TSTP Solution File: REL043+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL043+2 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 01:38:07 EST 2010
% Result : Theorem 95.97s
% Output : CNFRefutation 95.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 11
% Syntax : Number of formulae : 239 ( 234 unt; 0 def)
% Number of atoms : 244 ( 242 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 0 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 12 ( 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 : 388 ( 49 sgn 50 !; 6 ?)
% 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/tmpUSo8po/sel_REL043+2.p_2',modular_law_1) ).
fof(3,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/tmp/tmpUSo8po/sel_REL043+2.p_2',converse_multiplicativity) ).
fof(4,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmpUSo8po/sel_REL043+2.p_2',converse_idempotence) ).
fof(5,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/tmp/tmpUSo8po/sel_REL043+2.p_2',composition_distributivity) ).
fof(6,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpUSo8po/sel_REL043+2.p_2',converse_additivity) ).
fof(7,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpUSo8po/sel_REL043+2.p_2',maddux1_join_commutativity) ).
fof(10,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/tmp/tmpUSo8po/sel_REL043+2.p_2',converse_cancellativity) ).
fof(11,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmpUSo8po/sel_REL043+2.p_2',maddux4_definiton_of_meet) ).
fof(12,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmpUSo8po/sel_REL043+2.p_2',maddux2_join_associativity) ).
fof(13,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/tmp/tmpUSo8po/sel_REL043+2.p_2',maddux3_a_kind_of_de_Morgan) ).
fof(14,conjecture,
! [X1,X2,X3] :
( join(composition(X1,converse(X2)),X3) = X3
=> join(composition(complement(X3),X2),complement(X1)) = complement(X1) ),
file('/tmp/tmpUSo8po/sel_REL043+2.p_2',goals) ).
fof(15,negated_conjecture,
~ ! [X1,X2,X3] :
( join(composition(X1,converse(X2)),X3) = X3
=> join(composition(complement(X3),X2),complement(X1)) = complement(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,X2,X3] :
( join(composition(X1,converse(X2)),X3) = X3
& join(composition(complement(X3),X2),complement(X1)) != complement(X1) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(43,negated_conjecture,
? [X4,X5,X6] :
( join(composition(X4,converse(X5)),X6) = X6
& join(composition(complement(X6),X5),complement(X4)) != complement(X4) ),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,negated_conjecture,
( join(composition(esk1_0,converse(esk2_0)),esk3_0) = esk3_0
& join(composition(complement(esk3_0),esk2_0),complement(esk1_0)) != complement(esk1_0) ),
inference(skolemize,[status(esa)],[43]) ).
cnf(45,negated_conjecture,
join(composition(complement(esk3_0),esk2_0),complement(esk1_0)) != complement(esk1_0),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(46,negated_conjecture,
join(composition(esk1_0,converse(esk2_0)),esk3_0) = esk3_0,
inference(split_conjunct,[status(thm)],[44]) ).
cnf(47,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,negated_conjecture,
join(esk3_0,composition(esk1_0,converse(esk2_0))) = esk3_0,
inference(rw,[status(thm)],[46,29,theory(equality)]) ).
cnf(51,plain,
composition(X1,converse(X2)) = converse(composition(X2,converse(X1))),
inference(spm,[status(thm)],[21,23,theory(equality)]) ).
cnf(52,plain,
composition(converse(X1),X2) = converse(composition(converse(X2),X1)),
inference(spm,[status(thm)],[21,23,theory(equality)]) ).
cnf(53,plain,
join(X1,converse(X2)) = converse(join(converse(X1),X2)),
inference(spm,[status(thm)],[27,23,theory(equality)]) ).
cnf(63,negated_conjecture,
join(esk3_0,X1) = join(esk3_0,join(composition(esk1_0,converse(esk2_0)),X1)),
inference(spm,[status(thm)],[39,50,theory(equality)]) ).
cnf(66,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[29,39,theory(equality)]) ).
cnf(68,plain,
join(join(X2,X1),X3) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[39,29,theory(equality)]) ).
cnf(72,plain,
join(X2,join(X1,X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[68,39,theory(equality)]) ).
cnf(74,negated_conjecture,
join(complement(esk1_0),composition(complement(esk3_0),esk2_0)) != complement(esk1_0),
inference(rw,[status(thm)],[45,29,theory(equality)]) ).
cnf(76,plain,
join(composition(X1,converse(X2)),converse(composition(X2,X3))) = composition(join(X1,converse(X3)),converse(X2)),
inference(spm,[status(thm)],[25,21,theory(equality)]) ).
cnf(84,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(rw,[status(thm)],[35,29,theory(equality)]) ).
cnf(88,plain,
join(complement(X1),X3) = join(complement(X1),join(composition(converse(X2),complement(composition(X2,X1))),X3)),
inference(spm,[status(thm)],[39,84,theory(equality)]) ).
cnf(90,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[41,29,theory(equality)]) ).
cnf(91,plain,
join(X1,X3) = join(complement(join(complement(X1),X2)),join(complement(join(complement(X1),complement(X2))),X3)),
inference(spm,[status(thm)],[39,90,theory(equality)]) ).
cnf(92,plain,
join(complement(complement(X1)),complement(join(complement(X1),complement(composition(converse(X2),complement(composition(X2,X1))))))) = X1,
inference(spm,[status(thm)],[90,84,theory(equality)]) ).
cnf(93,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)],[90,90,theory(equality)]) ).
cnf(94,plain,
join(complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2)))),complement(X1)) = join(complement(X1),X2),
inference(spm,[status(thm)],[90,90,theory(equality)]) ).
cnf(95,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[90,29,theory(equality)]) ).
cnf(96,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[90,29,theory(equality)]) ).
