TSTP Solution File: REL005+4 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL005+4 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 01:05:02 EST 2010
% Result : Theorem 11.37s
% Output : CNFRefutation 11.37s
% Verified :
% SZS Type : None (Could not find formula named 1185ry(equality))
% Syntax : Number of formulae : 144
% 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/tmpGCKNve/sel_REL005+4.p_1',modular_law_1) ).
fof(4,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmpGCKNve/sel_REL005+4.p_1',converse_idempotence) ).
fof(6,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpGCKNve/sel_REL005+4.p_1',converse_additivity) ).
fof(7,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpGCKNve/sel_REL005+4.p_1',maddux1_join_commutativity) ).
fof(10,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/tmp/tmpGCKNve/sel_REL005+4.p_1',converse_cancellativity) ).
fof(11,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmpGCKNve/sel_REL005+4.p_1',maddux4_definiton_of_meet) ).
fof(12,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmpGCKNve/sel_REL005+4.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/tmpGCKNve/sel_REL005+4.p_1',maddux3_a_kind_of_de_Morgan) ).
fof(14,conjecture,
! [X1,X2] :
( join(converse(meet(X1,X2)),meet(converse(X1),converse(X2))) = meet(converse(X1),converse(X2))
& join(meet(converse(X1),converse(X2)),converse(meet(X1,X2))) = converse(meet(X1,X2)) ),
file('/tmp/tmpGCKNve/sel_REL005+4.p_1',goals) ).
fof(15,negated_conjecture,
~ ! [X1,X2] :
( join(converse(meet(X1,X2)),meet(converse(X1),converse(X2))) = meet(converse(X1),converse(X2))
& join(meet(converse(X1),converse(X2)),converse(meet(X1,X2))) = converse(meet(X1,X2)) ),
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(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(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] :
( join(converse(meet(X1,X2)),meet(converse(X1),converse(X2))) != meet(converse(X1),converse(X2))
| join(meet(converse(X1),converse(X2)),converse(meet(X1,X2))) != converse(meet(X1,X2)) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(43,negated_conjecture,
? [X3,X4] :
( join(converse(meet(X3,X4)),meet(converse(X3),converse(X4))) != meet(converse(X3),converse(X4))
| join(meet(converse(X3),converse(X4)),converse(meet(X3,X4))) != converse(meet(X3,X4)) ),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,negated_conjecture,
( join(converse(meet(esk1_0,esk2_0)),meet(converse(esk1_0),converse(esk2_0))) != meet(converse(esk1_0),converse(esk2_0))
| join(meet(converse(esk1_0),converse(esk2_0)),converse(meet(esk1_0,esk2_0))) != converse(meet(esk1_0,esk2_0)) ),
inference(skolemize,[status(esa)],[43]) ).
cnf(45,negated_conjecture,
( join(meet(converse(esk1_0),converse(esk2_0)),converse(meet(esk1_0,esk2_0))) != converse(meet(esk1_0,esk2_0))
| join(converse(meet(esk1_0,esk2_0)),meet(converse(esk1_0),converse(esk2_0))) != meet(converse(esk1_0),converse(esk2_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(49,negated_conjecture,
( join(complement(join(complement(converse(esk1_0)),complement(converse(esk2_0)))),converse(complement(join(complement(esk1_0),complement(esk2_0))))) != converse(complement(join(complement(esk1_0),complement(esk2_0))))
| join(converse(complement(join(complement(esk1_0),complement(esk2_0)))),complement(join(complement(converse(esk1_0)),complement(converse(esk2_0))))) != complement(join(complement(converse(esk1_0)),complement(converse(esk2_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)],[45,37,theory(equality)]),37,theory(equality)]),37,theory(equality)]),37,theory(equality)]),37,theory(equality)]),37,theory(equality)]),
[unfolding] ).
cnf(50,plain,
join(X1,converse(X2)) = converse(join(converse(X1),X2)),
inference(spm,[status(thm)],[27,23,theory(equality)]) ).
