%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL010+2 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 01:03:33 EST 2010
% Result : Theorem 0.95s
% Output : CNFRefutation 0.95s
% Verified :
% SZS Type : None (Could not find formula named 3))
% Syntax : Number of formulae : 169
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3)) = meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3),
file('/tmp/tmpcTMqVu/sel_REL010+2.p_1',modular_law_2) ).
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/tmpcTMqVu/sel_REL010+2.p_1',modular_law_1) ).
fof(3,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/tmp/tmpcTMqVu/sel_REL010+2.p_1',converse_multiplicativity) ).
fof(4,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmpcTMqVu/sel_REL010+2.p_1',converse_idempotence) ).
fof(5,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/tmp/tmpcTMqVu/sel_REL010+2.p_1',composition_distributivity) ).
fof(6,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpcTMqVu/sel_REL010+2.p_1',converse_additivity) ).
fof(7,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpcTMqVu/sel_REL010+2.p_1',maddux1_join_commutativity) ).
fof(8,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/tmp/tmpcTMqVu/sel_REL010+2.p_1',composition_associativity) ).
fof(10,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/tmp/tmpcTMqVu/sel_REL010+2.p_1',def_zero) ).
fof(11,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/tmp/tmpcTMqVu/sel_REL010+2.p_1',converse_cancellativity) ).
fof(12,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmpcTMqVu/sel_REL010+2.p_1',maddux4_definiton_of_meet) ).
fof(13,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmpcTMqVu/sel_REL010+2.p_1',maddux2_join_associativity) ).
fof(14,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/tmp/tmpcTMqVu/sel_REL010+2.p_1',maddux3_a_kind_of_de_Morgan) ).
fof(15,conjecture,
! [X1,X2,X3] :
( meet(composition(X1,X2),X3) = zero
=> meet(X2,composition(converse(X1),X3)) = zero ),
file('/tmp/tmpcTMqVu/sel_REL010+2.p_1',goals) ).
fof(16,negated_conjecture,
~ ! [X1,X2,X3] :
( meet(composition(X1,X2),X3) = zero
=> meet(X2,composition(converse(X1),X3)) = zero ),
inference(assume_negation,[status(cth)],[15]) ).
fof(17,plain,
! [X4,X5,X6] : join(meet(composition(X4,X5),X6),meet(composition(meet(X4,composition(X6,converse(X5))),X5),X6)) = meet(composition(meet(X4,composition(X6,converse(X5))),X5),X6),
inference(variable_rename,[status(thm)],[1]) ).
cnf(18,plain,
join(meet(composition(X1,X2),X3),meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3)) = meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3),
inference(split_conjunct,[status(thm)],[17]) ).
fof(19,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(20,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)],[19]) ).
fof(21,plain,
! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(22,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[4]) ).
cnf(24,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[23]) ).
fof(25,plain,
! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
inference(variable_rename,[status(thm)],[5]) ).
cnf(26,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[25]) ).
fof(27,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[6]) ).
cnf(28,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[7]) ).
cnf(30,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X4,X5,X6] : composition(X4,composition(X5,X6)) = composition(composition(X4,X5),X6),
inference(variable_rename,[status(thm)],[8]) ).
cnf(32,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[31]) ).
fof(35,plain,
! [X2] : zero = meet(X2,complement(X2)),
inference(variable_rename,[status(thm)],[10]) ).
cnf(36,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X3,X4] : join(composition(converse(X3),complement(composition(X3,X4))),complement(X4)) = complement(X4),
inference(variable_rename,[status(thm)],[11]) ).
cnf(38,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,plain,
! [X3,X4] : meet(X3,X4) = complement(join(complement(X3),complement(X4))),
inference(variable_rename,[status(thm)],[12]) ).
cnf(40,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[39]) ).
fof(41,plain,
! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
inference(variable_rename,[status(thm)],[13]) ).
cnf(42,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[41]) ).
fof(43,plain,
! [X3,X4] : X3 = join(complement(join(complement(X3),complement(X4))),complement(join(complement(X3),X4))),
inference(variable_rename,[status(thm)],[14]) ).