cnf(99,plain,
join(complement(X1),complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2))))) = join(complement(X1),X2),
inference(rw,[status(thm)],[94,29,theory(equality)]) ).
cnf(100,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)],[47,29,theory(equality)]) ).
cnf(101,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)],[100,29,theory(equality)]) ).
cnf(107,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)],[39,101,theory(equality)]) ).
cnf(164,plain,
join(converse(X1),composition(X3,converse(X2))) = converse(join(X1,composition(X2,converse(X3)))),
inference(spm,[status(thm)],[27,51,theory(equality)]) ).
cnf(189,plain,
join(composition(converse(X2),X1),converse(X3)) = converse(join(composition(converse(X1),X2),X3)),
inference(spm,[status(thm)],[27,52,theory(equality)]) ).
cnf(282,negated_conjecture,
join(esk3_0,join(X1,composition(esk1_0,converse(esk2_0)))) = join(esk3_0,X1),
inference(spm,[status(thm)],[63,29,theory(equality)]) ).
cnf(345,plain,
join(X1,converse(join(X2,X3))) = join(converse(X3),join(X1,converse(X2))),
inference(spm,[status(thm)],[66,27,theory(equality)]) ).
cnf(358,plain,
join(complement(join(X2,join(X3,complement(X1)))),complement(join(complement(X1),complement(join(X2,X3))))) = X1,
inference(spm,[status(thm)],[90,66,theory(equality)]) ).
cnf(367,plain,
converse(join(X3,join(converse(X1),X2))) = join(X1,converse(join(X2,X3))),
inference(spm,[status(thm)],[53,66,theory(equality)]) ).
cnf(479,plain,
join(X1,X2) = join(complement(join(complement(X2),X3)),join(X1,complement(join(complement(X2),complement(X3))))),
inference(spm,[status(thm)],[72,90,theory(equality)]) ).
cnf(1342,plain,
join(X1,join(complement(X2),X4)) = join(join(composition(converse(X3),complement(composition(X3,X2))),X4),join(X1,complement(X2))),
inference(spm,[status(thm)],[66,88,theory(equality)]) ).
cnf(1366,plain,
join(X1,join(complement(X2),X4)) = join(composition(converse(X3),complement(composition(X3,X2))),join(X4,join(X1,complement(X2)))),
inference(rw,[status(thm)],[1342,39,theory(equality)]) ).
cnf(1382,plain,
join(complement(join(complement(X1),X2)),X1) = join(X1,complement(join(complement(X1),complement(complement(X2))))),
inference(spm,[status(thm)],[91,90,theory(equality)]) ).
cnf(1400,plain,
join(complement(join(complement(X1),X2)),join(X1,X3)) = join(X1,join(complement(join(complement(X1),complement(complement(X2)))),X3)),
inference(spm,[status(thm)],[91,91,theory(equality)]) ).
cnf(1434,plain,
join(X1,complement(join(complement(X1),X2))) = join(X1,complement(join(complement(X1),complement(complement(X2))))),
inference(rw,[status(thm)],[1382,29,theory(equality)]) ).
cnf(1448,plain,
join(X1,join(complement(join(complement(X1),X2)),X3)) = join(X1,join(complement(join(complement(X1),complement(complement(X2)))),X3)),
inference(rw,[status(thm)],[1400,72,theory(equality)]) ).
cnf(1473,plain,
join(complement(X1),join(complement(join(complement(complement(X1)),complement(complement(join(complement(X1),complement(composition(converse(X2),complement(composition(X2,X1))))))))),X3)) = join(complement(X1),X3),
inference(spm,[status(thm)],[91,92,theory(equality)]) ).
cnf(1745,negated_conjecture,
converse(esk3_0) = join(converse(esk3_0),composition(esk2_0,converse(esk1_0))),
inference(spm,[status(thm)],[164,50,theory(equality)]) ).
cnf(1833,negated_conjecture,
join(converse(esk3_0),X1) = join(converse(esk3_0),join(composition(esk2_0,converse(esk1_0)),X1)),
inference(spm,[status(thm)],[39,1745,theory(equality)]) ).
cnf(1854,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)],[99,66,theory(equality)]),29,theory(equality)]) ).
cnf(1955,plain,
converse(composition(join(converse(X1),converse(X3)),converse(X2))) = join(composition(converse(converse(X2)),X1),converse(converse(composition(X2,X3)))),
inference(spm,[status(thm)],[189,76,theory(equality)]) ).
cnf(2009,plain,
composition(X2,join(X1,X3)) = join(composition(converse(converse(X2)),X1),converse(converse(composition(X2,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1955,27,theory(equality)]),21,theory(equality)]),23,theory(equality)]) ).
cnf(2010,plain,
composition(X2,join(X1,X3)) = join(composition(X2,X1),composition(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2009,23,theory(equality)]),23,theory(equality)]) ).
cnf(2037,plain,
join(complement(X1),composition(converse(X2),join(complement(composition(X2,X1)),X3))) = join(complement(X1),composition(converse(X2),X3)),
inference(spm,[status(thm)],[88,2010,theory(equality)]) ).
cnf(2269,plain,
join(complement(join(X1,complement(X2))),complement(join(complement(X1),complement(X2)))) = X2,
inference(spm,[status(thm)],[95,29,theory(equality)]) ).
cnf(2314,negated_conjecture,
join(converse(esk3_0),converse(X1)) = join(composition(esk2_0,converse(esk1_0)),converse(join(X1,esk3_0))),
inference(spm,[status(thm)],[345,1833,theory(equality)]) ).
cnf(2342,negated_conjecture,
converse(join(esk3_0,X1)) = join(composition(esk2_0,converse(esk1_0)),converse(join(X1,esk3_0))),
inference(rw,[status(thm)],[2314,27,theory(equality)]) ).