cnf(58,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[29,39,theory(equality)]) ).
cnf(60,plain,
join(join(X2,X1),X3) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[39,29,theory(equality)]) ).
cnf(64,plain,
join(X2,join(X1,X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[60,39,theory(equality)]) ).
cnf(66,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[41,29,theory(equality)]) ).
cnf(67,plain,
join(X1,X3) = join(complement(join(complement(X1),X2)),join(complement(join(complement(X1),complement(X2))),X3)),
inference(spm,[status(thm)],[39,66,theory(equality)]) ).
cnf(69,plain,
join(complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2)))),complement(X1)) = join(complement(X1),X2),
inference(spm,[status(thm)],[66,66,theory(equality)]) ).
cnf(70,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[66,29,theory(equality)]) ).
cnf(71,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[66,29,theory(equality)]) ).
cnf(74,plain,
join(complement(X1),complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2))))) = join(complement(X1),X2),
inference(rw,[status(thm)],[69,29,theory(equality)]) ).
cnf(77,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(rw,[status(thm)],[35,29,theory(equality)]) ).
cnf(80,plain,
join(complement(complement(X1)),complement(join(complement(X1),complement(composition(converse(X2),complement(composition(X2,X1))))))) = X1,
inference(spm,[status(thm)],[66,77,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(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3))),
inference(rw,[status(thm)],[46,29,theory(equality)]) ).
cnf(98,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)],[97,29,theory(equality)]) ).
cnf(100,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)],[39,98,theory(equality)]) ).
cnf(134,negated_conjecture,
( join(converse(complement(join(complement(esk1_0),complement(esk2_0)))),complement(join(complement(converse(esk1_0)),complement(converse(esk2_0))))) != converse(complement(join(complement(esk1_0),complement(esk2_0))))
| join(converse(complement(join(complement(esk1_0),complement(esk2_0)))),complement(join(complement(converse(esk1_0)),complement(converse(esk2_0))))) != complement(join(complement(converse(esk1_0)),complement(converse(esk2_0)))) ),
inference(rw,[status(thm)],[49,29,theory(equality)]) ).
cnf(252,plain,
join(complement(join(X3,join(complement(X1),X2))),complement(join(complement(X1),complement(join(X2,X3))))) = X1,
inference(spm,[status(thm)],[66,58,theory(equality)]) ).
cnf(351,plain,
join(complement(join(X2,join(complement(X1),X3))),complement(join(complement(X1),complement(join(X2,X3))))) = X1,
inference(spm,[status(thm)],[66,64,theory(equality)]) ).
cnf(353,plain,
join(X1,X2) = join(complement(join(complement(X2),X3)),join(X1,complement(join(complement(X2),complement(X3))))),
inference(spm,[status(thm)],[64,66,theory(equality)]) ).
cnf(578,plain,
join(complement(join(complement(X1),X2)),X1) = join(X1,complement(join(complement(X1),complement(complement(X2))))),
inference(spm,[status(thm)],[67,66,theory(equality)]) ).
cnf(592,plain,
join(complement(join(X2,complement(X1))),join(complement(join(complement(X1),complement(X2))),X3)) = join(X1,X3),
inference(spm,[status(thm)],[67,29,theory(equality)]) ).
cnf(616,plain,
join(X1,complement(join(complement(X1),X2))) = join(X1,complement(join(complement(X1),complement(complement(X2))))),
inference(rw,[status(thm)],[578,29,theory(equality)]) ).
cnf(819,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)],[74,58,theory(equality)]),29,theory(equality)]) ).
cnf(994,plain,
join(complement(join(complement(X1),X2)),X2) = join(X1,complement(join(complement(X2),complement(complement(X1))))),
inference(spm,[status(thm)],[67,70,theory(equality)]) ).
cnf(1005,plain,
join(complement(join(X1,complement(X2))),complement(join(complement(X1),complement(X2)))) = X2,
inference(spm,[status(thm)],[70,29,theory(equality)]) ).