cnf(44,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[43]) ).
fof(45,negated_conjecture,
? [X1,X2,X3] :
( meet(composition(X1,X2),X3) = zero
& meet(X2,composition(converse(X1),X3)) != zero ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(46,negated_conjecture,
? [X4,X5,X6] :
( meet(composition(X4,X5),X6) = zero
& meet(X5,composition(converse(X4),X6)) != zero ),
inference(variable_rename,[status(thm)],[45]) ).
fof(47,negated_conjecture,
( meet(composition(esk1_0,esk2_0),esk3_0) = zero
& meet(esk2_0,composition(converse(esk1_0),esk3_0)) != zero ),
inference(skolemize,[status(esa)],[46]) ).
cnf(48,negated_conjecture,
meet(esk2_0,composition(converse(esk1_0),esk3_0)) != zero,
inference(split_conjunct,[status(thm)],[47]) ).
cnf(49,negated_conjecture,
meet(composition(esk1_0,esk2_0),esk3_0) = zero,
inference(split_conjunct,[status(thm)],[47]) ).
cnf(50,plain,
complement(join(complement(X1),complement(complement(X1)))) = zero,
inference(rw,[status(thm)],[36,40,theory(equality)]),
[unfolding] ).
cnf(51,negated_conjecture,
complement(join(complement(composition(esk1_0,esk2_0)),complement(esk3_0))) = zero,
inference(rw,[status(thm)],[49,40,theory(equality)]),
[unfolding] ).
cnf(52,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)],[20,40,theory(equality)]),40,theory(equality)]),40,theory(equality)]),40,theory(equality)]),40,theory(equality)]),
[unfolding] ).
cnf(53,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2)),complement(X3)))) = complement(join(complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2)),complement(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[18,40,theory(equality)]),40,theory(equality)]),40,theory(equality)]),40,theory(equality)]),40,theory(equality)]),
[unfolding] ).
cnf(55,negated_conjecture,
complement(join(complement(esk2_0),complement(composition(converse(esk1_0),esk3_0)))) != zero,
inference(rw,[status(thm)],[48,40,theory(equality)]),
[unfolding] ).
cnf(56,plain,
complement(join(zero,complement(zero))) = zero,
inference(spm,[status(thm)],[50,50,theory(equality)]) ).
cnf(58,plain,
composition(converse(X1),X2) = converse(composition(converse(X2),X1)),
inference(spm,[status(thm)],[22,24,theory(equality)]) ).
cnf(59,negated_conjecture,
complement(join(complement(esk3_0),complement(composition(esk1_0,esk2_0)))) = zero,
inference(rw,[status(thm)],[51,30,theory(equality)]) ).
cnf(61,plain,
join(X1,converse(X2)) = converse(join(converse(X1),X2)),
inference(spm,[status(thm)],[28,24,theory(equality)]) ).
cnf(62,plain,
join(converse(X1),X2) = converse(join(X1,converse(X2))),
inference(spm,[status(thm)],[28,24,theory(equality)]) ).
cnf(71,plain,
join(converse(join(X1,X2)),X3) = join(converse(X1),join(converse(X2),X3)),
inference(spm,[status(thm)],[42,28,theory(equality)]) ).
cnf(73,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[30,42,theory(equality)]) ).
cnf(75,plain,
join(join(X2,X1),X3) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[42,30,theory(equality)]) ).
cnf(79,plain,
join(X2,join(X1,X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[75,42,theory(equality)]) ).
cnf(90,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(rw,[status(thm)],[38,30,theory(equality)]) ).
cnf(98,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[44,30,theory(equality)]) ).
cnf(100,plain,
join(zero,complement(join(complement(X1),complement(complement(complement(X1)))))) = X1,
inference(spm,[status(thm)],[98,50,theory(equality)]) ).
cnf(102,plain,
join(complement(join(complement(X1),complement(X1))),zero) = X1,
inference(spm,[status(thm)],[98,50,theory(equality)]) ).
cnf(106,negated_conjecture,
join(complement(join(complement(esk3_0),composition(esk1_0,esk2_0))),zero) = esk3_0,
inference(spm,[status(thm)],[98,59,theory(equality)]) ).
