883,plain,
join(complement(X1),join(complement(X1),complement(complement(X1)))) = top,
inference(spm,[status(thm)],[52,877,theory(equality)]) ).
cnf(895,plain,
join(complement(top),complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[881,30,theory(equality)]),26,theory(equality)]) ).
cnf(897,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[883,30,theory(equality)]),26,theory(equality)]) ).
cnf(919,plain,
top = join(X1,top),
inference(rw,[status(thm)],[207,897,theory(equality)]) ).
cnf(947,plain,
join(top,join(X1,complement(top))) = top,
inference(spm,[status(thm)],[150,919,theory(equality)]) ).
cnf(967,plain,
join(top,X1) = top,
inference(rw,[status(thm)],[947,221,theory(equality)]) ).
cnf(979,plain,
converse(top) = join(X1,converse(complement(converse(X1)))),
inference(spm,[status(thm)],[66,30,theory(equality)]) ).
cnf(999,plain,
converse(top) = join(X1,converse(top)),
inference(spm,[status(thm)],[66,919,theory(equality)]) ).
cnf(1151,plain,
converse(top) = top,
inference(spm,[status(thm)],[967,999,theory(equality)]) ).
cnf(1790,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[979,1151,theory(equality)]) ).
cnf(2959,plain,
join(composition(converse(composition(X1,X2)),complement(composition(X1,composition(X2,X3)))),join(complement(X3),complement(complement(X3)))) = top,
inference(spm,[status(thm)],[150,91,theory(equality)]) ).
cnf(3006,plain,
join(complement(X3),complement(complement(X3))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[2959,55,theory(equality)]),26,theory(equality)]),91,theory(equality)]),26,theory(equality)]) ).
cnf(3038,plain,
join(top,X2) = join(complement(X1),join(complement(complement(X1)),X2)),
inference(spm,[status(thm)],[36,3006,theory(equality)]) ).
cnf(3051,plain,
top = join(complement(X1),join(complement(complement(X1)),X2)),
inference(rw,[status(thm)],[3038,967,theory(equality)]) ).
cnf(4403,plain,
join(complement(join(complement(complement(X1)),join(complement(X1),complement(composition(converse(X2),complement(composition(X2,X1))))))),complement(X1)) = complement(X1),
inference(spm,[status(thm)],[95,99,theory(equality)]) ).
cnf(4437,plain,
join(complement(top),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[4403,61,theory(equality)]),3051,theory(equality)]) ).
cnf(4484,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[895,4437,theory(equality)]) ).
cnf(4502,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[877,4484,theory(equality)]) ).
cnf(4509,plain,
join(complement(top),X1) = X1,
inference(spm,[status(thm)],[4437,4484,theory(equality)]) ).
cnf(4517,negated_conjecture,
( join(complement(join(esk1_0,complement(one))),complement(join(complement(one),composition(esk1_0,top)))) != complement(join(complement(one),complement(complement(composition(esk1_0,top)))))
| join(complement(join(complement(one),complement(complement(esk1_0)))),complement(join(complement(one),complement(complement(composition(esk1_0,top)))))) != complement(join(complement(one),complement(complement(esk1_0)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[111,4484,theory(equality)]),26,theory(equality)]),4484,theory(equality)]) ).
cnf(4518,negated_conjecture,
( join(complement(join(esk1_0,complement(one))),complement(join(complement(one),composition(esk1_0,top)))) != complement(join(complement(one),composition(esk1_0,top)))
| join(complement(join(complement(one),complement(complement(esk1_0)))),complement(join(complement(one),complement(complement(composition(esk1_0,top)))))) != complement(join(complement(one),complement(complement(esk1_0)))) ),
inference(rw,[status(thm)],[4517,4484,theory(equality)]) ).
cnf(4519,negated_conjecture,
( join(complement(join(esk1_0,complement(one))),complement(join(complement(one),composition(esk1_0,top)))) != complement(join(complement(one),composition(esk1_0,top)))
| join(complement(join(esk1_0,complement(one))),complement(join(complement(one),composition(esk1_0,top)))) != complement(join(complement(one),complement(complement(esk1_0)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[4518,4484,theory(equality)]),26,theory(equality)]),4484,theory(equality)]) ).
