TSTP Solution File: REL024+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL024+2 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 01:16:00 EST 2010
% Result : Theorem 4.80s
% Output : CNFRefutation 4.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 11
% Syntax : Number of formulae : 103 ( 103 unt; 0 def)
% Number of atoms : 103 ( 100 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 247 ( 32 sgn 50 !; 6 ?)
% 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/tmp953qXv/sel_REL024+2.p_1',modular_law_1) ).
fof(3,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/tmp/tmp953qXv/sel_REL024+2.p_1',converse_multiplicativity) ).
fof(4,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmp953qXv/sel_REL024+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/tmp953qXv/sel_REL024+2.p_1',composition_distributivity) ).
fof(6,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmp953qXv/sel_REL024+2.p_1',converse_additivity) ).
fof(7,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmp953qXv/sel_REL024+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/tmp953qXv/sel_REL024+2.p_1',converse_cancellativity) ).
fof(11,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmp953qXv/sel_REL024+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/tmp953qXv/sel_REL024+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/tmp953qXv/sel_REL024+2.p_1',maddux3_a_kind_of_de_Morgan) ).
fof(14,conjecture,
! [X1,X2,X3] : join(composition(meet(X1,converse(X2)),meet(X2,X3)),composition(meet(X1,converse(X2)),X3)) = composition(meet(X1,converse(X2)),X3),
file('/tmp/tmp953qXv/sel_REL024+2.p_1',goals) ).
fof(15,negated_conjecture,
~ ! [X1,X2,X3] : join(composition(meet(X1,converse(X2)),meet(X2,X3)),composition(meet(X1,converse(X2)),X3)) = composition(meet(X1,converse(X2)),X3),
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(24,plain,
! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
inference(variable_rename,[status(thm)],[5]) ).
cnf(25,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[24]) ).
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,X3] : join(composition(meet(X1,converse(X2)),meet(X2,X3)),composition(meet(X1,converse(X2)),X3)) != composition(meet(X1,converse(X2)),X3),
inference(fof_nnf,[status(thm)],[15]) ).
fof(43,negated_conjecture,
? [X4,X5,X6] : join(composition(meet(X4,converse(X5)),meet(X5,X6)),composition(meet(X4,converse(X5)),X6)) != composition(meet(X4,converse(X5)),X6),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,negated_conjecture,
join(composition(meet(esk1_0,converse(esk2_0)),meet(esk2_0,esk3_0)),composition(meet(esk1_0,converse(esk2_0)),esk3_0)) != composition(meet(esk1_0,converse(esk2_0)),esk3_0),
inference(skolemize,[status(esa)],[43]) ).
cnf(45,negated_conjecture,
join(composition(meet(esk1_0,converse(esk2_0)),meet(esk2_0,esk3_0)),composition(meet(esk1_0,converse(esk2_0)),esk3_0)) != composition(meet(esk1_0,converse(esk2_0)),esk3_0),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(46,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3)))) = complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[19,37,theory(equality)]),37,theory(equality)]),37,theory(equality)]),37,theory(equality)]),37,theory(equality)]),
[unfolding] ).
cnf(49,negated_conjecture,
join(composition(complement(join(complement(esk1_0),complement(converse(esk2_0)))),complement(join(complement(esk2_0),complement(esk3_0)))),composition(complement(join(complement(esk1_0),complement(converse(esk2_0)))),esk3_0)) != composition(complement(join(complement(esk1_0),complement(converse(esk2_0)))),esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[45,37,theory(equality)]),37,theory(equality)]),37,theory(equality)]),37,theory(equality)]),
[unfolding] ).
cnf(51,plain,
composition(converse(X1),X2) = converse(composition(converse(X2),X1)),
inference(spm,[status(thm)],[21,23,theory(equality)]) ).
cnf(64,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[29,39,theory(equality)]) ).
cnf(66,plain,
join(join(X2,X1),X3) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[39,29,theory(equality)]) ).
