%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL010+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 01:02:37 EST 2010
% Result : Theorem 23.73s
% Output : CNFRefutation 23.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 11
% Syntax : Number of formulae : 148 ( 143 unt; 0 def)
% Number of atoms : 153 ( 150 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 0 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 232 ( 23 sgn 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/tmp/tmpcvuTlx/sel_REL010+1.p_1',converse_multiplicativity) ).
fof(2,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmpcvuTlx/sel_REL010+1.p_1',converse_idempotence) ).
fof(3,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/tmp/tmpcvuTlx/sel_REL010+1.p_1',composition_distributivity) ).
fof(4,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpcvuTlx/sel_REL010+1.p_1',converse_additivity) ).
fof(5,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpcvuTlx/sel_REL010+1.p_1',maddux1_join_commutativity) ).
fof(7,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/tmp/tmpcvuTlx/sel_REL010+1.p_1',def_zero) ).
fof(8,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/tmp/tmpcvuTlx/sel_REL010+1.p_1',converse_cancellativity) ).
fof(9,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmpcvuTlx/sel_REL010+1.p_1',maddux4_definiton_of_meet) ).
fof(10,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmpcvuTlx/sel_REL010+1.p_1',maddux2_join_associativity) ).
fof(11,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/tmp/tmpcvuTlx/sel_REL010+1.p_1',maddux3_a_kind_of_de_Morgan) ).
fof(12,conjecture,
! [X1,X2,X3] :
( meet(composition(X1,X2),X3) = zero
=> meet(X2,composition(converse(X1),X3)) = zero ),
file('/tmp/tmpcvuTlx/sel_REL010+1.p_1',goals) ).
fof(13,negated_conjecture,
~ ! [X1,X2,X3] :
( meet(composition(X1,X2),X3) = zero
=> meet(X2,composition(converse(X1),X3)) = zero ),
inference(assume_negation,[status(cth)],[12]) ).
fof(14,plain,
! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
inference(variable_rename,[status(thm)],[1]) ).
cnf(15,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[14]) ).
fof(16,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(17,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[16]) ).
fof(18,plain,
! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(19,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[18]) ).
fof(20,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(21,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[20]) ).
fof(22,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(23,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[22]) ).
fof(26,plain,
! [X2] : zero = meet(X2,complement(X2)),
inference(variable_rename,[status(thm)],[7]) ).
cnf(27,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[26]) ).
fof(28,plain,
! [X3,X4] : join(composition(converse(X3),complement(composition(X3,X4))),complement(X4)) = complement(X4),
inference(variable_rename,[status(thm)],[8]) ).
cnf(29,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[28]) ).
fof(30,plain,
! [X3,X4] : meet(X3,X4) = complement(join(complement(X3),complement(X4))),
inference(variable_rename,[status(thm)],[9]) ).
cnf(31,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[30]) ).
fof(32,plain,
! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
inference(variable_rename,[status(thm)],[10]) ).
cnf(33,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[32]) ).
fof(34,plain,
! [X3,X4] : X3 = join(complement(join(complement(X3),complement(X4))),complement(join(complement(X3),X4))),
inference(variable_rename,[status(thm)],[11]) ).
cnf(35,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[34]) ).
fof(36,negated_conjecture,
? [X1,X2,X3] :
( meet(composition(X1,X2),X3) = zero
& meet(X2,composition(converse(X1),X3)) != zero ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(37,negated_conjecture,
? [X4,X5,X6] :
( meet(composition(X4,X5),X6) = zero
& meet(X5,composition(converse(X4),X6)) != zero ),
inference(variable_rename,[status(thm)],[36]) ).
fof(38,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)],[37]) ).
cnf(39,negated_conjecture,
meet(esk2_0,composition(converse(esk1_0),esk3_0)) != zero,
inference(split_conjunct,[status(thm)],[38]) ).
cnf(40,negated_conjecture,
meet(composition(esk1_0,esk2_0),esk3_0) = zero,
inference(split_conjunct,[status(thm)],[38]) ).
