TSTP Solution File: REL012+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL012+2 : 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 01:04:05 EST 2010
% Result : Theorem 9.22s
% Output : CNFRefutation 9.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 10
% Syntax : Number of formulae : 143 ( 143 unt; 0 def)
% Number of atoms : 143 ( 140 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 295 ( 49 sgn 42 !; 4 ?)
% 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/tmpV4NUcT/sel_REL012+2.p_1',modular_law_1) ).
fof(3,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/tmp/tmpV4NUcT/sel_REL012+2.p_1',converse_multiplicativity) ).
fof(4,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmpV4NUcT/sel_REL012+2.p_1',converse_idempotence) ).
fof(6,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpV4NUcT/sel_REL012+2.p_1',converse_additivity) ).
fof(7,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpV4NUcT/sel_REL012+2.p_1',maddux1_join_commutativity) ).
fof(10,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/tmp/tmpV4NUcT/sel_REL012+2.p_1',converse_cancellativity) ).
fof(11,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmpV4NUcT/sel_REL012+2.p_1',maddux4_definiton_of_meet) ).
fof(12,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmpV4NUcT/sel_REL012+2.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/tmpV4NUcT/sel_REL012+2.p_1',maddux3_a_kind_of_de_Morgan) ).
fof(14,conjecture,
! [X1,X2] : join(composition(complement(composition(X1,X2)),converse(X2)),complement(X1)) = complement(X1),
file('/tmp/tmpV4NUcT/sel_REL012+2.p_1',goals) ).
fof(15,negated_conjecture,
~ ! [X1,X2] : join(composition(complement(composition(X1,X2)),converse(X2)),complement(X1)) = complement(X1),
inference(assume_negation,[status(cth)],[14]) ).
fof(18,plain,
! [X4,X5,X6] : join(meet(composition(X4,X5),X6),meet(composition(X4,meet(X5,composition(converse(X4),X6))),X6)) = meet(composition(X4,meet(X5,composition(converse(X4),X6))),X6),
inference(variable_rename,[status(thm)],[2]) ).
cnf(19,plain,
join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
inference(split_conjunct,[status(thm)],[18]) ).
fof(20,plain,
! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(21,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[20]) ).
fof(22,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[4]) ).
cnf(23,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[22]) ).
fof(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(composition(complement(composition(X1,X2)),converse(X2)),complement(X1)) != complement(X1),
inference(fof_nnf,[status(thm)],[15]) ).
fof(43,negated_conjecture,
? [X3,X4] : join(composition(complement(composition(X3,X4)),converse(X4)),complement(X3)) != complement(X3),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,negated_conjecture,
join(composition(complement(composition(esk1_0,esk2_0)),converse(esk2_0)),complement(esk1_0)) != complement(esk1_0),
inference(skolemize,[status(esa)],[43]) ).
cnf(45,negated_conjecture,
join(composition(complement(composition(esk1_0,esk2_0)),converse(esk2_0)),complement(esk1_0)) != complement(esk1_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,plain,
composition(X1,converse(X2)) = converse(composition(X2,converse(X1))),
inference(spm,[status(thm)],[21,23,theory(equality)]) ).
cnf(51,plain,
join(X1,converse(X2)) = converse(join(converse(X1),X2)),
inference(spm,[status(thm)],[27,23,theory(equality)]) ).
cnf(63,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[29,39,theory(equality)]) ).
cnf(65,plain,
join(join(X2,X1),X3) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[39,29,theory(equality)]) ).
cnf(69,plain,
join(X2,join(X1,X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[65,39,theory(equality)]) ).
cnf(71,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(rw,[status(thm)],[35,29,theory(equality)]) ).
cnf(72,plain,
join(complement(X1),composition(X2,complement(composition(converse(X2),X1)))) = complement(X1),
inference(spm,[status(thm)],[71,23,theory(equality)]) ).
cnf(86,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[41,29,theory(equality)]) ).
cnf(87,plain,
join(X1,X3) = join(complement(join(complement(X1),X2)),join(complement(join(complement(X1),complement(X2))),X3)),
inference(spm,[status(thm)],[39,86,theory(equality)]) ).
cnf(88,plain,
join(complement(complement(X1)),complement(join(complement(X1),complement(composition(converse(X2),complement(composition(X2,X1))))))) = X1,
inference(spm,[status(thm)],[86,71,theory(equality)]) ).