cnf(3870,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),X3) = X3,
inference(spm,[status(thm)],[107,90,theory(equality)]) ).
cnf(3889,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),join(X3,X4)) = join(X3,X4),
inference(spm,[status(thm)],[107,91,theory(equality)]) ).
cnf(3945,plain,
join(X3,complement(join(complement(composition(X1,X2)),complement(X3)))) = X3,
inference(rw,[status(thm)],[3870,29,theory(equality)]) ).
cnf(3964,plain,
join(X3,join(complement(join(complement(composition(X1,X2)),complement(X3))),X4)) = join(X3,X4),
inference(rw,[status(thm)],[3889,72,theory(equality)]) ).
cnf(4039,plain,
join(X1,complement(join(complement(X1),complement(composition(X2,X3))))) = X1,
inference(spm,[status(thm)],[3945,29,theory(equality)]) ).
cnf(4043,plain,
join(X1,X2) = join(X2,join(X1,complement(join(complement(composition(X3,X4)),complement(X2))))),
inference(spm,[status(thm)],[72,3945,theory(equality)]) ).
cnf(26897,plain,
join(X1,X1) = join(X1,complement(join(complement(X1),complement(complement(composition(X2,X3)))))),
inference(spm,[status(thm)],[3964,95,theory(equality)]) ).
cnf(27058,plain,
join(X1,X1) = join(X1,complement(join(complement(X1),composition(X2,X3)))),
inference(rw,[status(thm)],[26897,1434,theory(equality)]) ).
cnf(27189,plain,
join(X1,complement(complement(X1))) = join(X1,X1),
inference(spm,[status(thm)],[27058,84,theory(equality)]) ).
cnf(27521,plain,
join(join(X1,X1),X2) = join(X1,join(complement(complement(X1)),X2)),
inference(spm,[status(thm)],[39,27189,theory(equality)]) ).
cnf(27544,plain,
join(complement(join(X1,X1)),complement(join(complement(complement(X1)),complement(X1)))) = complement(X1),
inference(spm,[status(thm)],[95,27189,theory(equality)]) ).
cnf(27641,plain,
join(X1,join(X2,X2)) = join(X2,join(X1,complement(complement(X2)))),
inference(spm,[status(thm)],[72,27189,theory(equality)]) ).
cnf(27646,plain,
join(X1,join(X1,X2)) = join(X1,join(complement(complement(X1)),X2)),
inference(rw,[status(thm)],[27521,39,theory(equality)]) ).
cnf(27665,plain,
join(complement(join(X1,X1)),complement(join(complement(X1),complement(complement(X1))))) = complement(X1),
inference(rw,[status(thm)],[27544,29,theory(equality)]) ).
cnf(28920,plain,
join(X1,join(X2,join(X2,X3))) = join(join(complement(complement(X2)),X3),join(X1,X2)),
inference(spm,[status(thm)],[66,27646,theory(equality)]) ).
cnf(29091,plain,
join(X1,join(X2,join(X2,X3))) = join(complement(complement(X2)),join(X3,join(X1,X2))),
inference(rw,[status(thm)],[28920,39,theory(equality)]) ).
cnf(29576,plain,
join(complement(join(complement(X1),complement(X2))),join(complement(join(complement(X1),X2)),complement(join(complement(X1),X2)))) = join(X1,complement(complement(complement(join(complement(X1),X2))))),
inference(spm,[status(thm)],[91,27641,theory(equality)]) ).
cnf(29676,plain,
join(X1,complement(join(complement(X1),X2))) = join(X1,complement(complement(complement(join(complement(X1),X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[29576,66,theory(equality)]),29,theory(equality)]),90,theory(equality)]),29,theory(equality)]) ).
cnf(31921,plain,
join(complement(join(complement(X1),X2)),X2) = join(complement(join(complement(X2),X1)),X1),
inference(spm,[status(thm)],[479,96,theory(equality)]) ).
cnf(31939,plain,
join(complement(join(complement(composition(X1,X2)),X3)),X3) = join(X3,composition(X1,X2)),
inference(spm,[status(thm)],[479,3945,theory(equality)]) ).
cnf(32181,plain,
join(X2,complement(join(complement(X1),X2))) = join(complement(join(complement(X2),X1)),X1),
inference(rw,[status(thm)],[31921,29,theory(equality)]) ).
cnf(32182,plain,
join(X2,complement(join(complement(X1),X2))) = join(X1,complement(join(complement(X2),X1))),
inference(rw,[status(thm)],[32181,29,theory(equality)]) ).
cnf(32199,plain,
join(X3,complement(join(complement(composition(X1,X2)),X3))) = join(X3,composition(X1,X2)),
inference(rw,[status(thm)],[31939,29,theory(equality)]) ).
cnf(35292,plain,
join(X1,complement(join(X1,complement(composition(X2,X3))))) = join(X1,composition(X2,X3)),
inference(spm,[status(thm)],[32199,29,theory(equality)]) ).
cnf(45421,plain,
join(complement(join(complement(X1),complement(X1))),complement(X1)) = join(complement(join(X1,X1)),X1),
inference(spm,[status(thm)],[479,27665,theory(equality)]) ).
cnf(45464,plain,
join(complement(X1),complement(join(complement(X1),complement(X1)))) = join(complement(join(X1,X1)),X1),
inference(rw,[status(thm)],[45421,29,theory(equality)]) ).
cnf(45465,plain,
join(complement(X1),complement(join(complement(X1),complement(X1)))) = join(X1,complement(join(X1,X1))),
inference(rw,[status(thm)],[45464,29,theory(equality)]) ).
cnf(82027,plain,
join(X1,join(complement(X1),composition(X2,X3))) = join(complement(X1),X1),
inference(spm,[status(thm)],[4043,32199,theory(equality)]) ).