cnf(70,plain,
join(X2,join(X1,X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[66,39,theory(equality)]) ).
cnf(72,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(rw,[status(thm)],[35,29,theory(equality)]) ).
cnf(79,plain,
join(composition(X1,converse(X2)),converse(composition(X2,X3))) = composition(join(X1,converse(X3)),converse(X2)),
inference(spm,[status(thm)],[25,21,theory(equality)]) ).
cnf(87,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[41,29,theory(equality)]) ).
cnf(88,plain,
join(X1,X3) = join(complement(join(complement(X1),X2)),join(complement(join(complement(X1),complement(X2))),X3)),
inference(spm,[status(thm)],[39,87,theory(equality)]) ).
cnf(89,plain,
join(complement(complement(X1)),complement(join(complement(X1),complement(composition(converse(X2),complement(composition(X2,X1))))))) = X1,
inference(spm,[status(thm)],[87,72,theory(equality)]) ).
cnf(92,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[87,29,theory(equality)]) ).
cnf(93,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[87,29,theory(equality)]) ).
cnf(97,negated_conjecture,
join(composition(complement(join(complement(esk1_0),complement(converse(esk2_0)))),esk3_0),composition(complement(join(complement(esk1_0),complement(converse(esk2_0)))),complement(join(complement(esk2_0),complement(esk3_0))))) != composition(complement(join(complement(esk1_0),complement(converse(esk2_0)))),esk3_0),
inference(rw,[status(thm)],[49,29,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(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3))),
inference(rw,[status(thm)],[46,29,theory(equality)]) ).
cnf(99,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)],[98,29,theory(equality)]) ).
cnf(105,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)],[39,99,theory(equality)]) ).
cnf(187,plain,
join(composition(converse(X2),X1),converse(X3)) = converse(join(composition(converse(X1),X2),X3)),
inference(spm,[status(thm)],[27,51,theory(equality)]) ).
cnf(441,plain,
join(X1,X2) = join(complement(join(complement(X2),X3)),join(X1,complement(join(complement(X2),complement(X3))))),
inference(spm,[status(thm)],[70,87,theory(equality)]) ).
cnf(1273,plain,
join(complement(join(complement(X1),X2)),X1) = join(X1,complement(join(complement(X1),complement(complement(X2))))),
inference(spm,[status(thm)],[88,87,theory(equality)]) ).
cnf(1325,plain,
join(X1,complement(join(complement(X1),X2))) = join(X1,complement(join(complement(X1),complement(complement(X2))))),
inference(rw,[status(thm)],[1273,29,theory(equality)]) ).
cnf(1693,plain,
converse(composition(join(converse(X1),converse(X3)),converse(X2))) = join(composition(converse(converse(X2)),X1),converse(converse(composition(X2,X3)))),
inference(spm,[status(thm)],[187,79,theory(equality)]) ).
cnf(1743,plain,
composition(X2,join(X1,X3)) = join(composition(converse(converse(X2)),X1),converse(converse(composition(X2,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1693,27,theory(equality)]),21,theory(equality)]),23,theory(equality)]) ).
cnf(1744,plain,
composition(X2,join(X1,X3)) = join(composition(X2,X1),composition(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1743,23,theory(equality)]),23,theory(equality)]) ).
cnf(1773,negated_conjecture,
composition(complement(join(complement(esk1_0),complement(converse(esk2_0)))),join(esk3_0,complement(join(complement(esk2_0),complement(esk3_0))))) != composition(complement(join(complement(esk1_0),complement(converse(esk2_0)))),esk3_0),
inference(rw,[status(thm)],[97,1744,theory(equality)]) ).
cnf(3457,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),X3) = X3,
inference(spm,[status(thm)],[105,87,theory(equality)]) ).
cnf(3476,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),join(X3,X4)) = join(X3,X4),
inference(spm,[status(thm)],[105,88,theory(equality)]) ).