cnf(41,plain,
complement(join(complement(X1),complement(complement(X1)))) = zero,
inference(rw,[status(thm)],[27,31,theory(equality)]),
[unfolding] ).
cnf(42,negated_conjecture,
complement(join(complement(composition(esk1_0,esk2_0)),complement(esk3_0))) = zero,
inference(rw,[status(thm)],[40,31,theory(equality)]),
[unfolding] ).
cnf(43,negated_conjecture,
complement(join(complement(esk2_0),complement(composition(converse(esk1_0),esk3_0)))) != zero,
inference(rw,[status(thm)],[39,31,theory(equality)]),
[unfolding] ).
cnf(44,plain,
complement(join(zero,complement(zero))) = zero,
inference(spm,[status(thm)],[41,41,theory(equality)]) ).
cnf(45,plain,
composition(X1,converse(X2)) = converse(composition(X2,converse(X1))),
inference(spm,[status(thm)],[15,17,theory(equality)]) ).
cnf(46,plain,
composition(converse(X1),X2) = converse(composition(converse(X2),X1)),
inference(spm,[status(thm)],[15,17,theory(equality)]) ).
cnf(47,negated_conjecture,
complement(join(complement(esk3_0),complement(composition(esk1_0,esk2_0)))) = zero,
inference(rw,[status(thm)],[42,23,theory(equality)]) ).
cnf(49,plain,
join(X1,converse(X2)) = converse(join(converse(X1),X2)),
inference(spm,[status(thm)],[21,17,theory(equality)]) ).
cnf(50,plain,
join(converse(X1),X2) = converse(join(X1,converse(X2))),
inference(spm,[status(thm)],[21,17,theory(equality)]) ).
cnf(61,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[23,33,theory(equality)]) ).
cnf(63,plain,
join(join(X2,X1),X3) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[33,23,theory(equality)]) ).
cnf(67,plain,
join(X2,join(X1,X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[63,33,theory(equality)]) ).
cnf(70,plain,
join(composition(X1,converse(X2)),converse(composition(X2,X3))) = composition(join(X1,converse(X3)),converse(X2)),
inference(spm,[status(thm)],[19,15,theory(equality)]) ).
cnf(78,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(rw,[status(thm)],[29,23,theory(equality)]) ).
cnf(86,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[35,23,theory(equality)]) ).
cnf(88,plain,
join(zero,complement(join(complement(X1),complement(complement(complement(X1)))))) = X1,
inference(spm,[status(thm)],[86,41,theory(equality)]) ).
cnf(90,plain,
join(complement(join(complement(X1),complement(X1))),zero) = X1,
inference(spm,[status(thm)],[86,41,theory(equality)]) ).
cnf(96,plain,
join(complement(complement(X1)),complement(join(complement(X1),complement(composition(converse(X2),complement(composition(X2,X1))))))) = X1,
inference(spm,[status(thm)],[86,78,theory(equality)]) ).
cnf(98,plain,
join(complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2)))),complement(X1)) = join(complement(X1),X2),
inference(spm,[status(thm)],[86,86,theory(equality)]) ).
cnf(99,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[86,23,theory(equality)]) ).
cnf(100,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[86,23,theory(equality)]) ).
cnf(104,plain,
join(zero,complement(join(complement(X1),complement(X1)))) = X1,
inference(rw,[status(thm)],[90,23,theory(equality)]) ).
cnf(107,plain,
join(complement(X1),complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2))))) = join(complement(X1),X2),
inference(rw,[status(thm)],[98,23,theory(equality)]) ).
cnf(122,plain,
join(converse(X1),composition(X3,converse(X2))) = converse(join(X1,composition(X2,converse(X3)))),
inference(spm,[status(thm)],[21,45,theory(equality)]) ).
cnf(139,plain,
join(composition(converse(X2),X1),converse(X3)) = converse(join(composition(converse(X1),X2),X3)),
inference(spm,[status(thm)],[21,46,theory(equality)]) ).