cnf(82294,plain,
join(X1,join(complement(X1),composition(X2,X3))) = join(X1,complement(X1)),
inference(rw,[status(thm)],[82027,29,theory(equality)]) ).
cnf(84165,plain,
join(X1,complement(X1)) = join(composition(X2,X3),join(X1,complement(X1))),
inference(spm,[status(thm)],[66,82294,theory(equality)]) ).
cnf(124147,negated_conjecture,
join(esk3_0,join(X1,complement(join(complement(composition(esk1_0,converse(esk2_0))),X1)))) = join(esk3_0,complement(join(complement(X1),composition(esk1_0,converse(esk2_0))))),
inference(spm,[status(thm)],[63,32182,theory(equality)]) ).
cnf(125007,negated_conjecture,
join(esk3_0,X1) = join(esk3_0,complement(join(complement(X1),composition(esk1_0,converse(esk2_0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[124147,32199,theory(equality)]),282,theory(equality)]) ).
cnf(126121,negated_conjecture,
join(esk3_0,complement(join(composition(esk1_0,converse(esk2_0)),complement(X1)))) = join(esk3_0,X1),
inference(spm,[status(thm)],[125007,29,theory(equality)]) ).
cnf(126233,negated_conjecture,
join(esk3_0,complement(join(X1,complement(join(complement(composition(esk1_0,converse(esk2_0))),X1))))) = join(esk3_0,join(complement(X1),composition(esk1_0,converse(esk2_0)))),
inference(spm,[status(thm)],[126121,32182,theory(equality)]) ).
cnf(126292,negated_conjecture,
join(esk3_0,complement(join(X1,composition(esk1_0,converse(esk2_0))))) = join(esk3_0,join(complement(X1),composition(esk1_0,converse(esk2_0)))),
inference(rw,[status(thm)],[126233,32199,theory(equality)]) ).
cnf(126293,negated_conjecture,
join(esk3_0,complement(join(X1,composition(esk1_0,converse(esk2_0))))) = join(esk3_0,complement(X1)),
inference(rw,[status(thm)],[126292,282,theory(equality)]) ).
cnf(126768,negated_conjecture,
join(esk3_0,complement(complement(X1))) = join(esk3_0,X1),
inference(rw,[status(thm)],[125007,126293,theory(equality)]) ).
cnf(126816,negated_conjecture,
join(complement(join(esk3_0,X1)),complement(join(complement(complement(X1)),complement(esk3_0)))) = complement(X1),
inference(spm,[status(thm)],[95,126768,theory(equality)]) ).
cnf(126910,negated_conjecture,
join(complement(join(esk3_0,X1)),complement(join(complement(esk3_0),complement(complement(X1))))) = complement(X1),
inference(rw,[status(thm)],[126816,29,theory(equality)]) ).
cnf(131070,negated_conjecture,
join(complement(join(esk3_0,complement(esk3_0))),complement(join(complement(esk3_0),complement(esk3_0)))) = complement(complement(esk3_0)),
inference(spm,[status(thm)],[126910,27189,theory(equality)]) ).
cnf(131171,negated_conjecture,
join(complement(join(esk3_0,complement(join(complement(complement(esk3_0)),X1)))),complement(join(complement(esk3_0),complement(join(complement(complement(esk3_0)),X1))))) = complement(complement(join(complement(complement(esk3_0)),X1))),
inference(spm,[status(thm)],[126910,29676,theory(equality)]) ).
cnf(131312,negated_conjecture,
esk3_0 = complement(complement(esk3_0)),
inference(rw,[status(thm)],[131070,2269,theory(equality)]) ).
cnf(131339,negated_conjecture,
join(complement(complement(esk3_0)),X1) = complement(complement(join(complement(complement(esk3_0)),X1))),
inference(rw,[status(thm)],[131171,2269,theory(equality)]) ).
cnf(131373,negated_conjecture,
join(complement(join(esk3_0,X1)),complement(join(esk3_0,complement(X1)))) = complement(esk3_0),
inference(spm,[status(thm)],[90,131312,theory(equality)]) ).
cnf(132512,negated_conjecture,
complement(complement(join(esk3_0,X1))) = join(complement(complement(esk3_0)),X1),
inference(rw,[status(thm)],[131339,131312,theory(equality)]) ).
cnf(132513,negated_conjecture,
complement(complement(join(esk3_0,X1))) = join(esk3_0,X1),
inference(rw,[status(thm)],[132512,131312,theory(equality)]) ).
cnf(134841,negated_conjecture,
join(complement(esk3_0),complement(join(esk3_0,complement(composition(esk1_0,converse(esk2_0)))))) = complement(esk3_0),
inference(spm,[status(thm)],[131373,50,theory(equality)]) ).
cnf(137190,negated_conjecture,
join(complement(complement(esk3_0)),complement(join(complement(join(esk3_0,complement(composition(esk1_0,converse(esk2_0))))),complement(complement(esk3_0))))) = join(esk3_0,complement(composition(esk1_0,converse(esk2_0)))),
inference(spm,[status(thm)],[95,134841,theory(equality)]) ).
cnf(137245,negated_conjecture,
join(esk3_0,complement(esk3_0)) = join(esk3_0,complement(composition(esk1_0,converse(esk2_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[137190,131312,theory(equality)]),131312,theory(equality)]),29,theory(equality)]),35292,theory(equality)]),50,theory(equality)]) ).
cnf(137300,negated_conjecture,
join(esk3_0,complement(join(esk3_0,complement(esk3_0)))) = join(esk3_0,composition(esk1_0,converse(esk2_0))),
inference(spm,[status(thm)],[35292,137245,theory(equality)]) ).
cnf(137337,negated_conjecture,
join(complement(esk3_0),complement(join(esk3_0,complement(esk3_0)))) = complement(esk3_0),
inference(rw,[status(thm)],[134841,137245,theory(equality)]) ).