cnf(3533,plain,
join(X3,complement(join(complement(composition(X1,X2)),complement(X3)))) = X3,
inference(rw,[status(thm)],[3457,29,theory(equality)]) ).
cnf(3552,plain,
join(X3,join(complement(join(complement(composition(X1,X2)),complement(X3))),X4)) = join(X3,X4),
inference(rw,[status(thm)],[3476,70,theory(equality)]) ).
cnf(3627,plain,
join(X1,X2) = join(X2,join(X1,complement(join(complement(composition(X3,X4)),complement(X2))))),
inference(spm,[status(thm)],[70,3533,theory(equality)]) ).
cnf(10832,plain,
join(X1,X1) = join(X1,complement(join(complement(X1),complement(complement(composition(X2,X3)))))),
inference(spm,[status(thm)],[3552,92,theory(equality)]) ).
cnf(10934,plain,
join(X1,X1) = join(X1,complement(join(complement(X1),composition(X2,X3)))),
inference(rw,[status(thm)],[10832,1325,theory(equality)]) ).
cnf(11215,plain,
join(X1,complement(complement(X1))) = join(X1,X1),
inference(spm,[status(thm)],[10934,72,theory(equality)]) ).
cnf(11409,plain,
join(complement(join(X1,X1)),complement(join(complement(complement(X1)),complement(X1)))) = complement(X1),
inference(spm,[status(thm)],[92,11215,theory(equality)]) ).
cnf(11476,plain,
join(complement(join(X1,X1)),complement(join(complement(X1),complement(complement(X1))))) = complement(X1),
inference(rw,[status(thm)],[11409,29,theory(equality)]) ).
cnf(33373,plain,
join(X1,composition(X2,X3)) = join(complement(join(complement(composition(X2,X3)),X1)),X1),
inference(spm,[status(thm)],[3627,87,theory(equality)]) ).
cnf(33398,plain,
join(X1,composition(X2,X3)) = join(complement(join(X1,complement(composition(X2,X3)))),X1),
inference(spm,[status(thm)],[3627,92,theory(equality)]) ).
cnf(33523,plain,
join(X1,composition(X2,X3)) = join(X1,complement(join(complement(composition(X2,X3)),X1))),
inference(rw,[status(thm)],[33373,29,theory(equality)]) ).
cnf(33548,plain,
join(X1,composition(X2,X3)) = join(X1,complement(join(X1,complement(composition(X2,X3))))),
inference(rw,[status(thm)],[33398,29,theory(equality)]) ).
cnf(33874,plain,
join(X1,join(complement(X1),composition(X2,X3))) = join(complement(X1),X1),
inference(spm,[status(thm)],[3627,33523,theory(equality)]) ).
cnf(34124,plain,
join(X1,join(complement(X1),composition(X2,X3))) = join(X1,complement(X1)),
inference(rw,[status(thm)],[33874,29,theory(equality)]) ).
cnf(34236,plain,
join(X1,join(composition(X2,X3),complement(X1))) = join(X1,complement(X1)),
inference(spm,[status(thm)],[34124,29,theory(equality)]) ).
cnf(34239,plain,
join(X1,complement(X1)) = join(composition(X2,X3),join(X1,complement(X1))),
inference(spm,[status(thm)],[64,34124,theory(equality)]) ).
cnf(34459,plain,
join(X1,join(X2,complement(X2))) = join(join(composition(X3,X4),complement(X2)),join(X1,X2)),
inference(spm,[status(thm)],[64,34236,theory(equality)]) ).
cnf(34575,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)],[34459,39,theory(equality)]),64,theory(equality)]) ).
cnf(71029,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)],[34575,89,theory(equality)]) ).
cnf(71399,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)],[71029,29,theory(equality)]),34239,theory(equality)]) ).
cnf(71400,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)],[71399,64,theory(equality)]),29,theory(equality)]),33548,theory(equality)]),72,theory(equality)]),29,theory(equality)]) ).