cnf(90,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(91,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[86,29,theory(equality)]) ).
cnf(92,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[86,29,theory(equality)]) ).
cnf(95,plain,
join(complement(X1),complement(join(complement(join(complement(X1),X2)),join(complement(X1),complement(X2))))) = join(complement(X1),X2),
inference(rw,[status(thm)],[90,29,theory(equality)]) ).
cnf(96,negated_conjecture,
join(complement(esk1_0),composition(complement(composition(esk1_0,esk2_0)),converse(esk2_0))) != complement(esk1_0),
inference(rw,[status(thm)],[45,29,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(104,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(336,plain,
join(complement(join(X3,join(complement(X1),X2))),complement(join(complement(X1),complement(join(X2,X3))))) = X1,
inference(spm,[status(thm)],[86,63,theory(equality)]) ).
cnf(438,plain,
join(complement(join(X2,join(complement(X1),X3))),complement(join(complement(X1),complement(join(X2,X3))))) = X1,
inference(spm,[status(thm)],[86,69,theory(equality)]) ).
cnf(440,plain,
join(X1,X2) = join(complement(join(complement(X2),X3)),join(X1,complement(join(complement(X2),complement(X3))))),
inference(spm,[status(thm)],[69,86,theory(equality)]) ).
cnf(1272,plain,
join(complement(join(complement(X1),X2)),X1) = join(X1,complement(join(complement(X1),complement(complement(X2))))),
inference(spm,[status(thm)],[87,86,theory(equality)]) ).
cnf(1324,plain,
join(X1,complement(join(complement(X1),X2))) = join(X1,complement(join(complement(X1),complement(complement(X2))))),
inference(rw,[status(thm)],[1272,29,theory(equality)]) ).
cnf(2362,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)],[95,63,theory(equality)]),29,theory(equality)]) ).
cnf(2715,plain,
join(complement(join(X1,complement(X2))),complement(join(complement(X1),complement(X2)))) = X2,
inference(spm,[status(thm)],[91,29,theory(equality)]) ).
cnf(3728,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),X3) = X3,
inference(spm,[status(thm)],[104,86,theory(equality)]) ).
cnf(3747,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),join(X3,X4)) = join(X3,X4),
inference(spm,[status(thm)],[104,87,theory(equality)]) ).
cnf(3807,plain,
join(X3,complement(join(complement(composition(X1,X2)),complement(X3)))) = X3,
inference(rw,[status(thm)],[3728,29,theory(equality)]) ).
cnf(3826,plain,
join(X3,join(complement(join(complement(composition(X1,X2)),complement(X3))),X4)) = join(X3,X4),
inference(rw,[status(thm)],[3747,69,theory(equality)]) ).
cnf(3899,plain,
join(X1,complement(join(complement(X1),complement(composition(X2,X3))))) = X1,
inference(spm,[status(thm)],[3807,29,theory(equality)]) ).
cnf(3903,plain,
join(X1,X2) = join(X2,join(X1,complement(join(complement(composition(X3,X4)),complement(X2))))),
inference(spm,[status(thm)],[69,3807,theory(equality)]) ).
cnf(10830,plain,
join(X1,X1) = join(X1,complement(join(complement(X1),complement(complement(composition(X2,X3)))))),
inference(spm,[status(thm)],[3826,91,theory(equality)]) ).
cnf(10932,plain,
join(X1,X1) = join(X1,complement(join(complement(X1),composition(X2,X3)))),
inference(rw,[status(thm)],[10830,1324,theory(equality)]) ).
cnf(11213,plain,
join(X1,complement(complement(X1))) = join(X1,X1),
inference(spm,[status(thm)],[10932,71,theory(equality)]) ).
cnf(11407,plain,
join(complement(join(X1,X1)),complement(join(complement(complement(X1)),complement(X1)))) = complement(X1),
inference(spm,[status(thm)],[91,11213,theory(equality)]) ).
cnf(11474,plain,
join(complement(join(X1,X1)),complement(join(complement(X1),complement(complement(X1))))) = complement(X1),
inference(rw,[status(thm)],[11407,29,theory(equality)]) ).
cnf(33367,plain,
join(X1,composition(X2,X3)) = join(complement(join(complement(composition(X2,X3)),X1)),X1),
inference(spm,[status(thm)],[3903,86,theory(equality)]) ).