cnf(1024,plain,
join(X2,complement(join(complement(X1),X2))) = join(X1,complement(join(complement(X2),complement(complement(X1))))),
inference(rw,[status(thm)],[994,29,theory(equality)]) ).
cnf(1233,plain,
join(complement(join(complement(X1),X2)),X2) = join(X1,complement(join(complement(complement(X1)),complement(X2)))),
inference(spm,[status(thm)],[67,1005,theory(equality)]) ).
cnf(1268,plain,
join(X2,complement(join(complement(X1),X2))) = join(X1,complement(join(complement(complement(X1)),complement(X2)))),
inference(rw,[status(thm)],[1233,29,theory(equality)]) ).
cnf(3630,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),X3) = X3,
inference(spm,[status(thm)],[100,66,theory(equality)]) ).
cnf(3647,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),join(X3,X4)) = join(X3,X4),
inference(spm,[status(thm)],[100,67,theory(equality)]) ).
cnf(3712,plain,
join(X3,complement(join(complement(composition(X1,X2)),complement(X3)))) = X3,
inference(rw,[status(thm)],[3630,29,theory(equality)]) ).
cnf(3730,plain,
join(X3,join(complement(join(complement(composition(X1,X2)),complement(X3))),X4)) = join(X3,X4),
inference(rw,[status(thm)],[3647,64,theory(equality)]) ).
cnf(3820,plain,
join(X1,X2) = join(X2,join(X1,complement(join(complement(composition(X3,X4)),complement(X2))))),
inference(spm,[status(thm)],[64,3712,theory(equality)]) ).
cnf(9144,plain,
join(X1,X1) = join(X1,complement(join(complement(X1),complement(complement(composition(X2,X3)))))),
inference(spm,[status(thm)],[3730,70,theory(equality)]) ).
cnf(9250,plain,
join(X1,X1) = join(X1,complement(join(complement(X1),composition(X2,X3)))),
inference(rw,[status(thm)],[9144,616,theory(equality)]) ).
cnf(9492,plain,
join(X1,complement(complement(X1))) = join(X1,X1),
inference(spm,[status(thm)],[9250,77,theory(equality)]) ).
cnf(9642,plain,
join(complement(join(X1,X1)),complement(join(complement(complement(X1)),complement(X1)))) = complement(X1),
inference(spm,[status(thm)],[70,9492,theory(equality)]) ).
cnf(9702,plain,
join(complement(join(X1,X1)),complement(join(complement(X1),complement(complement(X1))))) = complement(X1),
inference(rw,[status(thm)],[9642,29,theory(equality)]) ).
cnf(38446,plain,
join(complement(join(complement(X1),X2)),X2) = join(complement(join(complement(X2),X1)),X1),
inference(spm,[status(thm)],[353,71,theory(equality)]) ).
cnf(38473,plain,
join(complement(join(complement(composition(X1,X2)),X3)),X3) = join(X3,composition(X1,X2)),
inference(spm,[status(thm)],[353,3712,theory(equality)]) ).
cnf(38763,plain,
join(X2,complement(join(complement(X1),X2))) = join(complement(join(complement(X2),X1)),X1),
inference(rw,[status(thm)],[38446,29,theory(equality)]) ).
cnf(38764,plain,
join(X2,complement(join(complement(X1),X2))) = join(X1,complement(join(complement(X2),X1))),
inference(rw,[status(thm)],[38763,29,theory(equality)]) ).
cnf(38786,plain,
join(X3,complement(join(complement(composition(X1,X2)),X3))) = join(X3,composition(X1,X2)),
inference(rw,[status(thm)],[38473,29,theory(equality)]) ).
cnf(41628,plain,
join(X2,complement(join(complement(X1),X2))) = join(X2,complement(join(complement(X1),complement(complement(X2))))),
inference(spm,[status(thm)],[1024,38764,theory(equality)]) ).
cnf(44752,plain,
join(X1,complement(join(X1,complement(composition(X2,X3))))) = join(X1,composition(X2,X3)),
inference(spm,[status(thm)],[38786,29,theory(equality)]) ).