cnf(110,plain,
join(complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2)))),complement(X1)) = join(complement(X1),X2),
inference(spm,[status(thm)],[98,98,theory(equality)]) ).
cnf(111,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[98,30,theory(equality)]) ).
cnf(112,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[98,30,theory(equality)]) ).
cnf(116,plain,
join(zero,complement(join(complement(X1),complement(X1)))) = X1,
inference(rw,[status(thm)],[102,30,theory(equality)]) ).
cnf(118,negated_conjecture,
join(zero,complement(join(complement(esk3_0),composition(esk1_0,esk2_0)))) = esk3_0,
inference(rw,[status(thm)],[106,30,theory(equality)]) ).
cnf(119,plain,
join(complement(X1),complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2))))) = join(complement(X1),X2),
inference(rw,[status(thm)],[110,30,theory(equality)]) ).
cnf(120,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)],[52,30,theory(equality)]) ).
cnf(121,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)],[120,30,theory(equality)]) ).
cnf(127,plain,
join(complement(join(complement(composition(X1,X2)),complement(converse(X3)))),complement(join(complement(converse(X3)),complement(composition(X1,complement(join(complement(X2),complement(converse(composition(X3,X1)))))))))) = complement(join(complement(converse(X3)),complement(composition(X1,complement(join(complement(X2),complement(converse(composition(X3,X1))))))))),
inference(spm,[status(thm)],[121,22,theory(equality)]) ).
cnf(147,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2))))) = complement(join(complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2)),complement(X3))),
inference(rw,[status(thm)],[53,30,theory(equality)]) ).
cnf(148,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2))))) = complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2)))),
inference(rw,[status(thm)],[147,30,theory(equality)]) ).
cnf(202,plain,
join(zero,composition(converse(X1),complement(composition(X1,join(zero,complement(zero)))))) = zero,
inference(spm,[status(thm)],[90,56,theory(equality)]) ).
cnf(341,plain,
join(zero,complement(join(zero,zero))) = join(complement(X1),complement(complement(X1))),
inference(spm,[status(thm)],[116,50,theory(equality)]) ).
cnf(344,plain,
join(zero,complement(join(zero,zero))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[116,56,theory(equality)]) ).
cnf(367,plain,
join(zero,complement(join(zero,complement(complement(zero))))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[100,56,theory(equality)]) ).
cnf(870,plain,
join(zero,complement(zero)) = join(complement(X1),complement(complement(X1))),
inference(rw,[status(thm)],[341,344,theory(equality)]) ).
cnf(2157,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)],[119,73,theory(equality)]),30,theory(equality)]) ).
cnf(2414,plain,
join(complement(join(complement(complement(X1)),X1)),complement(join(zero,complement(zero)))) = complement(X1),
inference(spm,[status(thm)],[112,870,theory(equality)]) ).
cnf(2472,plain,
join(zero,complement(join(X1,complement(complement(X1))))) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[2414,30,theory(equality)]),56,theory(equality)]),30,theory(equality)]) ).
cnf(2518,plain,
complement(zero) = join(zero,complement(zero)),
inference(rw,[status(thm)],[367,2472,theory(equality)]) ).
cnf(2519,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[100,2472,theory(equality)]) ).
cnf(2550,plain,
join(zero,complement(join(X1,X1))) = complement(X1),
inference(rw,[status(thm)],[2472,2519,theory(equality)]) ).
cnf(2562,plain,
join(complement(X1),X1) = join(zero,complement(zero)),
inference(rw,[status(thm)],[870,2519,theory(equality)]) ).
cnf(2563,plain,
join(X1,complement(X1)) = join(zero,complement(zero)),
inference(rw,[status(thm)],[2562,30,theory(equality)]) ).
cnf(2585,plain,
join(zero,composition(converse(X1),complement(composition(X1,complement(zero))))) = zero,
inference(rw,[status(thm)],[202,2518,theory(equality)]) ).