cnf(33392,plain,
join(X1,composition(X2,X3)) = join(complement(join(X1,complement(composition(X2,X3)))),X1),
inference(spm,[status(thm)],[3903,91,theory(equality)]) ).
cnf(33517,plain,
join(X1,composition(X2,X3)) = join(X1,complement(join(complement(composition(X2,X3)),X1))),
inference(rw,[status(thm)],[33367,29,theory(equality)]) ).
cnf(33542,plain,
join(X1,composition(X2,X3)) = join(X1,complement(join(X1,complement(composition(X2,X3))))),
inference(rw,[status(thm)],[33392,29,theory(equality)]) ).
cnf(33869,plain,
join(X1,join(complement(X1),composition(X2,X3))) = join(complement(X1),X1),
inference(spm,[status(thm)],[3903,33517,theory(equality)]) ).
cnf(34119,plain,
join(X1,join(complement(X1),composition(X2,X3))) = join(X1,complement(X1)),
inference(rw,[status(thm)],[33869,29,theory(equality)]) ).
cnf(34231,plain,
join(X1,join(composition(X2,X3),complement(X1))) = join(X1,complement(X1)),
inference(spm,[status(thm)],[34119,29,theory(equality)]) ).
cnf(34234,plain,
join(X1,complement(X1)) = join(composition(X2,X3),join(X1,complement(X1))),
inference(spm,[status(thm)],[63,34119,theory(equality)]) ).
cnf(34453,plain,
join(X1,join(X2,complement(X2))) = join(join(composition(X3,X4),complement(X2)),join(X1,X2)),
inference(spm,[status(thm)],[63,34231,theory(equality)]) ).
cnf(34569,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)],[34453,39,theory(equality)]),63,theory(equality)]) ).
cnf(48137,plain,
join(complement(join(complement(X1),complement(X1))),complement(X1)) = join(complement(join(X1,X1)),X1),
inference(spm,[status(thm)],[440,11474,theory(equality)]) ).
cnf(48439,plain,
join(complement(X1),complement(join(complement(X1),complement(X1)))) = join(complement(join(X1,X1)),X1),
inference(rw,[status(thm)],[48137,29,theory(equality)]) ).
cnf(48440,plain,
join(complement(X1),complement(join(complement(X1),complement(X1)))) = join(X1,complement(join(X1,X1))),
inference(rw,[status(thm)],[48439,29,theory(equality)]) ).
cnf(70262,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)],[34569,88,theory(equality)]) ).
cnf(70630,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)],[70262,29,theory(equality)]),34234,theory(equality)]) ).
cnf(70631,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)],[70630,63,theory(equality)]),29,theory(equality)]),33542,theory(equality)]),71,theory(equality)]),29,theory(equality)]) ).
cnf(71317,plain,
join(complement(join(X1,X1)),complement(join(X1,complement(X1)))) = complement(X1),
inference(rw,[status(thm)],[11474,70631,theory(equality)]) ).
cnf(71432,plain,
complement(complement(X1)) = X1,
inference(spm,[status(thm)],[86,71317,theory(equality)]) ).
cnf(71578,plain,
join(complement(join(X1,X2)),complement(join(X1,complement(X2)))) = complement(X1),
inference(spm,[status(thm)],[86,71432,theory(equality)]) ).
cnf(71596,plain,
join(complement(join(X1,X2)),complement(join(complement(X2),X1))) = complement(X1),
inference(spm,[status(thm)],[92,71432,theory(equality)]) ).
cnf(71609,plain,
join(complement(X1),complement(join(complement(composition(X2,X3)),X1))) = complement(X1),
inference(spm,[status(thm)],[3807,71432,theory(equality)]) ).
cnf(74954,plain,
join(complement(join(X1,join(complement(X1),complement(composition(X2,X3))))),complement(complement(X1))) = X1,
inference(spm,[status(thm)],[336,71609,theory(equality)]) ).
cnf(75195,plain,
join(X1,complement(join(X1,join(complement(X1),complement(composition(X2,X3)))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[74954,71432,theory(equality)]),29,theory(equality)]) ).
cnf(116826,plain,
join(complement(X1),complement(join(complement(join(complement(complement(X1)),complement(composition(X2,X3)))),complement(X1)))) = join(complement(X1),join(complement(complement(X1)),complement(composition(X2,X3)))),
inference(spm,[status(thm)],[2362,75195,theory(equality)]) ).