cnf(47212,plain,
join(complement(X1),join(X1,complement(join(complement(composition(X2,X3)),X1)))) = join(X1,complement(X1)),
inference(spm,[status(thm)],[3820,41628,theory(equality)]) ).
cnf(47425,plain,
join(X1,join(complement(X1),composition(X2,X3))) = join(X1,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[47212,38786,theory(equality)]),64,theory(equality)]) ).
cnf(47868,plain,
join(X1,join(composition(X2,X3),complement(X1))) = join(X1,complement(X1)),
inference(spm,[status(thm)],[47425,29,theory(equality)]) ).
cnf(47871,plain,
join(X1,complement(X1)) = join(composition(X2,X3),join(X1,complement(X1))),
inference(spm,[status(thm)],[58,47425,theory(equality)]) ).
cnf(48129,plain,
join(X1,join(X2,complement(X2))) = join(join(composition(X3,X4),complement(X2)),join(X1,X2)),
inference(spm,[status(thm)],[58,47868,theory(equality)]) ).
cnf(48278,plain,
join(X1,join(X2,complement(X2))) = join(composition(X3,X4),join(X2,join(complement(X2),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[48129,39,theory(equality)]),58,theory(equality)]) ).
cnf(105993,plain,
join(composition(X1,X2),join(complement(X3),X3)) = join(complement(join(complement(X3),complement(composition(converse(X4),complement(composition(X4,X3)))))),join(complement(X3),complement(complement(X3)))),
inference(spm,[status(thm)],[48278,80,theory(equality)]) ).
cnf(106409,plain,
join(X3,complement(X3)) = join(complement(join(complement(X3),complement(composition(converse(X4),complement(composition(X4,X3)))))),join(complement(X3),complement(complement(X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[105993,29,theory(equality)]),47871,theory(equality)]) ).
cnf(106410,plain,
join(X3,complement(X3)) = join(complement(X3),complement(complement(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[106409,58,theory(equality)]),29,theory(equality)]),44752,theory(equality)]),77,theory(equality)]),29,theory(equality)]) ).
cnf(107242,plain,
join(complement(join(X1,X1)),complement(join(X1,complement(X1)))) = complement(X1),
inference(rw,[status(thm)],[9702,106410,theory(equality)]) ).
cnf(107423,plain,
complement(complement(X1)) = X1,
inference(spm,[status(thm)],[66,107242,theory(equality)]) ).
cnf(107726,plain,
join(complement(join(X1,X2)),complement(join(X1,complement(X2)))) = complement(X1),
inference(spm,[status(thm)],[66,107423,theory(equality)]) ).
cnf(107740,plain,
join(complement(join(X1,X2)),complement(join(X2,complement(X1)))) = complement(X2),
inference(spm,[status(thm)],[70,107423,theory(equality)]) ).
cnf(107742,plain,
join(complement(join(X1,X2)),complement(join(complement(X2),X1))) = complement(X1),
inference(spm,[status(thm)],[71,107423,theory(equality)]) ).
cnf(108566,plain,
join(complement(converse(join(X1,X2))),complement(join(converse(X1),complement(converse(X2))))) = complement(converse(X1)),
inference(spm,[status(thm)],[107726,27,theory(equality)]) ).
cnf(110067,plain,
join(complement(converse(join(X1,X2))),complement(join(complement(converse(X2)),converse(X1)))) = complement(converse(X1)),
inference(spm,[status(thm)],[107742,27,theory(equality)]) ).
cnf(110116,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)],[107742,3712,theory(equality)]) ).
cnf(110543,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)],[110116,29,theory(equality)]),41628,theory(equality)]),38786,theory(equality)]),107423,theory(equality)]),29,theory(equality)]) ).
cnf(110544,plain,
join(X3,complement(join(X3,composition(X1,X2)))) = join(complement(composition(X1,X2)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[110543,107423,theory(equality)]),107423,theory(equality)]) ).
