TSTP Solution File: REL005+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL005+3 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 01:00:27 EST 2010
% Result : Theorem 11.79s
% Output : CNFRefutation 11.79s
% Verified :
% SZS Type : None (Could not find formula named equality))
% Syntax : Number of formulae : 139
% 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/tmpDPJPsg/sel_REL005+3.p_1',modular_law_1) ).
fof(4,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmpDPJPsg/sel_REL005+3.p_1',converse_idempotence) ).
fof(6,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpDPJPsg/sel_REL005+3.p_1',converse_additivity) ).
fof(7,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpDPJPsg/sel_REL005+3.p_1',maddux1_join_commutativity) ).
fof(10,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/tmp/tmpDPJPsg/sel_REL005+3.p_1',converse_cancellativity) ).
fof(11,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmpDPJPsg/sel_REL005+3.p_1',maddux4_definiton_of_meet) ).
fof(12,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmpDPJPsg/sel_REL005+3.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/tmpDPJPsg/sel_REL005+3.p_1',maddux3_a_kind_of_de_Morgan) ).
fof(14,conjecture,
! [X1,X2] : converse(meet(X1,X2)) = meet(converse(X1),converse(X2)),
file('/tmp/tmpDPJPsg/sel_REL005+3.p_1',goals) ).
fof(15,negated_conjecture,
~ ! [X1,X2] : converse(meet(X1,X2)) = meet(converse(X1),converse(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] : converse(meet(X1,X2)) != meet(converse(X1),converse(X2)),
inference(fof_nnf,[status(thm)],[15]) ).
fof(43,negated_conjecture,
? [X3,X4] : converse(meet(X3,X4)) != meet(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,negated_conjecture,
converse(meet(esk1_0,esk2_0)) != meet(converse(esk1_0),converse(esk2_0)),
inference(skolemize,[status(esa)],[43]) ).
cnf(45,negated_conjecture,
converse(meet(esk1_0,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,
complement(join(complement(converse(esk1_0)),complement(converse(esk2_0)))) != converse(complement(join(complement(esk1_0),complement(esk2_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[45,37,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(251,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(350,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(352,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(577,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(591,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(615,plain,
join(X1,complement(join(complement(X1),X2))) = join(X1,complement(join(complement(X1),complement(complement(X2))))),
inference(rw,[status(thm)],[577,29,theory(equality)]) ).
cnf(818,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(993,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(1004,plain,
join(complement(join(X1,complement(X2))),complement(join(complement(X1),complement(X2)))) = X2,
inference(spm,[status(thm)],[70,29,theory(equality)]) ).
cnf(1023,plain,
join(X2,complement(join(complement(X1),X2))) = join(X1,complement(join(complement(X2),complement(complement(X1))))),
inference(rw,[status(thm)],[993,29,theory(equality)]) ).
cnf(1232,plain,
join(complement(join(complement(X1),X2)),X2) = join(X1,complement(join(complement(complement(X1)),complement(X2)))),
inference(spm,[status(thm)],[67,1004,theory(equality)]) ).
cnf(1267,plain,
join(X2,complement(join(complement(X1),X2))) = join(X1,complement(join(complement(complement(X1)),complement(X2)))),
inference(rw,[status(thm)],[1232,29,theory(equality)]) ).
cnf(3629,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),X3) = X3,
inference(spm,[status(thm)],[100,66,theory(equality)]) ).
cnf(3646,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(3711,plain,
join(X3,complement(join(complement(composition(X1,X2)),complement(X3)))) = X3,
inference(rw,[status(thm)],[3629,29,theory(equality)]) ).
cnf(3729,plain,
join(X3,join(complement(join(complement(composition(X1,X2)),complement(X3))),X4)) = join(X3,X4),
inference(rw,[status(thm)],[3646,64,theory(equality)]) ).
cnf(3819,plain,
join(X1,X2) = join(X2,join(X1,complement(join(complement(composition(X3,X4)),complement(X2))))),
inference(spm,[status(thm)],[64,3711,theory(equality)]) ).
cnf(9143,plain,
join(X1,X1) = join(X1,complement(join(complement(X1),complement(complement(composition(X2,X3)))))),
inference(spm,[status(thm)],[3729,70,theory(equality)]) ).