cnf(214,plain,
join(zero,complement(join(zero,zero))) = join(complement(X1),complement(complement(X1))),
inference(spm,[status(thm)],[104,41,theory(equality)]) ).
cnf(215,negated_conjecture,
join(zero,complement(join(zero,zero))) = join(complement(esk3_0),complement(composition(esk1_0,esk2_0))),
inference(spm,[status(thm)],[104,47,theory(equality)]) ).
cnf(217,plain,
join(zero,complement(join(zero,zero))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[104,44,theory(equality)]) ).
cnf(262,plain,
join(X1,converse(join(X2,X3))) = join(converse(X3),join(X1,converse(X2))),
inference(spm,[status(thm)],[61,21,theory(equality)]) ).
cnf(319,negated_conjecture,
join(complement(esk3_0),complement(composition(esk1_0,esk2_0))) = join(zero,complement(zero)),
inference(rw,[status(thm)],[215,217,theory(equality)]) ).
cnf(337,plain,
join(zero,complement(join(zero,complement(complement(zero))))) = join(zero,complement(zero)),
inference(spm,[status(thm)],[88,44,theory(equality)]) ).
cnf(351,plain,
join(X1,complement(X2)) = join(complement(X2),join(X1,composition(converse(X3),complement(composition(X3,X2))))),
inference(spm,[status(thm)],[67,78,theory(equality)]) ).
cnf(742,plain,
join(zero,complement(zero)) = join(complement(X1),complement(complement(X1))),
inference(rw,[status(thm)],[214,217,theory(equality)]) ).
cnf(1719,plain,
join(converse(X1),composition(join(X2,converse(X4)),converse(X3))) = join(composition(X2,converse(X3)),converse(join(composition(X3,X4),X1))),
inference(spm,[status(thm)],[262,70,theory(equality)]) ).
cnf(1893,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)],[107,61,theory(equality)]),23,theory(equality)]) ).
cnf(1989,negated_conjecture,
join(complement(join(zero,complement(zero))),complement(join(complement(composition(esk1_0,esk2_0)),complement(complement(esk3_0))))) = composition(esk1_0,esk2_0),
inference(spm,[status(thm)],[99,319,theory(equality)]) ).
cnf(2036,negated_conjecture,
join(zero,complement(join(complement(complement(esk3_0)),complement(composition(esk1_0,esk2_0))))) = composition(esk1_0,esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1989,44,theory(equality)]),23,theory(equality)]) ).
cnf(2173,plain,
join(complement(join(complement(complement(X1)),X1)),complement(join(zero,complement(zero)))) = complement(X1),
inference(spm,[status(thm)],[100,742,theory(equality)]) ).
cnf(2226,plain,
join(zero,complement(join(X1,complement(complement(X1))))) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[2173,23,theory(equality)]),44,theory(equality)]),23,theory(equality)]) ).
cnf(2272,plain,
complement(zero) = join(zero,complement(zero)),
inference(rw,[status(thm)],[337,2226,theory(equality)]) ).
cnf(2273,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[88,2226,theory(equality)]) ).
cnf(2297,plain,
join(zero,complement(join(X1,X1))) = complement(X1),
inference(rw,[status(thm)],[2226,2273,theory(equality)]) ).
cnf(2298,negated_conjecture,
join(zero,complement(join(esk3_0,complement(composition(esk1_0,esk2_0))))) = composition(esk1_0,esk2_0),
inference(rw,[status(thm)],[2036,2273,theory(equality)]) ).
cnf(2303,plain,
join(X1,complement(join(complement(X1),complement(composition(converse(X2),complement(composition(X2,X1))))))) = X1,
inference(rw,[status(thm)],[96,2273,theory(equality)]) ).
cnf(2309,plain,
join(complement(X1),X1) = join(zero,complement(zero)),
inference(rw,[status(thm)],[742,2273,theory(equality)]) ).