cnf(2641,plain,
join(X1,complement(X1)) = complement(zero),
inference(rw,[status(thm)],[2563,2518,theory(equality)]) ).
cnf(2642,plain,
join(complement(zero),X2) = join(X1,join(complement(X1),X2)),
inference(spm,[status(thm)],[42,2641,theory(equality)]) ).
cnf(2649,plain,
converse(complement(zero)) = join(X1,converse(complement(converse(X1)))),
inference(spm,[status(thm)],[61,2641,theory(equality)]) ).
cnf(2670,plain,
join(X1,complement(zero)) = join(X2,join(X1,complement(X2))),
inference(spm,[status(thm)],[79,2641,theory(equality)]) ).
cnf(3055,plain,
join(join(X1,X1),complement(X1)) = join(zero,complement(zero)),
inference(spm,[status(thm)],[2670,2550,theory(equality)]) ).
cnf(3118,plain,
join(X1,complement(zero)) = join(zero,complement(zero)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3055,42,theory(equality)]),2641,theory(equality)]) ).
cnf(3119,plain,
join(X1,complement(zero)) = complement(zero),
inference(rw,[status(thm)],[3118,2641,theory(equality)]) ).
cnf(3154,plain,
join(zero,complement(complement(zero))) = complement(complement(zero)),
inference(spm,[status(thm)],[2550,3119,theory(equality)]) ).
cnf(3156,plain,
complement(zero) = join(complement(zero),X1),
inference(spm,[status(thm)],[30,3119,theory(equality)]) ).
cnf(3164,plain,
join(X1,join(X2,complement(X1))) = complement(zero),
inference(rw,[status(thm)],[2670,3119,theory(equality)]) ).
cnf(3193,plain,
join(zero,zero) = complement(complement(zero)),
inference(rw,[status(thm)],[3154,2519,theory(equality)]) ).
cnf(3194,plain,
join(zero,zero) = zero,
inference(rw,[status(thm)],[3193,2519,theory(equality)]) ).
cnf(3205,plain,
join(zero,X1) = join(zero,join(zero,X1)),
inference(spm,[status(thm)],[42,3194,theory(equality)]) ).
cnf(3248,plain,
complement(zero) = converse(complement(zero)),
inference(spm,[status(thm)],[2649,3156,theory(equality)]) ).
cnf(3390,plain,
converse(complement(zero)) = join(X1,converse(join(X2,complement(converse(X1))))),
inference(spm,[status(thm)],[61,3164,theory(equality)]) ).
cnf(3393,plain,
complement(zero) = join(converse(join(X1,X2)),complement(converse(X1))),
inference(spm,[status(thm)],[71,3164,theory(equality)]) ).
cnf(3419,plain,
join(X1,complement(zero)) = join(join(X3,complement(X2)),join(X1,X2)),
inference(spm,[status(thm)],[73,3164,theory(equality)]) ).
cnf(3434,plain,
complement(zero) = join(X1,converse(join(X2,complement(converse(X1))))),
inference(rw,[status(thm)],[3390,3248,theory(equality)]) ).
cnf(3438,plain,
complement(zero) = join(complement(converse(X1)),converse(join(X1,X2))),
inference(rw,[status(thm)],[3393,30,theory(equality)]) ).
cnf(3467,plain,
complement(zero) = join(join(X3,complement(X2)),join(X1,X2)),
inference(rw,[status(thm)],[3419,3119,theory(equality)]) ).
cnf(3468,plain,
complement(zero) = join(X3,complement(zero)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[3467,42,theory(equality)]),73,theory(equality)]),2642,theory(equality)]),3156,theory(equality)]) ).
cnf(3640,plain,
join(zero,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[3205,2550,theory(equality)]) ).
cnf(3706,plain,
join(complement(complement(X1)),complement(join(complement(X1),complement(zero)))) = X1,
inference(spm,[status(thm)],[111,3640,theory(equality)]) ).
cnf(3707,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[3640,2519,theory(equality)]) ).
cnf(3718,plain,
complement(join(X1,X1)) = complement(X1),
inference(rw,[status(thm)],[2550,3640,theory(equality)]) ).