cnf(137351,negated_conjecture,
join(esk3_0,complement(join(esk3_0,complement(esk3_0)))) = esk3_0,
inference(rw,[status(thm)],[137300,50,theory(equality)]) ).
cnf(137384,negated_conjecture,
join(complement(esk3_0),X1) = join(complement(esk3_0),join(complement(join(esk3_0,complement(esk3_0))),X1)),
inference(spm,[status(thm)],[39,137337,theory(equality)]) ).
cnf(137762,negated_conjecture,
join(esk3_0,X1) = join(esk3_0,join(complement(join(esk3_0,complement(esk3_0))),X1)),
inference(spm,[status(thm)],[39,137351,theory(equality)]) ).
cnf(137801,negated_conjecture,
join(complement(esk3_0),complement(join(esk3_0,complement(complement(join(esk3_0,complement(esk3_0))))))) = complement(esk3_0),
inference(spm,[status(thm)],[131373,137351,theory(equality)]) ).
cnf(137849,negated_conjecture,
join(complement(esk3_0),complement(join(esk3_0,join(esk3_0,complement(esk3_0))))) = complement(esk3_0),
inference(rw,[status(thm)],[137801,126768,theory(equality)]) ).
cnf(138592,negated_conjecture,
join(esk3_0,esk3_0) = join(esk3_0,complement(join(complement(esk3_0),complement(esk3_0)))),
inference(spm,[status(thm)],[137762,95,theory(equality)]) ).
cnf(138768,negated_conjecture,
join(esk3_0,complement(esk3_0)) = join(esk3_0,complement(join(esk3_0,complement(complement(esk3_0))))),
inference(spm,[status(thm)],[137762,131373,theory(equality)]) ).
cnf(139079,negated_conjecture,
join(esk3_0,complement(esk3_0)) = join(esk3_0,complement(join(esk3_0,esk3_0))),
inference(rw,[status(thm)],[138768,27189,theory(equality)]) ).
cnf(139133,negated_conjecture,
join(complement(join(esk3_0,complement(esk3_0))),complement(join(esk3_0,complement(complement(join(esk3_0,esk3_0)))))) = complement(esk3_0),
inference(spm,[status(thm)],[131373,139079,theory(equality)]) ).
cnf(139184,negated_conjecture,
join(complement(join(esk3_0,complement(esk3_0))),complement(join(esk3_0,join(esk3_0,esk3_0)))) = complement(esk3_0),
inference(rw,[status(thm)],[139133,132513,theory(equality)]) ).
cnf(139194,negated_conjecture,
join(complement(join(esk3_0,esk3_0)),complement(join(complement(join(complement(esk3_0),complement(esk3_0))),complement(esk3_0)))) = join(complement(esk3_0),complement(esk3_0)),
inference(spm,[status(thm)],[95,138592,theory(equality)]) ).
cnf(139246,negated_conjecture,
complement(esk3_0) = join(complement(esk3_0),complement(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[139194,29,theory(equality)]),45465,theory(equality)]),139079,theory(equality)]),131373,theory(equality)]) ).
cnf(139293,negated_conjecture,
join(complement(esk3_0),X1) = join(complement(esk3_0),join(complement(esk3_0),X1)),
inference(spm,[status(thm)],[39,139246,theory(equality)]) ).
cnf(139316,negated_conjecture,
join(complement(join(X1,complement(esk3_0))),complement(join(complement(esk3_0),complement(join(X1,complement(esk3_0)))))) = esk3_0,
inference(spm,[status(thm)],[358,139246,theory(equality)]) ).
cnf(139346,negated_conjecture,
join(X1,complement(esk3_0)) = join(complement(esk3_0),join(X1,complement(esk3_0))),
inference(spm,[status(thm)],[66,139246,theory(equality)]) ).
cnf(139391,negated_conjecture,
join(esk3_0,complement(join(esk3_0,join(X1,complement(esk3_0))))) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[139316,32182,theory(equality)]),29,theory(equality)]),126768,theory(equality)]) ).
cnf(140413,negated_conjecture,
join(complement(join(complement(esk3_0),X1)),complement(join(complement(esk3_0),complement(join(complement(esk3_0),X1))))) = esk3_0,
inference(spm,[status(thm)],[90,139293,theory(equality)]) ).
cnf(140605,negated_conjecture,
join(esk3_0,complement(join(esk3_0,join(complement(esk3_0),X1)))) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[140413,32182,theory(equality)]),29,theory(equality)]),126768,theory(equality)]) ).
cnf(140931,negated_conjecture,
join(complement(esk3_0),complement(join(esk3_0,complement(complement(join(esk3_0,join(X1,complement(esk3_0)))))))) = complement(esk3_0),
inference(spm,[status(thm)],[131373,139391,theory(equality)]) ).
cnf(141016,negated_conjecture,
join(complement(esk3_0),complement(join(esk3_0,join(esk3_0,join(X1,complement(esk3_0)))))) = complement(esk3_0),
inference(rw,[status(thm)],[140931,132513,theory(equality)]) ).
cnf(165082,negated_conjecture,
join(complement(complement(esk3_0)),complement(join(complement(join(esk3_0,join(esk3_0,esk3_0))),complement(complement(join(esk3_0,complement(esk3_0))))))) = join(esk3_0,join(esk3_0,esk3_0)),
inference(spm,[status(thm)],[95,139184,theory(equality)]) ).
cnf(165153,negated_conjecture,
esk3_0 = join(esk3_0,join(esk3_0,esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[165082,131312,theory(equality)]),132513,theory(equality)]),66,theory(equality)]),29,theory(equality)]),72,theory(equality)]),140605,theory(equality)]) ).