cnf(2310,plain,
join(X1,complement(X1)) = join(zero,complement(zero)),
inference(rw,[status(thm)],[2309,23,theory(equality)]) ).
cnf(2388,plain,
join(X1,complement(X1)) = complement(zero),
inference(rw,[status(thm)],[2310,2272,theory(equality)]) ).
cnf(2389,plain,
join(complement(zero),X2) = join(X1,join(complement(X1),X2)),
inference(spm,[status(thm)],[33,2388,theory(equality)]) ).
cnf(2393,plain,
converse(complement(zero)) = join(X1,converse(complement(converse(X1)))),
inference(spm,[status(thm)],[49,2388,theory(equality)]) ).
cnf(2414,plain,
join(X1,complement(zero)) = join(X2,join(X1,complement(X2))),
inference(spm,[status(thm)],[67,2388,theory(equality)]) ).
cnf(2717,plain,
join(join(X1,X1),complement(X1)) = join(zero,complement(zero)),
inference(spm,[status(thm)],[2414,2297,theory(equality)]) ).
cnf(2777,plain,
join(X1,complement(zero)) = join(zero,complement(zero)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2717,33,theory(equality)]),2388,theory(equality)]) ).
cnf(2778,plain,
join(X1,complement(zero)) = complement(zero),
inference(rw,[status(thm)],[2777,2388,theory(equality)]) ).
cnf(2811,plain,
complement(zero) = join(complement(zero),X1),
inference(spm,[status(thm)],[23,2778,theory(equality)]) ).
cnf(2819,plain,
join(X1,join(X2,complement(X1))) = complement(zero),
inference(rw,[status(thm)],[2414,2778,theory(equality)]) ).
cnf(2894,plain,
complement(zero) = converse(complement(zero)),
inference(spm,[status(thm)],[2393,2811,theory(equality)]) ).
cnf(2982,plain,
join(X1,converse(complement(converse(X1)))) = complement(zero),
inference(rw,[status(thm)],[2393,2894,theory(equality)]) ).
cnf(3039,plain,
join(X1,complement(zero)) = join(join(X3,complement(X2)),join(X1,X2)),
inference(spm,[status(thm)],[61,2819,theory(equality)]) ).
cnf(3084,plain,
complement(zero) = join(join(X3,complement(X2)),join(X1,X2)),
inference(rw,[status(thm)],[3039,2778,theory(equality)]) ).
cnf(3085,plain,
complement(zero) = join(X3,complement(zero)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[3084,33,theory(equality)]),61,theory(equality)]),2389,theory(equality)]),2811,theory(equality)]) ).
cnf(3119,plain,
join(complement(X1),complement(join(complement(complement(join(complement(complement(X1)),complement(composition(converse(X2),complement(composition(X2,complement(X1)))))))),join(complement(X1),complement(complement(X1)))))) = complement(X1),
inference(spm,[status(thm)],[1893,2303,theory(equality)]) ).
cnf(3152,plain,
join(zero,complement(X1)) = 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[3119,2273,theory(equality)]),2273,theory(equality)]),23,theory(equality)]),2388,theory(equality)]),23,theory(equality)]),2811,theory(equality)]),2273,theory(equality)]),23,theory(equality)]) ).
cnf(3236,plain,
join(complement(complement(X1)),complement(join(complement(X1),complement(zero)))) = X1,
inference(spm,[status(thm)],[99,3152,theory(equality)]) ).
cnf(3237,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[3152,2273,theory(equality)]) ).
cnf(3246,negated_conjecture,
complement(join(esk3_0,complement(composition(esk1_0,esk2_0)))) = composition(esk1_0,esk2_0),
inference(rw,[status(thm)],[2298,3152,theory(equality)]) ).
cnf(3247,plain,
complement(join(X1,X1)) = complement(X1),
inference(rw,[status(thm)],[2297,3152,theory(equality)]) ).
cnf(3249,plain,
join(X1,zero) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[3236,2273,theory(equality)]),3085,theory(equality)]),2273,theory(equality)]) ).