cnf(9249,plain,
join(X1,X1) = join(X1,complement(join(complement(X1),composition(X2,X3)))),
inference(rw,[status(thm)],[9143,615,theory(equality)]) ).
cnf(9491,plain,
join(X1,complement(complement(X1))) = join(X1,X1),
inference(spm,[status(thm)],[9249,77,theory(equality)]) ).
cnf(9641,plain,
join(complement(join(X1,X1)),complement(join(complement(complement(X1)),complement(X1)))) = complement(X1),
inference(spm,[status(thm)],[70,9491,theory(equality)]) ).
cnf(9701,plain,
join(complement(join(X1,X1)),complement(join(complement(X1),complement(complement(X1))))) = complement(X1),
inference(rw,[status(thm)],[9641,29,theory(equality)]) ).
cnf(38445,plain,
join(complement(join(complement(X1),X2)),X2) = join(complement(join(complement(X2),X1)),X1),
inference(spm,[status(thm)],[352,71,theory(equality)]) ).
cnf(38472,plain,
join(complement(join(complement(composition(X1,X2)),X3)),X3) = join(X3,composition(X1,X2)),
inference(spm,[status(thm)],[352,3711,theory(equality)]) ).
cnf(38762,plain,
join(X2,complement(join(complement(X1),X2))) = join(complement(join(complement(X2),X1)),X1),
inference(rw,[status(thm)],[38445,29,theory(equality)]) ).
cnf(38763,plain,
join(X2,complement(join(complement(X1),X2))) = join(X1,complement(join(complement(X2),X1))),
inference(rw,[status(thm)],[38762,29,theory(equality)]) ).
cnf(38785,plain,
join(X3,complement(join(complement(composition(X1,X2)),X3))) = join(X3,composition(X1,X2)),
inference(rw,[status(thm)],[38472,29,theory(equality)]) ).
cnf(41627,plain,
join(X2,complement(join(complement(X1),X2))) = join(X2,complement(join(complement(X1),complement(complement(X2))))),
inference(spm,[status(thm)],[1023,38763,theory(equality)]) ).
cnf(44751,plain,
join(X1,complement(join(X1,complement(composition(X2,X3))))) = join(X1,composition(X2,X3)),
inference(spm,[status(thm)],[38785,29,theory(equality)]) ).
cnf(47211,plain,
join(complement(X1),join(X1,complement(join(complement(composition(X2,X3)),X1)))) = join(X1,complement(X1)),
inference(spm,[status(thm)],[3819,41627,theory(equality)]) ).
cnf(47424,plain,
join(X1,join(complement(X1),composition(X2,X3))) = join(X1,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[47211,38785,theory(equality)]),64,theory(equality)]) ).
cnf(47867,plain,
join(X1,join(composition(X2,X3),complement(X1))) = join(X1,complement(X1)),
inference(spm,[status(thm)],[47424,29,theory(equality)]) ).
cnf(47870,plain,
join(X1,complement(X1)) = join(composition(X2,X3),join(X1,complement(X1))),
inference(spm,[status(thm)],[58,47424,theory(equality)]) ).
cnf(48128,plain,
join(X1,join(X2,complement(X2))) = join(join(composition(X3,X4),complement(X2)),join(X1,X2)),
inference(spm,[status(thm)],[58,47867,theory(equality)]) ).
cnf(48277,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)],[48128,39,theory(equality)]),58,theory(equality)]) ).
cnf(105992,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)],[48277,80,theory(equality)]) ).
cnf(106408,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)],[105992,29,theory(equality)]),47870,theory(equality)]) ).
cnf(106409,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)],[106408,58,theory(equality)]),29,theory(equality)]),44751,theory(equality)]),77,theory(equality)]),29,theory(equality)]) ).
cnf(107241,plain,
join(complement(join(X1,X1)),complement(join(X1,complement(X1)))) = complement(X1),
inference(rw,[status(thm)],[9701,106409,theory(equality)]) ).
cnf(107422,plain,
complement(complement(X1)) = X1,
inference(spm,[status(thm)],[66,107241,theory(equality)]) ).
cnf(107725,plain,
join(complement(join(X1,X2)),complement(join(X1,complement(X2)))) = complement(X1),
inference(spm,[status(thm)],[66,107422,theory(equality)]) ).