cnf(118388,plain,
join(complement(join(complement(X1),composition(X2,X3))),complement(join(complement(composition(X2,X3)),complement(X1)))) = join(X1,complement(join(complement(complement(join(complement(X1),composition(X2,X3)))),X1))),
inference(spm,[status(thm)],[38764,110544,theory(equality)]) ).
cnf(118580,plain,
X1 = join(X1,complement(join(complement(complement(join(complement(X1),composition(X2,X3)))),X1))),
inference(rw,[status(thm)],[118388,71,theory(equality)]) ).
cnf(118581,plain,
X1 = join(X1,complement(join(X1,complement(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[118580,107423,theory(equality)]),39,theory(equality)]),58,theory(equality)]),47425,theory(equality)]) ).
cnf(118604,plain,
join(complement(X1),complement(join(complement(complement(complement(X1))),complement(X1)))) = join(complement(X1),complement(complement(X1))),
inference(spm,[status(thm)],[819,118581,theory(equality)]) ).
cnf(118764,plain,
join(complement(X1),complement(join(complement(X1),X1))) = complement(X1),
inference(spm,[status(thm)],[118581,107423,theory(equality)]) ).
cnf(118790,plain,
join(complement(join(complement(X1),complement(complement(X1)))),complement(complement(X1))) = join(X1,complement(join(complement(complement(join(complement(X1),complement(complement(X1))))),X1))),
inference(spm,[status(thm)],[38764,118581,theory(equality)]) ).
cnf(118810,plain,
join(X1,complement(join(X1,X1))) = join(complement(X1),complement(complement(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[118604,29,theory(equality)]),9492,theory(equality)]),38764,theory(equality)]),29,theory(equality)]),107423,theory(equality)]) ).
cnf(118811,plain,
join(X1,complement(join(X1,X1))) = join(X1,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[118810,107423,theory(equality)]),29,theory(equality)]) ).
cnf(119028,plain,
join(complement(X1),complement(join(X1,complement(X1)))) = complement(X1),
inference(rw,[status(thm)],[118764,29,theory(equality)]) ).
cnf(119057,plain,
X1 = join(X1,complement(join(complement(complement(join(complement(X1),complement(complement(X1))))),X1))),
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)],[118790,29,theory(equality)]),1024,theory(equality)]),29,theory(equality)]),106410,theory(equality)]),107423,theory(equality)]),29,theory(equality)]),118581,theory(equality)]) ).
cnf(119058,plain,
X1 = join(X1,complement(join(X1,join(X1,complement(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[119057,29,theory(equality)]),107423,theory(equality)]),29,theory(equality)]),107423,theory(equality)]) ).
cnf(121267,plain,
join(complement(X1),complement(join(complement(join(complement(X1),complement(complement(X1)))),complement(X1)))) = join(complement(X1),join(complement(X1),complement(complement(X1)))),
inference(spm,[status(thm)],[819,119058,theory(equality)]) ).
cnf(121478,plain,
join(X1,complement(X1)) = join(complement(X1),join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[121267,29,theory(equality)]),107423,theory(equality)]),29,theory(equality)]),119028,theory(equality)]),107423,theory(equality)]),29,theory(equality)]) ).
cnf(121479,plain,
join(X1,complement(X1)) = join(X1,join(complement(X1),complement(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[121478,107423,theory(equality)]),29,theory(equality)]),64,theory(equality)]) ).
cnf(121892,plain,
join(join(complement(complement(X1)),complement(complement(X1))),complement(join(complement(X1),complement(complement(X1))))) = join(X1,complement(join(complement(join(complement(complement(X1)),complement(complement(X1)))),X1))),
inference(spm,[status(thm)],[38764,121479,theory(equality)]) ).
cnf(122047,plain,
join(X1,X1) = join(X1,complement(join(complement(join(complement(complement(X1)),complement(complement(X1)))),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[121892,107423,theory(equality)]),107423,theory(equality)]),107423,theory(equality)]),29,theory(equality)]),39,theory(equality)]),118581,theory(equality)]) ).