cnf(72091,plain,
join(complement(join(X1,X1)),complement(join(X1,complement(X1)))) = complement(X1),
inference(rw,[status(thm)],[11476,71400,theory(equality)]) ).
cnf(72206,plain,
complement(complement(X1)) = X1,
inference(spm,[status(thm)],[87,72091,theory(equality)]) ).
cnf(72370,plain,
join(complement(join(X1,X2)),complement(join(complement(X2),X1))) = complement(X1),
inference(spm,[status(thm)],[93,72206,theory(equality)]) ).
cnf(74012,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)],[72370,3533,theory(equality)]) ).
cnf(74406,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)],[74012,29,theory(equality)]),72206,theory(equality)]),33523,theory(equality)]),72206,theory(equality)]),29,theory(equality)]) ).
cnf(74407,plain,
join(X3,complement(join(X3,composition(X1,X2)))) = join(complement(composition(X1,X2)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[74406,72206,theory(equality)]),72206,theory(equality)]) ).
cnf(77361,plain,
join(complement(join(complement(composition(X1,X2)),composition(X3,X4))),complement(join(complement(composition(X3,X4)),complement(composition(X1,X2))))) = join(complement(join(complement(composition(X1,X2)),composition(X3,X4))),composition(X1,X2)),
inference(spm,[status(thm)],[33523,74407,theory(equality)]) ).
cnf(77546,plain,
composition(X1,X2) = join(complement(join(complement(composition(X1,X2)),composition(X3,X4))),composition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[77361,72370,theory(equality)]),72206,theory(equality)]) ).
cnf(77547,plain,
composition(X1,X2) = composition(X1,join(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[77546,29,theory(equality)]),10934,theory(equality)]),1744,theory(equality)]) ).
cnf(77646,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(join(X2,X2),X3)),
inference(spm,[status(thm)],[1744,77547,theory(equality)]) ).
cnf(77929,plain,
composition(X1,join(X2,X3)) = composition(X1,join(join(X2,X2),X3)),
inference(rw,[status(thm)],[77646,1744,theory(equality)]) ).
cnf(77930,plain,
composition(X1,join(X2,X3)) = composition(X1,join(X2,join(X2,X3))),
inference(rw,[status(thm)],[77929,39,theory(equality)]) ).
cnf(81007,plain,
composition(X1,join(complement(join(complement(X2),X3)),X2)) = composition(X1,join(complement(join(complement(X2),X3)),complement(join(complement(X2),complement(X3))))),
inference(spm,[status(thm)],[77930,441,theory(equality)]) ).
cnf(81397,plain,
composition(X1,join(X2,complement(join(complement(X2),X3)))) = composition(X1,join(complement(join(complement(X2),X3)),complement(join(complement(X2),complement(X3))))),
inference(rw,[status(thm)],[81007,29,theory(equality)]) ).
cnf(81398,plain,
composition(X1,join(X2,complement(join(complement(X2),X3)))) = composition(X1,X2),
inference(rw,[status(thm)],[81397,87,theory(equality)]) ).
cnf(85858,plain,
composition(X1,join(X2,complement(join(X3,complement(X2))))) = composition(X1,X2),
inference(spm,[status(thm)],[81398,3627,theory(equality)]) ).
cnf(89282,negated_conjecture,
$false,
inference(rw,[status(thm)],[1773,85858,theory(equality)]) ).
cnf(89283,negated_conjecture,
$false,
inference(cn,[status(thm)],[89282,theory(equality)]) ).
cnf(89284,negated_conjecture,
$false,
89283,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL024+2.p
% --creating new selector for [REL001+0.ax, REL001+1.ax]
% -running prover on /tmp/tmp953qXv/sel_REL024+2.p_1 with time limit 29
% -prover status Theorem
% Problem REL024+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL024+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL024+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
%
%------------------------------------------------------------------------------