cnf(107739,plain,
join(complement(join(X1,X2)),complement(join(X2,complement(X1)))) = complement(X2),
inference(spm,[status(thm)],[70,107422,theory(equality)]) ).
cnf(107741,plain,
join(complement(join(X1,X2)),complement(join(complement(X2),X1))) = complement(X1),
inference(spm,[status(thm)],[71,107422,theory(equality)]) ).
cnf(108565,plain,
join(complement(converse(join(X1,X2))),complement(join(converse(X1),complement(converse(X2))))) = complement(converse(X1)),
inference(spm,[status(thm)],[107725,27,theory(equality)]) ).
cnf(110066,plain,
join(complement(converse(join(X1,X2))),complement(join(complement(converse(X2)),converse(X1)))) = complement(converse(X1)),
inference(spm,[status(thm)],[107741,27,theory(equality)]) ).
cnf(110115,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)],[107741,3711,theory(equality)]) ).
cnf(110542,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)],[110115,29,theory(equality)]),41627,theory(equality)]),38785,theory(equality)]),107422,theory(equality)]),29,theory(equality)]) ).
cnf(110543,plain,
join(X3,complement(join(X3,composition(X1,X2)))) = join(complement(composition(X1,X2)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[110542,107422,theory(equality)]),107422,theory(equality)]) ).
cnf(118387,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)],[38763,110543,theory(equality)]) ).
cnf(118579,plain,
X1 = join(X1,complement(join(complement(complement(join(complement(X1),composition(X2,X3)))),X1))),
inference(rw,[status(thm)],[118387,71,theory(equality)]) ).
cnf(118580,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)],[118579,107422,theory(equality)]),39,theory(equality)]),58,theory(equality)]),47424,theory(equality)]) ).
cnf(118603,plain,
join(complement(X1),complement(join(complement(complement(complement(X1))),complement(X1)))) = join(complement(X1),complement(complement(X1))),
inference(spm,[status(thm)],[818,118580,theory(equality)]) ).
cnf(118763,plain,
join(complement(X1),complement(join(complement(X1),X1))) = complement(X1),
inference(spm,[status(thm)],[118580,107422,theory(equality)]) ).
cnf(118789,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)],[38763,118580,theory(equality)]) ).
cnf(118809,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)],[118603,29,theory(equality)]),9491,theory(equality)]),38763,theory(equality)]),29,theory(equality)]),107422,theory(equality)]) ).
cnf(118810,plain,
join(X1,complement(join(X1,X1))) = join(X1,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[118809,107422,theory(equality)]),29,theory(equality)]) ).
cnf(119027,plain,
join(complement(X1),complement(join(X1,complement(X1)))) = complement(X1),
inference(rw,[status(thm)],[118763,29,theory(equality)]) ).
cnf(119056,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)],[118789,29,theory(equality)]),1023,theory(equality)]),29,theory(equality)]),106409,theory(equality)]),107422,theory(equality)]),29,theory(equality)]),118580,theory(equality)]) ).
cnf(119057,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)],[119056,29,theory(equality)]),107422,theory(equality)]),29,theory(equality)]),107422,theory(equality)]) ).
cnf(121266,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)],[818,119057,theory(equality)]) ).
cnf(121477,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)],[121266,29,theory(equality)]),107422,theory(equality)]),29,theory(equality)]),119027,theory(equality)]),107422,theory(equality)]),29,theory(equality)]) ).
cnf(121478,plain,
join(X1,complement(X1)) = join(X1,join(complement(X1),complement(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[121477,107422,theory(equality)]),29,theory(equality)]),64,theory(equality)]) ).
cnf(121891,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)],[38763,121478,theory(equality)]) ).
cnf(122046,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)],[121891,107422,theory(equality)]),107422,theory(equality)]),107422,theory(equality)]),29,theory(equality)]),39,theory(equality)]),118580,theory(equality)]) ).
cnf(122047,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)],[122046,29,theory(equality)]),1267,theory(equality)]),38763,theory(equality)]),29,theory(equality)]),107422,theory(equality)]),118810,theory(equality)]),118580,theory(equality)]) ).
cnf(123241,plain,
join(X1,X2) = join(X2,join(X1,X2)),
inference(spm,[status(thm)],[58,122047,theory(equality)]) ).