cnf(4520,negated_conjecture,
( join(complement(join(esk1_0,complement(one))),complement(join(complement(one),composition(esk1_0,top)))) != complement(join(complement(one),composition(esk1_0,top)))
| join(complement(join(esk1_0,complement(one))),complement(join(complement(one),composition(esk1_0,top)))) != complement(join(esk1_0,complement(one))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[4519,4484,theory(equality)]),26,theory(equality)]) ).
cnf(4525,plain,
join(X1,X2) = join(X1,join(X1,X2)),
inference(spm,[status(thm)],[36,4502,theory(equality)]) ).
cnf(4529,plain,
join(complement(complement(X1)),complement(join(complement(X1),complement(complement(X1))))) = X1,
inference(spm,[status(thm)],[95,4502,theory(equality)]) ).
cnf(4583,plain,
join(X1,complement(top)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[4529,4484,theory(equality)]),4484,theory(equality)]),26,theory(equality)]),30,theory(equality)]) ).
cnf(5308,plain,
join(complement(join(complement(X1),X2)),X1) = X1,
inference(spm,[status(thm)],[4525,95,theory(equality)]) ).
cnf(5416,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[5308,26,theory(equality)]) ).
cnf(5566,plain,
join(complement(join(X1,complement(X2))),X2) = X2,
inference(spm,[status(thm)],[4525,102,theory(equality)]) ).
cnf(5606,plain,
join(X2,complement(join(X1,complement(X2)))) = X2,
inference(rw,[status(thm)],[5566,26,theory(equality)]) ).
cnf(6458,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[5606,4484,theory(equality)]) ).
cnf(8427,plain,
complement(join(complement(X1),complement(join(X2,complement(join(complement(X1),X2)))))) = X1,
inference(rw,[status(thm)],[142,4509,theory(equality)]) ).
cnf(8492,plain,
join(join(X1,complement(join(complement(X2),X1))),X2) = join(X1,complement(join(complement(X2),X1))),
inference(spm,[status(thm)],[5606,8427,theory(equality)]) ).
cnf(8569,plain,
join(X1,X2) = join(X1,complement(join(complement(X2),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[8492,36,theory(equality)]),26,theory(equality)]),5416,theory(equality)]) ).
cnf(16240,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[8569,4484,theory(equality)]) ).
cnf(16545,plain,
join(join(X1,complement(join(X1,X2))),complement(top)) = join(join(X1,complement(join(X1,X2))),complement(X2)),
inference(spm,[status(thm)],[16240,150,theory(equality)]) ).
cnf(16713,plain,
join(X1,complement(join(X1,X2))) = join(join(X1,complement(join(X1,X2))),complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[16545,36,theory(equality)]),26,theory(equality)]),4509,theory(equality)]) ).
cnf(16714,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[16713,36,theory(equality)]),26,theory(equality)]),6458,theory(equality)]) ).
cnf(17214,plain,
join(X1,complement(top)) = join(X1,complement(converse(complement(converse(X1))))),
inference(spm,[status(thm)],[16714,1790,theory(equality)]) ).
cnf(17394,plain,
X1 = join(X1,complement(converse(complement(converse(X1))))),
inference(rw,[status(thm)],[17214,4583,theory(equality)]) ).
cnf(17818,plain,
converse(converse(X1)) = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(spm,[status(thm)],[66,17394,theory(equality)]) ).
cnf(17893,plain,
X1 = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(rw,[status(thm)],[17818,18,theory(equality)]) ).
cnf(17894,plain,
X1 = join(X1,converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[17893,18,theory(equality)]) ).
cnf(18760,plain,
join(complement(converse(complement(converse(complement(X1))))),complement(X1)) = complement(converse(complement(converse(complement(X1))))),
inference(spm,[status(thm)],[6458,17894,theory(equality)]) ).