cnf(3719,negated_conjecture,
complement(join(complement(esk3_0),composition(esk1_0,esk2_0))) = esk3_0,
inference(rw,[status(thm)],[118,3640,theory(equality)]) ).
cnf(3720,plain,
join(X1,zero) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[3706,2519,theory(equality)]),3468,theory(equality)]),2519,theory(equality)]) ).
cnf(3730,plain,
converse(converse(X1)) = join(X1,converse(zero)),
inference(spm,[status(thm)],[61,3720,theory(equality)]) ).
cnf(3752,plain,
X1 = join(X1,converse(zero)),
inference(rw,[status(thm)],[3730,24,theory(equality)]) ).
cnf(3800,plain,
composition(converse(X1),complement(composition(X1,complement(zero)))) = zero,
inference(rw,[status(thm)],[2585,3707,theory(equality)]) ).
cnf(3836,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = join(X1,X1),
inference(spm,[status(thm)],[98,3718,theory(equality)]) ).
cnf(3884,plain,
X1 = join(X1,X1),
inference(rw,[status(thm)],[3836,98,theory(equality)]) ).
cnf(3964,plain,
join(X1,X2) = join(X1,join(X1,X2)),
inference(spm,[status(thm)],[42,3884,theory(equality)]) ).
cnf(4073,plain,
zero = converse(zero),
inference(spm,[status(thm)],[3707,3752,theory(equality)]) ).
cnf(4185,negated_conjecture,
join(complement(esk3_0),complement(join(complement(composition(esk1_0,esk2_0)),join(complement(esk3_0),esk3_0)))) = join(complement(esk3_0),composition(esk1_0,esk2_0)),
inference(spm,[status(thm)],[2157,3719,theory(equality)]) ).
cnf(4204,negated_conjecture,
complement(esk3_0) = join(complement(esk3_0),composition(esk1_0,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)],[inference(rw,[status(thm)],[4185,30,theory(equality)]),2641,theory(equality)]),30,theory(equality)]),3156,theory(equality)]),2519,theory(equality)]),30,theory(equality)]),3707,theory(equality)]) ).
cnf(4212,negated_conjecture,
join(complement(esk3_0),X1) = join(complement(esk3_0),join(composition(esk1_0,esk2_0),X1)),
inference(spm,[status(thm)],[42,4204,theory(equality)]) ).
cnf(4268,plain,
composition(complement(zero),complement(composition(complement(zero),complement(zero)))) = zero,
inference(spm,[status(thm)],[3800,3248,theory(equality)]) ).
cnf(4823,plain,
join(zero,composition(X1,complement(composition(complement(zero),complement(zero))))) = composition(join(complement(zero),X1),complement(composition(complement(zero),complement(zero)))),
inference(spm,[status(thm)],[26,4268,theory(equality)]) ).
cnf(4843,plain,
composition(X1,complement(composition(complement(zero),complement(zero)))) = composition(join(complement(zero),X1),complement(composition(complement(zero),complement(zero)))),
inference(rw,[status(thm)],[4823,3707,theory(equality)]) ).
cnf(4844,plain,
composition(X1,complement(composition(complement(zero),complement(zero)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[4843,3156,theory(equality)]),4268,theory(equality)]) ).
cnf(5026,plain,
join(complement(join(complement(X1),X2)),X1) = X1,
inference(spm,[status(thm)],[3964,98,theory(equality)]) ).
cnf(5056,plain,
join(complement(join(X1,complement(X2))),X2) = X2,
inference(spm,[status(thm)],[3964,111,theory(equality)]) ).
cnf(5103,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[5026,30,theory(equality)]) ).
cnf(5140,plain,
join(X2,complement(join(X1,complement(X2)))) = X2,
inference(rw,[status(thm)],[5056,30,theory(equality)]) ).
cnf(5169,plain,
zero = composition(X1,composition(X2,complement(composition(complement(zero),complement(zero))))),
inference(spm,[status(thm)],[32,4844,theory(equality)]) ).
cnf(5204,plain,
zero = composition(X1,zero),
inference(rw,[status(thm)],[5169,4844,theory(equality)]) ).