cnf(117041,plain,
join(X1,complement(X1)) = join(complement(X1),join(complement(complement(X1)),complement(composition(X2,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[116826,29,theory(equality)]),3899,theory(equality)]),71432,theory(equality)]),29,theory(equality)]) ).
cnf(117042,plain,
join(X1,complement(X1)) = join(X1,join(complement(X1),complement(composition(X2,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[117041,71432,theory(equality)]),69,theory(equality)]) ).
cnf(117352,plain,
join(complement(join(X1,complement(X1))),complement(join(X1,complement(join(complement(X1),complement(composition(X2,X3))))))) = complement(X1),
inference(spm,[status(thm)],[71578,117042,theory(equality)]) ).
cnf(117432,plain,
join(X1,complement(join(X1,complement(X1)))) = X1,
inference(rw,[status(thm)],[75195,117042,theory(equality)]) ).
cnf(117509,plain,
join(complement(X1),complement(join(X1,complement(X1)))) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[117352,3899,theory(equality)]),29,theory(equality)]) ).
cnf(117608,plain,
join(complement(X1),complement(join(complement(complement(complement(X1))),complement(X1)))) = join(complement(X1),complement(complement(X1))),
inference(spm,[status(thm)],[2362,117432,theory(equality)]) ).
cnf(117782,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)],[117608,29,theory(equality)]),11213,theory(equality)]),48440,theory(equality)]) ).
cnf(117783,plain,
join(X1,complement(join(X1,X1))) = join(X1,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[117782,71432,theory(equality)]),29,theory(equality)]) ).
cnf(118074,plain,
join(complement(join(complement(X1),complement(X1))),complement(complement(X1))) = join(complement(complement(X1)),X1),
inference(spm,[status(thm)],[440,117509,theory(equality)]) ).
cnf(118216,plain,
join(X1,complement(join(complement(X1),complement(X1)))) = join(complement(complement(X1)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[118074,29,theory(equality)]),71432,theory(equality)]) ).
cnf(118217,plain,
join(X1,complement(join(complement(X1),complement(X1)))) = join(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[118216,29,theory(equality)]),71432,theory(equality)]) ).
cnf(118919,plain,
join(complement(join(complement(join(complement(complement(X1)),complement(complement(X1)))),X1)),complement(join(complement(X1),complement(X1)))) = complement(complement(join(complement(complement(X1)),complement(complement(X1))))),
inference(spm,[status(thm)],[71596,118217,theory(equality)]) ).
cnf(119189,plain,
X1 = complement(complement(join(complement(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)],[118919,29,theory(equality)]),71432,theory(equality)]),71432,theory(equality)]),117783,theory(equality)]),2715,theory(equality)]) ).
cnf(119190,plain,
X1 = join(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[119189,71432,theory(equality)]),71432,theory(equality)]),71432,theory(equality)]) ).
cnf(119270,plain,
join(X1,X2) = join(X1,join(X1,X2)),
inference(spm,[status(thm)],[39,119190,theory(equality)]) ).
cnf(120229,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = join(complement(join(complement(X1),X2)),X1),
inference(spm,[status(thm)],[440,119270,theory(equality)]) ).
cnf(120551,plain,
X1 = join(complement(join(complement(X1),X2)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[120229,71578,theory(equality)]),71432,theory(equality)]) ).
cnf(120552,plain,
X1 = join(X1,complement(join(complement(X1),X2))),
inference(rw,[status(thm)],[120551,29,theory(equality)]) ).
cnf(121448,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[120552,3903,theory(equality)]) ).
cnf(122085,plain,
join(complement(join(complement(X1),X2)),X2) = join(X2,X1),
inference(spm,[status(thm)],[440,121448,theory(equality)]) ).
cnf(122333,plain,
join(X2,complement(join(complement(X1),X2))) = join(X2,X1),
inference(rw,[status(thm)],[122085,29,theory(equality)]) ).
cnf(124133,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)],[34569,122333,theory(equality)]) ).
cnf(124134,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[122333,71432,theory(equality)]) ).
cnf(124480,plain,
join(X4,join(X3,complement(X3))) = join(complement(join(complement(X4),complement(X3))),join(X3,complement(X3))),
inference(rw,[status(thm)],[124133,34569,theory(equality)]) ).