cnf(165247,negated_conjecture,
join(complement(esk3_0),complement(join(complement(esk3_0),complement(complement(join(esk3_0,esk3_0)))))) = complement(join(esk3_0,esk3_0)),
inference(spm,[status(thm)],[126910,165153,theory(equality)]) ).
cnf(165326,negated_conjecture,
complement(esk3_0) = complement(join(esk3_0,esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[165247,132513,theory(equality)]),66,theory(equality)]),29,theory(equality)]),137849,theory(equality)]) ).
cnf(165355,negated_conjecture,
join(complement(join(complement(esk3_0),X1)),complement(join(complement(esk3_0),complement(X1)))) = join(esk3_0,esk3_0),
inference(spm,[status(thm)],[90,165326,theory(equality)]) ).
cnf(165621,negated_conjecture,
esk3_0 = join(esk3_0,esk3_0),
inference(rw,[status(thm)],[165355,90,theory(equality)]) ).
cnf(165855,negated_conjecture,
join(esk3_0,X1) = join(esk3_0,join(esk3_0,X1)),
inference(spm,[status(thm)],[39,165621,theory(equality)]) ).
cnf(226753,negated_conjecture,
join(complement(esk3_0),complement(join(esk3_0,join(X1,complement(esk3_0))))) = complement(esk3_0),
inference(rw,[status(thm)],[141016,165855,theory(equality)]) ).
cnf(226762,negated_conjecture,
join(complement(esk3_0),complement(join(complement(join(complement(esk3_0),join(esk3_0,join(X1,complement(esk3_0))))),complement(complement(complement(esk3_0)))))) = join(complement(esk3_0),join(esk3_0,join(X1,complement(esk3_0)))),
inference(spm,[status(thm)],[93,226753,theory(equality)]) ).
cnf(226880,negated_conjecture,
join(esk3_0,complement(esk3_0)) = join(complement(esk3_0),join(esk3_0,join(X1,complement(esk3_0)))),
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)],[226762,72,theory(equality)]),139346,theory(equality)]),131312,theory(equality)]),29,theory(equality)]),226753,theory(equality)]),131312,theory(equality)]),29,theory(equality)]) ).
cnf(226881,negated_conjecture,
join(esk3_0,complement(esk3_0)) = join(esk3_0,join(X1,complement(esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[226880,72,theory(equality)]),139346,theory(equality)]) ).
cnf(226996,negated_conjecture,
converse(join(esk3_0,complement(esk3_0))) = join(X1,converse(join(complement(esk3_0),esk3_0))),
inference(spm,[status(thm)],[367,226881,theory(equality)]) ).
cnf(227017,negated_conjecture,
join(complement(complement(complement(esk3_0))),join(esk3_0,complement(esk3_0))) = join(X1,join(complement(esk3_0),join(complement(esk3_0),esk3_0))),
inference(spm,[status(thm)],[29091,226881,theory(equality)]) ).
cnf(227089,negated_conjecture,
join(esk3_0,join(complement(esk3_0),X1)) = join(esk3_0,complement(esk3_0)),
inference(spm,[status(thm)],[226881,29,theory(equality)]) ).
cnf(227108,negated_conjecture,
converse(join(esk3_0,complement(esk3_0))) = join(X1,converse(join(esk3_0,complement(esk3_0)))),
inference(rw,[status(thm)],[226996,29,theory(equality)]) ).
cnf(227134,negated_conjecture,
join(esk3_0,complement(esk3_0)) = join(X1,join(complement(esk3_0),join(complement(esk3_0),esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[227017,66,theory(equality)]),29,theory(equality)]),126768,theory(equality)]),72,theory(equality)]),139246,theory(equality)]) ).
cnf(227135,negated_conjecture,
join(esk3_0,complement(esk3_0)) = join(X1,join(esk3_0,complement(esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[227134,29,theory(equality)]),72,theory(equality)]),139246,theory(equality)]) ).
cnf(237642,negated_conjecture,
join(esk3_0,converse(join(esk3_0,complement(esk3_0)))) = join(esk3_0,complement(esk3_0)),
inference(spm,[status(thm)],[227089,227108,theory(equality)]) ).
cnf(237974,negated_conjecture,
converse(join(esk3_0,complement(esk3_0))) = join(esk3_0,complement(esk3_0)),
inference(rw,[status(thm)],[237642,227108,theory(equality)]) ).
cnf(274009,plain,
join(complement(X1),join(complement(join(complement(X1),join(complement(complement(X1)),complement(composition(converse(X2),complement(composition(X2,X1))))))),X3)) = join(complement(X1),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1473,1448,theory(equality)]),72,theory(equality)]) ).
cnf(274016,plain,
join(complement(X1),X1) = join(complement(X1),complement(join(complement(X1),complement(join(complement(complement(X1)),complement(composition(converse(X2),complement(composition(X2,X1))))))))),
inference(spm,[status(thm)],[274009,90,theory(equality)]) ).
cnf(274465,plain,
join(X1,complement(X1)) = join(complement(X1),complement(join(complement(X1),complement(join(complement(complement(X1)),complement(composition(converse(X2),complement(composition(X2,X1))))))))),
inference(rw,[status(thm)],[274016,29,theory(equality)]) ).
cnf(274466,plain,
join(X1,complement(X1)) = join(complement(X1),complement(complement(X1))),
inference(rw,[status(thm)],[274465,4039,theory(equality)]) ).
cnf(275183,plain,
join(complement(join(X1,X1)),complement(join(X1,complement(X1)))) = complement(X1),
inference(rw,[status(thm)],[27665,274466,theory(equality)]) ).
cnf(275392,plain,
complement(complement(X1)) = X1,
inference(spm,[status(thm)],[90,275183,theory(equality)]) ).