cnf(5260,plain,
converse(zero) = composition(converse(zero),X1),
inference(spm,[status(thm)],[58,5204,theory(equality)]) ).
cnf(5303,plain,
zero = composition(converse(zero),X1),
inference(rw,[status(thm)],[5260,4073,theory(equality)]) ).
cnf(5304,plain,
zero = composition(zero,X1),
inference(rw,[status(thm)],[5303,4073,theory(equality)]) ).
cnf(6702,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(spm,[status(thm)],[5103,2519,theory(equality)]) ).
cnf(6736,plain,
join(X1,complement(join(X2,join(X3,complement(X1))))) = X1,
inference(spm,[status(thm)],[5103,73,theory(equality)]) ).
cnf(6813,plain,
converse(converse(X1)) = join(X1,converse(complement(join(X2,complement(converse(X1)))))),
inference(spm,[status(thm)],[61,5140,theory(equality)]) ).
cnf(6866,plain,
X1 = join(X1,converse(complement(join(X2,complement(converse(X1)))))),
inference(rw,[status(thm)],[6813,24,theory(equality)]) ).
cnf(8384,plain,
join(X1,converse(complement(converse(X1)))) = complement(zero),
inference(spm,[status(thm)],[3434,3707,theory(equality)]) ).
cnf(9165,negated_conjecture,
join(complement(esk3_0),complement(zero)) = join(complement(esk3_0),converse(complement(converse(composition(esk1_0,esk2_0))))),
inference(spm,[status(thm)],[4212,8384,theory(equality)]) ).
cnf(9210,negated_conjecture,
complement(zero) = join(complement(esk3_0),converse(complement(converse(composition(esk1_0,esk2_0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[9165,30,theory(equality)]),3156,theory(equality)]) ).
cnf(9418,negated_conjecture,
join(complement(complement(zero)),complement(join(complement(esk3_0),complement(converse(complement(converse(composition(esk1_0,esk2_0)))))))) = esk3_0,
inference(spm,[status(thm)],[98,9210,theory(equality)]) ).
cnf(9440,negated_conjecture,
complement(join(complement(esk3_0),complement(converse(complement(converse(composition(esk1_0,esk2_0))))))) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[9418,2519,theory(equality)]),3707,theory(equality)]) ).
cnf(12187,negated_conjecture,
join(complement(esk3_0),complement(join(complement(complement(converse(complement(converse(composition(esk1_0,esk2_0)))))),join(complement(esk3_0),esk3_0)))) = join(complement(esk3_0),complement(converse(complement(converse(composition(esk1_0,esk2_0)))))),
inference(spm,[status(thm)],[2157,9440,theory(equality)]) ).
cnf(12245,negated_conjecture,
complement(esk3_0) = join(complement(esk3_0),complement(converse(complement(converse(composition(esk1_0,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)],[12187,30,theory(equality)]),2641,theory(equality)]),3468,theory(equality)]),2519,theory(equality)]),30,theory(equality)]),3707,theory(equality)]) ).
cnf(14780,plain,
join(complement(join(join(X1,join(X2,complement(complement(X3)))),complement(X3))),complement(complement(X3))) = X3,
inference(spm,[status(thm)],[111,6736,theory(equality)]) ).
cnf(14923,plain,
complement(complement(X3)) = X3,
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)],[inference(rw,[status(thm)],[14780,42,theory(equality)]),42,theory(equality)]),30,theory(equality)]),2641,theory(equality)]),3119,theory(equality)]),3119,theory(equality)]),2519,theory(equality)]),3707,theory(equality)]) ).
cnf(18801,negated_conjecture,
join(complement(converse(composition(esk1_0,esk2_0))),converse(complement(complement(esk3_0)))) = complement(converse(composition(esk1_0,esk2_0))),
inference(spm,[status(thm)],[6866,12245,theory(equality)]) ).
cnf(18873,negated_conjecture,
join(converse(esk3_0),complement(converse(composition(esk1_0,esk2_0)))) = complement(converse(composition(esk1_0,esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[18801,2519,theory(equality)]),30,theory(equality)]) ).