cnf(122048,plain,
join(X1,X1) = X1,
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)],[122047,29,theory(equality)]),1268,theory(equality)]),38764,theory(equality)]),29,theory(equality)]),107423,theory(equality)]),118811,theory(equality)]),118581,theory(equality)]) ).
cnf(123242,plain,
join(X1,X2) = join(X2,join(X1,X2)),
inference(spm,[status(thm)],[58,122048,theory(equality)]) ).
cnf(124741,plain,
join(complement(join(complement(X2),complement(X1))),complement(join(X1,complement(X2)))) = join(X2,complement(join(X1,complement(X2)))),
inference(spm,[status(thm)],[592,123242,theory(equality)]) ).
cnf(125123,plain,
X2 = join(X2,complement(join(X1,complement(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[124741,29,theory(equality)]),107740,theory(equality)]),107423,theory(equality)]) ).
cnf(126140,plain,
join(complement(join(complement(X1),X2)),X2) = join(X2,X1),
inference(spm,[status(thm)],[353,125123,theory(equality)]) ).
cnf(126436,plain,
join(X2,complement(join(complement(X1),X2))) = join(X2,X1),
inference(rw,[status(thm)],[126140,29,theory(equality)]) ).
cnf(132350,plain,
join(composition(X1,X2),join(X3,join(complement(X3),X4))) = join(complement(join(complement(X4),complement(X3))),join(X3,complement(X3))),
inference(spm,[status(thm)],[48278,126436,theory(equality)]) ).
cnf(132351,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[126436,107423,theory(equality)]) ).
cnf(132758,plain,
join(X4,join(X3,complement(X3))) = join(complement(join(complement(X4),complement(X3))),join(X3,complement(X3))),
inference(rw,[status(thm)],[132350,48278,theory(equality)]) ).
cnf(132759,plain,
join(X4,join(X3,complement(X3))) = join(X3,complement(X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[132758,58,theory(equality)]),29,theory(equality)]),125123,theory(equality)]),29,theory(equality)]) ).
cnf(132890,plain,
converse(join(X2,complement(X2))) = join(X1,converse(join(X2,complement(X2)))),
inference(spm,[status(thm)],[50,132759,theory(equality)]) ).
cnf(172466,plain,
join(complement(join(X1,converse(join(X3,complement(X3))))),complement(join(complement(X2),complement(join(X1,converse(join(X3,complement(X3)))))))) = X2,
inference(spm,[status(thm)],[351,132890,theory(equality)]) ).
cnf(172678,plain,
join(complement(converse(join(X3,complement(X3)))),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[172466,132890,theory(equality)]),132890,theory(equality)]),132351,theory(equality)]),107423,theory(equality)]) ).
cnf(173094,plain,
complement(join(converse(X1),complement(converse(complement(X1))))) = complement(converse(X1)),
inference(spm,[status(thm)],[108566,172678,theory(equality)]) ).
cnf(176295,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)],[252,173094,theory(equality)]) ).
cnf(176554,plain,
converse(X2) = join(converse(X2),complement(converse(complement(X2)))),
inference(rw,[status(thm)],[176295,252,theory(equality)]) ).
cnf(176712,plain,
converse(converse(X1)) = join(X1,converse(complement(converse(complement(X1))))),
inference(spm,[status(thm)],[50,176554,theory(equality)]) ).
cnf(176838,plain,
X1 = join(X1,converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[176712,23,theory(equality)]) ).
cnf(177606,plain,
join(complement(converse(join(complement(converse(complement(complement(converse(X1))))),X1))),complement(complement(converse(X1)))) = complement(converse(complement(converse(complement(complement(converse(X1))))))),
inference(spm,[status(thm)],[110067,176838,theory(equality)]) ).
cnf(177826,plain,
converse(X1) = complement(converse(complement(converse(complement(complement(converse(X1))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[177606,29,theory(equality)]),107423,theory(equality)]),23,theory(equality)]),107423,theory(equality)]),172678,theory(equality)]) ).