cnf(276080,negated_conjecture,
join(complement(join(esk3_0,X1)),complement(join(complement(esk3_0),X1))) = complement(X1),
inference(rw,[status(thm)],[126910,275392,theory(equality)]) ).
cnf(279640,negated_conjecture,
join(complement(join(esk3_0,X1)),complement(join(complement(esk3_0),join(complement(join(esk3_0,complement(esk3_0))),X1)))) = complement(join(complement(join(esk3_0,complement(esk3_0))),X1)),
inference(spm,[status(thm)],[276080,137762,theory(equality)]) ).
cnf(279980,negated_conjecture,
complement(X1) = complement(join(complement(join(esk3_0,complement(esk3_0))),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[279640,137384,theory(equality)]),276080,theory(equality)]) ).
cnf(284542,negated_conjecture,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = join(complement(join(esk3_0,complement(esk3_0))),X1),
inference(spm,[status(thm)],[90,279980,theory(equality)]) ).
cnf(285142,negated_conjecture,
X1 = join(complement(join(esk3_0,complement(esk3_0))),X1),
inference(rw,[status(thm)],[284542,90,theory(equality)]) ).
cnf(285749,negated_conjecture,
join(complement(X1),complement(join(complement(join(esk3_0,complement(esk3_0))),complement(X1)))) = join(esk3_0,complement(esk3_0)),
inference(spm,[status(thm)],[90,285142,theory(equality)]) ).
cnf(285770,negated_conjecture,
join(complement(join(esk3_0,complement(esk3_0))),complement(join(complement(X1),join(complement(join(esk3_0,complement(esk3_0))),complement(X1))))) = X1,
inference(spm,[status(thm)],[1854,285142,theory(equality)]) ).
cnf(285775,negated_conjecture,
join(complement(complement(X1)),complement(join(complement(X1),complement(complement(join(esk3_0,complement(esk3_0))))))) = X1,
inference(spm,[status(thm)],[95,285142,theory(equality)]) ).
cnf(286303,negated_conjecture,
join(X1,complement(X1)) = join(esk3_0,complement(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[285749,279980,theory(equality)]),275392,theory(equality)]),29,theory(equality)]) ).
cnf(286333,negated_conjecture,
complement(join(complement(X1),complement(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[285770,285142,theory(equality)]),285142,theory(equality)]) ).
cnf(286341,negated_conjecture,
join(X1,complement(join(esk3_0,complement(esk3_0)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[285775,275392,theory(equality)]),132513,theory(equality)]),72,theory(equality)]),226881,theory(equality)]) ).
cnf(287493,negated_conjecture,
complement(join(X1,X1)) = complement(X1),
inference(spm,[status(thm)],[286333,275392,theory(equality)]) ).
cnf(287991,negated_conjecture,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = join(X1,X1),
inference(spm,[status(thm)],[90,287493,theory(equality)]) ).
cnf(288543,negated_conjecture,
X1 = join(X1,X1),
inference(rw,[status(thm)],[287991,90,theory(equality)]) ).
cnf(289079,negated_conjecture,
join(X1,X2) = join(X1,join(X1,X2)),
inference(spm,[status(thm)],[39,288543,theory(equality)]) ).
cnf(290780,negated_conjecture,
join(complement(join(complement(X1),X2)),X1) = X1,
inference(spm,[status(thm)],[289079,90,theory(equality)]) ).
cnf(290821,negated_conjecture,
join(complement(join(X1,complement(X2))),X2) = X2,
inference(spm,[status(thm)],[289079,95,theory(equality)]) ).
cnf(291429,negated_conjecture,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[290780,29,theory(equality)]) ).
cnf(291480,negated_conjecture,
join(X2,complement(join(X1,complement(X2)))) = X2,
inference(rw,[status(thm)],[290821,29,theory(equality)]) ).
cnf(298196,negated_conjecture,
converse(join(esk3_0,complement(esk3_0))) = join(X1,converse(complement(converse(X1)))),
inference(spm,[status(thm)],[53,286303,theory(equality)]) ).
cnf(298546,negated_conjecture,
join(complement(join(X2,complement(X2))),X1) = X1,
inference(spm,[status(thm)],[285142,286303,theory(equality)]) ).
cnf(298554,negated_conjecture,
join(X1,complement(join(X2,complement(X2)))) = X1,
inference(spm,[status(thm)],[286341,286303,theory(equality)]) ).
cnf(298578,negated_conjecture,
join(X1,complement(X1)) = join(X2,complement(X2)),
inference(spm,[status(thm)],[286303,286303,theory(equality)]) ).
cnf(298589,negated_conjecture,
join(esk3_0,complement(esk3_0)) = join(X1,converse(complement(converse(X1)))),
inference(rw,[status(thm)],[298196,237974,theory(equality)]) ).
cnf(303417,negated_conjecture,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(spm,[status(thm)],[291429,275392,theory(equality)]) ).
cnf(304221,negated_conjecture,
join(complement(join(complement(X1),X2)),X2) = join(X2,X1),
inference(spm,[status(thm)],[479,291480,theory(equality)]) ).
cnf(304416,negated_conjecture,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[291480,275392,theory(equality)]) ).
cnf(304662,negated_conjecture,
join(X2,complement(join(complement(X1),X2))) = join(X2,X1),
inference(rw,[status(thm)],[304221,29,theory(equality)]) ).
cnf(315887,negated_conjecture,
join(X1,join(X2,complement(X2))) = join(X2,complement(X2)),
inference(spm,[status(thm)],[227135,298578,theory(equality)]) ).
cnf(324233,negated_conjecture,
join(complement(composition(esk2_0,converse(esk1_0))),complement(converse(join(esk3_0,X1)))) = complement(composition(esk2_0,converse(esk1_0))),
inference(spm,[status(thm)],[303417,2342,theory(equality)]) ).