cnf(18821,plain,
complement(X1) = complement(converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[18760,26,theory(equality)]),17394,theory(equality)]) ).
cnf(19025,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = converse(complement(converse(complement(X1)))),
inference(spm,[status(thm)],[95,18821,theory(equality)]) ).
cnf(19068,plain,
X1 = converse(complement(converse(complement(X1)))),
inference(rw,[status(thm)],[19025,95,theory(equality)]) ).
cnf(19096,plain,
converse(X1) = complement(converse(complement(X1))),
inference(spm,[status(thm)],[18,19068,theory(equality)]) ).
cnf(19152,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[4484,19096,theory(equality)]) ).
cnf(34592,plain,
join(X1,composition(complement(one),X1)) = composition(top,X1),
inference(spm,[status(thm)],[870,30,theory(equality)]) ).
cnf(34602,negated_conjecture,
join(X1,composition(esk1_0,X1)) = composition(one,X1),
inference(spm,[status(thm)],[870,45,theory(equality)]) ).
cnf(34810,negated_conjecture,
join(X1,composition(esk1_0,X1)) = X1,
inference(rw,[status(thm)],[34602,860,theory(equality)]) ).
cnf(35006,negated_conjecture,
join(X1,X2) = join(composition(esk1_0,X2),join(X1,X2)),
inference(spm,[status(thm)],[55,34810,theory(equality)]) ).
cnf(35093,negated_conjecture,
join(X1,X2) = join(X2,join(X1,composition(esk1_0,X2))),
inference(rw,[status(thm)],[35006,346,theory(equality)]) ).
cnf(40323,plain,
converse(composition(top,converse(X1))) = join(X1,converse(composition(complement(one),converse(X1)))),
inference(spm,[status(thm)],[66,34592,theory(equality)]) ).
cnf(40410,plain,
composition(X1,top) = join(X1,converse(composition(complement(one),converse(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[40323,63,theory(equality)]),1151,theory(equality)]) ).
cnf(40411,plain,
composition(X1,top) = join(X1,composition(X1,complement(one))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[40410,63,theory(equality)]),19152,theory(equality)]),829,theory(equality)]) ).
cnf(77023,negated_conjecture,
join(complement(one),composition(esk1_0,top)) = join(esk1_0,complement(one)),
inference(spm,[status(thm)],[35093,40411,theory(equality)]) ).
cnf(77384,negated_conjecture,
( complement(join(esk1_0,complement(one))) != complement(join(complement(one),composition(esk1_0,top)))
| join(complement(join(esk1_0,complement(one))),complement(join(complement(one),composition(esk1_0,top)))) != complement(join(esk1_0,complement(one))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[4520,77023,theory(equality)]),4502,theory(equality)]) ).
cnf(77385,negated_conjecture,
( $false
| join(complement(join(esk1_0,complement(one))),complement(join(complement(one),composition(esk1_0,top)))) != complement(join(esk1_0,complement(one))) ),
inference(rw,[status(thm)],[77384,77023,theory(equality)]) ).
cnf(77386,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[77385,77023,theory(equality)]),4502,theory(equality)]) ).
cnf(77387,negated_conjecture,
$false,
inference(cn,[status(thm)],[77386,theory(equality)]) ).
cnf(77388,negated_conjecture,
$false,
77387,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL027+2.p
% --creating new selector for [REL001+0.ax]
% eprover: CPU time limit exceeded, terminating
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpnFtilz/sel_REL027+2.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpnFtilz/sel_REL027+2.p_2 with time limit 80
% -prover status ResourceOut
% --creating new selector for [REL001+0.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpnFtilz/sel_REL027+2.p_3 with time limit 75
% -prover status ResourceOut
% --creating new selector for [REL001+0.ax]
% -running prover on /tmp/tmpnFtilz/sel_REL027+2.p_4 with time limit 55
% -prover status Theorem
% Problem REL027+2.p solved in phase 3.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL027+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL027+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
%
%------------------------------------------------------------------------------