cnf(124481,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)],[124480,63,theory(equality)]),29,theory(equality)]),121448,theory(equality)]),29,theory(equality)]) ).
cnf(124580,plain,
converse(join(X2,complement(X2))) = join(X1,converse(join(X2,complement(X2)))),
inference(spm,[status(thm)],[51,124481,theory(equality)]) ).
cnf(128140,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[124134,29,theory(equality)]) ).
cnf(139293,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)],[438,124580,theory(equality)]) ).
cnf(139434,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)],[139293,124580,theory(equality)]),124580,theory(equality)]),124134,theory(equality)]),71432,theory(equality)]) ).
cnf(139515,plain,
join(complement(join(X1,converse(complement(converse(X1))))),X2) = X2,
inference(spm,[status(thm)],[139434,51,theory(equality)]) ).
cnf(143754,plain,
complement(join(X1,complement(converse(complement(converse(X1)))))) = complement(X1),
inference(spm,[status(thm)],[71578,139515,theory(equality)]) ).
cnf(144502,plain,
join(complement(join(X1,join(complement(X2),X3))),complement(join(complement(X2),complement(join(X3,X1))))) = join(X2,complement(converse(complement(converse(X2))))),
inference(spm,[status(thm)],[336,143754,theory(equality)]) ).
cnf(144739,plain,
X2 = join(X2,complement(converse(complement(converse(X2))))),
inference(rw,[status(thm)],[144502,336,theory(equality)]) ).
cnf(144850,plain,
converse(converse(X1)) = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(spm,[status(thm)],[51,144739,theory(equality)]) ).
cnf(145041,plain,
X1 = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(rw,[status(thm)],[144850,23,theory(equality)]) ).
cnf(145042,plain,
X1 = join(X1,converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[145041,23,theory(equality)]) ).
cnf(145330,plain,
join(complement(join(converse(complement(converse(complement(complement(X1))))),X1)),complement(complement(X1))) = complement(converse(complement(converse(complement(complement(X1)))))),
inference(spm,[status(thm)],[71596,145042,theory(equality)]) ).
cnf(145449,plain,
X1 = complement(converse(complement(converse(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)],[145330,29,theory(equality)]),71432,theory(equality)]),71432,theory(equality)]),29,theory(equality)]),128140,theory(equality)]),144739,theory(equality)]) ).
cnf(145450,plain,
X1 = complement(converse(complement(converse(X1)))),
inference(rw,[status(thm)],[145449,71432,theory(equality)]) ).
cnf(145509,plain,
complement(converse(complement(X1))) = converse(X1),
inference(spm,[status(thm)],[145450,23,theory(equality)]) ).
cnf(146144,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[71432,145509,theory(equality)]) ).
cnf(146439,plain,
converse(composition(X1,complement(converse(X2)))) = composition(complement(X2),converse(X1)),
inference(spm,[status(thm)],[49,146144,theory(equality)]) ).
cnf(146441,plain,
converse(join(complement(converse(X1)),X2)) = join(complement(X1),converse(X2)),
inference(spm,[status(thm)],[51,146144,theory(equality)]) ).
cnf(152906,plain,
converse(complement(converse(X1))) = join(complement(X1),converse(composition(X2,complement(composition(converse(X2),converse(X1)))))),
inference(spm,[status(thm)],[146441,72,theory(equality)]) ).
cnf(153247,plain,
complement(X1) = join(complement(X1),converse(composition(X2,complement(composition(converse(X2),converse(X1)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[152906,146144,theory(equality)]),23,theory(equality)]) ).
cnf(153248,plain,
complement(X1) = join(complement(X1),composition(complement(composition(X1,X2)),converse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[153247,21,theory(equality)]),146439,theory(equality)]) ).
cnf(179770,negated_conjecture,
$false,
inference(rw,[status(thm)],[96,153248,theory(equality)]) ).
cnf(179771,negated_conjecture,
$false,
inference(cn,[status(thm)],[179770,theory(equality)]) ).
cnf(179772,negated_conjecture,
$false,
179771,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL012+2.p
% --creating new selector for [REL001+0.ax, REL001+1.ax]
% -running prover on /tmp/tmpV4NUcT/sel_REL012+2.p_1 with time limit 29
% -prover status Theorem
% Problem REL012+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL012+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL012+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
%
%------------------------------------------------------------------------------