cnf(19574,negated_conjecture,
join(complement(converse(esk3_0)),complement(complement(converse(composition(esk1_0,esk2_0))))) = complement(converse(esk3_0)),
inference(spm,[status(thm)],[6702,18873,theory(equality)]) ).
cnf(19598,negated_conjecture,
join(complement(converse(esk3_0)),converse(composition(esk1_0,esk2_0))) = complement(converse(esk3_0)),
inference(rw,[status(thm)],[19574,14923,theory(equality)]) ).
cnf(19615,negated_conjecture,
converse(complement(converse(esk3_0))) = join(converse(complement(converse(esk3_0))),composition(esk1_0,esk2_0)),
inference(spm,[status(thm)],[62,19598,theory(equality)]) ).
cnf(19647,negated_conjecture,
converse(complement(converse(esk3_0))) = join(composition(esk1_0,esk2_0),converse(complement(converse(esk3_0)))),
inference(rw,[status(thm)],[19615,30,theory(equality)]) ).
cnf(19684,negated_conjecture,
join(complement(converse(composition(esk1_0,esk2_0))),converse(converse(complement(converse(esk3_0))))) = complement(zero),
inference(spm,[status(thm)],[3438,19647,theory(equality)]) ).
cnf(19707,negated_conjecture,
join(complement(converse(esk3_0)),complement(converse(composition(esk1_0,esk2_0)))) = complement(zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[19684,24,theory(equality)]),30,theory(equality)]) ).
cnf(20270,negated_conjecture,
join(complement(join(complement(composition(esk2_0,converse(esk3_0))),complement(converse(esk1_0)))),complement(join(complement(converse(esk1_0)),complement(composition(esk2_0,complement(complement(zero))))))) = complement(join(complement(converse(esk1_0)),complement(composition(esk2_0,complement(complement(zero)))))),
inference(spm,[status(thm)],[127,19707,theory(equality)]) ).
cnf(20314,negated_conjecture,
complement(join(complement(converse(esk1_0)),complement(composition(esk2_0,converse(esk3_0))))) = complement(join(complement(converse(esk1_0)),complement(composition(esk2_0,complement(complement(zero)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[20270,30,theory(equality)]),2519,theory(equality)]),5204,theory(equality)]),3468,theory(equality)]),2519,theory(equality)]),3720,theory(equality)]) ).
cnf(20315,negated_conjecture,
complement(join(complement(converse(esk1_0)),complement(composition(esk2_0,converse(esk3_0))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[20314,2519,theory(equality)]),5204,theory(equality)]),3468,theory(equality)]),2519,theory(equality)]) ).
cnf(20364,negated_conjecture,
join(complement(join(complement(composition(converse(esk1_0),esk3_0)),complement(esk2_0))),complement(join(complement(esk2_0),complement(composition(zero,esk3_0))))) = complement(join(complement(esk2_0),complement(composition(zero,esk3_0)))),
inference(spm,[status(thm)],[148,20315,theory(equality)]) ).
cnf(20481,negated_conjecture,
complement(join(complement(esk2_0),complement(composition(converse(esk1_0),esk3_0)))) = complement(join(complement(esk2_0),complement(composition(zero,esk3_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[20364,30,theory(equality)]),5304,theory(equality)]),3468,theory(equality)]),2519,theory(equality)]),3720,theory(equality)]) ).
cnf(20482,negated_conjecture,
complement(join(complement(esk2_0),complement(composition(converse(esk1_0),esk3_0)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[20481,5304,theory(equality)]),3468,theory(equality)]),2519,theory(equality)]) ).
cnf(20483,negated_conjecture,
$false,
inference(sr,[status(thm)],[20482,55,theory(equality)]) ).
cnf(20484,negated_conjecture,
$false,
20483,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL010+2.p
% --creating new selector for [REL001+0.ax, REL001+1.ax]
% -running prover on /tmp/tmpcTMqVu/sel_REL010+2.p_1 with time limit 29
% -prover status Theorem
% Problem REL010+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL010+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL010+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
%
%------------------------------------------------------------------------------