cnf(3258,plain,
converse(converse(X1)) = join(X1,converse(zero)),
inference(spm,[status(thm)],[49,3249,theory(equality)]) ).
cnf(3279,plain,
X1 = join(X1,converse(zero)),
inference(rw,[status(thm)],[3258,17,theory(equality)]) ).
cnf(3355,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = join(X1,X1),
inference(spm,[status(thm)],[86,3247,theory(equality)]) ).
cnf(3389,plain,
X1 = join(X1,X1),
inference(rw,[status(thm)],[3355,86,theory(equality)]) ).
cnf(3421,plain,
join(X1,X2) = join(X1,join(X1,X2)),
inference(spm,[status(thm)],[33,3389,theory(equality)]) ).
cnf(3511,plain,
zero = converse(zero),
inference(spm,[status(thm)],[3237,3279,theory(equality)]) ).
cnf(3598,plain,
join(complement(complement(zero)),complement(join(complement(X1),complement(converse(complement(converse(complement(X1)))))))) = X1,
inference(spm,[status(thm)],[86,2982,theory(equality)]) ).
cnf(3630,plain,
complement(join(complement(X1),complement(converse(complement(converse(complement(X1))))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3598,2273,theory(equality)]),3237,theory(equality)]) ).
cnf(3680,negated_conjecture,
complement(composition(esk1_0,esk2_0)) = join(esk3_0,complement(composition(esk1_0,esk2_0))),
inference(spm,[status(thm)],[2273,3246,theory(equality)]) ).
cnf(4290,plain,
join(complement(join(complement(X1),X2)),X1) = X1,
inference(spm,[status(thm)],[3421,86,theory(equality)]) ).
cnf(4317,plain,
join(complement(join(X1,complement(X2))),X2) = X2,
inference(spm,[status(thm)],[3421,99,theory(equality)]) ).
cnf(4362,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[4290,23,theory(equality)]) ).
cnf(4396,plain,
join(X2,complement(join(X1,complement(X2)))) = X2,
inference(rw,[status(thm)],[4317,23,theory(equality)]) ).
cnf(4940,plain,
converse(join(X1,composition(X2,join(converse(X3),X4)))) = join(converse(X1),composition(join(X3,converse(X4)),converse(X2))),
inference(spm,[status(thm)],[122,50,theory(equality)]) ).
cnf(5588,plain,
converse(complement(zero)) = join(composition(converse(X2),X1),converse(join(X3,complement(composition(converse(X1),X2))))),
inference(spm,[status(thm)],[139,2819,theory(equality)]) ).
cnf(5658,plain,
complement(zero) = join(composition(converse(X2),X1),converse(join(X3,complement(composition(converse(X1),X2))))),
inference(rw,[status(thm)],[5588,2894,theory(equality)]) ).
cnf(5742,plain,
join(X1,complement(join(X2,join(X3,complement(X1))))) = X1,
inference(spm,[status(thm)],[4362,61,theory(equality)]) ).
cnf(5820,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[4396,2273,theory(equality)]) ).
cnf(13881,plain,
join(complement(join(join(X1,join(X2,complement(complement(X3)))),complement(X3))),complement(complement(X3))) = X3,
inference(spm,[status(thm)],[99,5742,theory(equality)]) ).
cnf(14005,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)],[13881,33,theory(equality)]),33,theory(equality)]),23,theory(equality)]),2388,theory(equality)]),2778,theory(equality)]),2778,theory(equality)]),2273,theory(equality)]),3237,theory(equality)]) ).
cnf(19525,plain,
complement(join(X1,complement(converse(complement(converse(X1)))))) = complement(X1),
inference(spm,[status(thm)],[3630,14005,theory(equality)]) ).
cnf(19583,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = join(X1,complement(converse(complement(converse(X1))))),
inference(spm,[status(thm)],[86,19525,theory(equality)]) ).