cnf(124740,plain,
join(complement(join(complement(X2),complement(X1))),complement(join(X1,complement(X2)))) = join(X2,complement(join(X1,complement(X2)))),
inference(spm,[status(thm)],[591,123241,theory(equality)]) ).
cnf(125122,plain,
X2 = join(X2,complement(join(X1,complement(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[124740,29,theory(equality)]),107739,theory(equality)]),107422,theory(equality)]) ).
cnf(126139,plain,
join(complement(join(complement(X1),X2)),X2) = join(X2,X1),
inference(spm,[status(thm)],[352,125122,theory(equality)]) ).
cnf(126435,plain,
join(X2,complement(join(complement(X1),X2))) = join(X2,X1),
inference(rw,[status(thm)],[126139,29,theory(equality)]) ).
cnf(132349,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)],[48277,126435,theory(equality)]) ).
cnf(132350,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[126435,107422,theory(equality)]) ).
cnf(132757,plain,
join(X4,join(X3,complement(X3))) = join(complement(join(complement(X4),complement(X3))),join(X3,complement(X3))),
inference(rw,[status(thm)],[132349,48277,theory(equality)]) ).
cnf(132758,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)],[132757,58,theory(equality)]),29,theory(equality)]),125122,theory(equality)]),29,theory(equality)]) ).
cnf(132889,plain,
converse(join(X2,complement(X2))) = join(X1,converse(join(X2,complement(X2)))),
inference(spm,[status(thm)],[50,132758,theory(equality)]) ).
cnf(172465,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)],[350,132889,theory(equality)]) ).
cnf(172677,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)],[172465,132889,theory(equality)]),132889,theory(equality)]),132350,theory(equality)]),107422,theory(equality)]) ).
cnf(173093,plain,
complement(join(converse(X1),complement(converse(complement(X1))))) = complement(converse(X1)),
inference(spm,[status(thm)],[108565,172677,theory(equality)]) ).
cnf(176294,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)],[251,173093,theory(equality)]) ).
cnf(176553,plain,
converse(X2) = join(converse(X2),complement(converse(complement(X2)))),
inference(rw,[status(thm)],[176294,251,theory(equality)]) ).
cnf(176711,plain,
converse(converse(X1)) = join(X1,converse(complement(converse(complement(X1))))),
inference(spm,[status(thm)],[50,176553,theory(equality)]) ).
cnf(176837,plain,
X1 = join(X1,converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[176711,23,theory(equality)]) ).
cnf(177605,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)],[110066,176837,theory(equality)]) ).
cnf(177825,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)],[177605,29,theory(equality)]),107422,theory(equality)]),23,theory(equality)]),107422,theory(equality)]),172677,theory(equality)]) ).
cnf(177826,plain,
converse(X1) = complement(converse(complement(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[177825,107422,theory(equality)]),23,theory(equality)]) ).
cnf(178074,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[107422,177826,theory(equality)]) ).
cnf(178391,plain,
join(complement(converse(X1)),converse(X2)) = converse(join(complement(X1),X2)),
inference(spm,[status(thm)],[27,178074,theory(equality)]) ).
cnf(178604,negated_conjecture,
complement(join(complement(converse(esk1_0)),complement(converse(esk2_0)))) != complement(converse(join(complement(esk1_0),complement(esk2_0)))),
inference(rw,[status(thm)],[49,178074,theory(equality)]) ).
cnf(183404,plain,
join(complement(converse(X1)),complement(converse(X2))) = converse(join(complement(X1),complement(X2))),
inference(spm,[status(thm)],[178391,178074,theory(equality)]) ).
cnf(204146,negated_conjecture,
$false,
inference(rw,[status(thm)],[178604,183404,theory(equality)]) ).
cnf(204147,negated_conjecture,
$false,
inference(cn,[status(thm)],[204146,theory(equality)]) ).
cnf(204148,negated_conjecture,
$false,
204147,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL005+3.p
% --creating new selector for [REL001+0.ax, REL001+1.ax]
% -running prover on /tmp/tmpDPJPsg/sel_REL005+3.p_1 with time limit 29
% -prover status Theorem
% Problem REL005+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL005+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL005+3.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------