cnf(177827,plain,
converse(X1) = complement(converse(complement(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[177826,107423,theory(equality)]),23,theory(equality)]) ).
cnf(178075,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[107423,177827,theory(equality)]) ).
cnf(178392,plain,
join(complement(converse(X1)),converse(X2)) = converse(join(complement(X1),X2)),
inference(spm,[status(thm)],[27,178075,theory(equality)]) ).
cnf(178605,negated_conjecture,
( join(complement(converse(join(complement(esk1_0),complement(esk2_0)))),complement(join(complement(converse(esk1_0)),complement(converse(esk2_0))))) != complement(join(complement(converse(esk1_0)),complement(converse(esk2_0))))
| join(converse(complement(join(complement(esk1_0),complement(esk2_0)))),complement(join(complement(converse(esk1_0)),complement(converse(esk2_0))))) != converse(complement(join(complement(esk1_0),complement(esk2_0)))) ),
inference(rw,[status(thm)],[134,178075,theory(equality)]) ).
cnf(178606,negated_conjecture,
( join(complement(converse(join(complement(esk1_0),complement(esk2_0)))),complement(join(complement(converse(esk1_0)),complement(converse(esk2_0))))) != complement(join(complement(converse(esk1_0)),complement(converse(esk2_0))))
| join(complement(converse(join(complement(esk1_0),complement(esk2_0)))),complement(join(complement(converse(esk1_0)),complement(converse(esk2_0))))) != converse(complement(join(complement(esk1_0),complement(esk2_0)))) ),
inference(rw,[status(thm)],[178605,178075,theory(equality)]) ).
cnf(178607,negated_conjecture,
( join(complement(converse(join(complement(esk1_0),complement(esk2_0)))),complement(join(complement(converse(esk1_0)),complement(converse(esk2_0))))) != complement(join(complement(converse(esk1_0)),complement(converse(esk2_0))))
| join(complement(converse(join(complement(esk1_0),complement(esk2_0)))),complement(join(complement(converse(esk1_0)),complement(converse(esk2_0))))) != complement(converse(join(complement(esk1_0),complement(esk2_0)))) ),
inference(rw,[status(thm)],[178606,178075,theory(equality)]) ).
cnf(183407,plain,
join(complement(converse(X1)),complement(converse(X2))) = converse(join(complement(X1),complement(X2))),
inference(spm,[status(thm)],[178392,178075,theory(equality)]) ).
cnf(204149,negated_conjecture,
( complement(converse(join(complement(esk1_0),complement(esk2_0)))) != complement(join(complement(converse(esk1_0)),complement(converse(esk2_0))))
| join(complement(converse(join(complement(esk1_0),complement(esk2_0)))),complement(join(complement(converse(esk1_0)),complement(converse(esk2_0))))) != complement(converse(join(complement(esk1_0),complement(esk2_0)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[178607,183407,theory(equality)]),183407,theory(equality)]),122048,theory(equality)]),178075,theory(equality)]) ).
cnf(204150,negated_conjecture,
( $false
| join(complement(converse(join(complement(esk1_0),complement(esk2_0)))),complement(join(complement(converse(esk1_0)),complement(converse(esk2_0))))) != complement(converse(join(complement(esk1_0),complement(esk2_0)))) ),
inference(rw,[status(thm)],[204149,183407,theory(equality)]) ).
cnf(204151,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[204150,183407,theory(equality)]),183407,theory(equality)]),122048,theory(equality)]),178075,theory(equality)]) ).
cnf(204152,negated_conjecture,
$false,
inference(cn,[status(thm)],[204151,theory(equality)]) ).
cnf(204153,negated_conjecture,
$false,
204152,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL005+4.p
% --creating new selector for [REL001+0.ax, REL001+1.ax]
% -running prover on /tmp/tmpGCKNve/sel_REL005+4.p_1 with time limit 29
% -prover status Theorem
% Problem REL005+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL005+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL005+4.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
%
%------------------------------------------------------------------------------