cnf(19662,plain,
X1 = join(X1,complement(converse(complement(converse(X1))))),
inference(rw,[status(thm)],[19583,86,theory(equality)]) ).
cnf(19728,plain,
converse(converse(X1)) = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(spm,[status(thm)],[49,19662,theory(equality)]) ).
cnf(19812,plain,
X1 = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(rw,[status(thm)],[19728,17,theory(equality)]) ).
cnf(19813,plain,
X1 = join(X1,converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[19812,17,theory(equality)]) ).
cnf(19913,plain,
join(complement(converse(complement(converse(complement(X1))))),complement(X1)) = complement(converse(complement(converse(complement(X1))))),
inference(spm,[status(thm)],[5820,19813,theory(equality)]) ).
cnf(19983,plain,
complement(X1) = complement(converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[19913,23,theory(equality)]),19662,theory(equality)]) ).
cnf(20381,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = converse(complement(converse(complement(X1)))),
inference(spm,[status(thm)],[86,19983,theory(equality)]) ).
cnf(20439,plain,
X1 = converse(complement(converse(complement(X1)))),
inference(rw,[status(thm)],[20381,86,theory(equality)]) ).
cnf(20656,plain,
converse(X1) = complement(converse(complement(X1))),
inference(spm,[status(thm)],[17,20439,theory(equality)]) ).
cnf(20787,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[14005,20656,theory(equality)]) ).
cnf(305262,plain,
converse(join(X1,composition(X4,join(converse(X2),X3)))) = join(composition(X2,converse(X4)),converse(join(composition(X4,X3),X1))),
inference(rw,[status(thm)],[1719,4940,theory(equality)]) ).
cnf(551976,plain,
complement(zero) = converse(join(complement(composition(converse(converse(X2)),X1)),composition(X2,join(converse(converse(X1)),X3)))),
inference(spm,[status(thm)],[305262,5658,theory(equality)]) ).
cnf(552571,plain,
complement(zero) = converse(join(complement(composition(X2,X1)),composition(X2,join(X1,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[551976,17,theory(equality)]),17,theory(equality)]) ).
cnf(552746,plain,
converse(complement(zero)) = join(complement(composition(X1,X2)),composition(X1,join(X2,X3))),
inference(spm,[status(thm)],[17,552571,theory(equality)]) ).
cnf(554144,plain,
complement(zero) = join(complement(composition(X1,X2)),composition(X1,join(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[552746,20787,theory(equality)]),3511,theory(equality)]) ).
cnf(555204,negated_conjecture,
join(complement(composition(X1,esk3_0)),composition(X1,complement(composition(esk1_0,esk2_0)))) = complement(zero),
inference(spm,[status(thm)],[554144,3680,theory(equality)]) ).
cnf(556884,negated_conjecture,
join(complement(esk2_0),complement(zero)) = join(complement(composition(converse(esk1_0),esk3_0)),complement(esk2_0)),
inference(spm,[status(thm)],[351,555204,theory(equality)]) ).
cnf(557102,negated_conjecture,
complement(zero) = join(complement(composition(converse(esk1_0),esk3_0)),complement(esk2_0)),
inference(rw,[status(thm)],[556884,3085,theory(equality)]) ).
cnf(557103,negated_conjecture,
complement(zero) = join(complement(esk2_0),complement(composition(converse(esk1_0),esk3_0))),
inference(rw,[status(thm)],[557102,23,theory(equality)]) ).
cnf(557472,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[43,557103,theory(equality)]),2273,theory(equality)]) ).
cnf(557473,negated_conjecture,
$false,
inference(cn,[status(thm)],[557472,theory(equality)]) ).
cnf(557474,negated_conjecture,
$false,
557473,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL010+1.p
% --creating new selector for [REL001+0.ax]
% -running prover on /tmp/tmpcvuTlx/sel_REL010+1.p_1 with time limit 29
% -prover status Theorem
% Problem REL010+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL010+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL010+1.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
%
%------------------------------------------------------------------------------