cnf(335689,negated_conjecture,
join(composition(converse(X1),complement(composition(X1,X2))),join(X2,complement(X2))) = join(X2,join(complement(X2),X3)),
inference(spm,[status(thm)],[1366,315887,theory(equality)]) ).
cnf(336037,negated_conjecture,
join(X2,complement(X2)) = join(X2,join(complement(X2),X3)),
inference(rw,[status(thm)],[335689,84165,theory(equality)]) ).
cnf(338685,negated_conjecture,
join(complement(join(X1,join(join(complement(X1),X2),complement(X3)))),complement(join(complement(X3),complement(join(X1,complement(X1)))))) = X3,
inference(spm,[status(thm)],[358,336037,theory(equality)]) ).
cnf(339241,negated_conjecture,
complement(complement(X3)) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[338685,39,theory(equality)]),336037,theory(equality)]),298554,theory(equality)]),298546,theory(equality)]) ).
cnf(345579,negated_conjecture,
join(complement(join(X1,X2)),complement(join(complement(join(complement(X2),X1)),complement(X1)))) = join(complement(X2),X1),
inference(spm,[status(thm)],[95,304662,theory(equality)]) ).
cnf(346148,negated_conjecture,
join(X1,complement(join(X1,X2))) = join(complement(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[345579,29,theory(equality)]),304416,theory(equality)]),275392,theory(equality)]),29,theory(equality)]) ).
cnf(348769,negated_conjecture,
join(X1,complement(join(esk3_0,complement(esk3_0)))) = join(complement(converse(complement(converse(X1)))),X1),
inference(spm,[status(thm)],[346148,298589,theory(equality)]) ).
cnf(349478,negated_conjecture,
X1 = join(complement(converse(complement(converse(X1)))),X1),
inference(rw,[status(thm)],[348769,298554,theory(equality)]) ).
cnf(349479,negated_conjecture,
X1 = join(X1,complement(converse(complement(converse(X1))))),
inference(rw,[status(thm)],[349478,29,theory(equality)]) ).
cnf(349599,negated_conjecture,
converse(converse(X1)) = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(spm,[status(thm)],[53,349479,theory(equality)]) ).
cnf(349947,negated_conjecture,
X1 = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(rw,[status(thm)],[349599,23,theory(equality)]) ).
cnf(349948,negated_conjecture,
X1 = join(X1,converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[349947,23,theory(equality)]) ).
cnf(351938,negated_conjecture,
join(complement(converse(complement(converse(complement(X1))))),complement(X1)) = complement(converse(complement(converse(complement(X1))))),
inference(spm,[status(thm)],[304416,349948,theory(equality)]) ).
cnf(352250,negated_conjecture,
complement(X1) = complement(converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[351938,29,theory(equality)]),349479,theory(equality)]) ).
cnf(355120,negated_conjecture,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = converse(complement(converse(complement(X1)))),
inference(spm,[status(thm)],[90,352250,theory(equality)]) ).
cnf(355425,negated_conjecture,
X1 = converse(complement(converse(complement(X1)))),
inference(rw,[status(thm)],[355120,90,theory(equality)]) ).
cnf(355691,negated_conjecture,
converse(X1) = complement(converse(complement(X1))),
inference(spm,[status(thm)],[23,355425,theory(equality)]) ).
cnf(356365,negated_conjecture,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[339241,355691,theory(equality)]) ).
cnf(356640,negated_conjecture,
composition(converse(X1),complement(converse(X2))) = converse(composition(complement(X2),X1)),
inference(spm,[status(thm)],[21,356365,theory(equality)]) ).
cnf(356641,negated_conjecture,
join(complement(converse(X1)),converse(X2)) = converse(join(complement(X1),X2)),
inference(spm,[status(thm)],[27,356365,theory(equality)]) ).
cnf(931179,negated_conjecture,
join(complement(converse(esk1_0)),composition(converse(esk2_0),complement(composition(esk2_0,converse(esk1_0))))) = join(complement(converse(esk1_0)),composition(converse(esk2_0),complement(converse(join(esk3_0,X1))))),
inference(spm,[status(thm)],[2037,324233,theory(equality)]) ).
cnf(931544,negated_conjecture,
complement(converse(esk1_0)) = join(complement(converse(esk1_0)),composition(converse(esk2_0),complement(converse(join(esk3_0,X1))))),
inference(rw,[status(thm)],[931179,84,theory(equality)]) ).
cnf(931545,negated_conjecture,
complement(converse(esk1_0)) = converse(join(complement(esk1_0),composition(complement(join(esk3_0,X1)),esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[931544,356640,theory(equality)]),356641,theory(equality)]) ).
cnf(931692,negated_conjecture,
converse(join(complement(esk1_0),composition(complement(esk3_0),esk2_0))) = complement(converse(esk1_0)),
inference(spm,[status(thm)],[931545,50,theory(equality)]) ).
cnf(933673,negated_conjecture,
converse(complement(converse(esk1_0))) = join(complement(esk1_0),composition(complement(esk3_0),esk2_0)),
inference(spm,[status(thm)],[23,931692,theory(equality)]) ).
cnf(934744,negated_conjecture,
complement(esk1_0) = join(complement(esk1_0),composition(complement(esk3_0),esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[933673,356365,theory(equality)]),23,theory(equality)]) ).
cnf(934745,negated_conjecture,
$false,
inference(sr,[status(thm)],[934744,74,theory(equality)]) ).
cnf(934746,negated_conjecture,
$false,
934745,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL043+2.p
% --creating new selector for [REL001+0.ax, REL001+1.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpUSo8po/sel_REL043+2.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpUSo8po/sel_REL043+2.p_2 with time limit 81
% -prover status Theorem
% Problem REL043+2.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL043+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL043+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
%
%------------------------------------------------------------------------------