TSTP Solution File: REL042+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL042+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 01:37:21 EST 2010
% Result : Theorem 12.22s
% Output : CNFRefutation 12.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 13
% Syntax : Number of formulae : 149 ( 143 unt; 0 def)
% Number of atoms : 155 ( 153 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 7 ~; 0 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 10 ( 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 : 212 ( 9 sgn 56 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/tmp/tmpfNXo0l/sel_REL042+1.p_1',converse_multiplicativity) ).
fof(2,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmpfNXo0l/sel_REL042+1.p_1',maddux4_definiton_of_meet) ).
fof(3,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmpfNXo0l/sel_REL042+1.p_1',converse_idempotence) ).
fof(4,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/tmp/tmpfNXo0l/sel_REL042+1.p_1',composition_distributivity) ).
fof(5,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpfNXo0l/sel_REL042+1.p_1',converse_additivity) ).
fof(6,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpfNXo0l/sel_REL042+1.p_1',maddux1_join_commutativity) ).
fof(7,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/tmp/tmpfNXo0l/sel_REL042+1.p_1',composition_associativity) ).
fof(8,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/tmp/tmpfNXo0l/sel_REL042+1.p_1',def_zero) ).
fof(9,axiom,
! [X1] : composition(X1,one) = X1,
file('/tmp/tmpfNXo0l/sel_REL042+1.p_1',composition_identity) ).
fof(10,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/tmp/tmpfNXo0l/sel_REL042+1.p_1',converse_cancellativity) ).
fof(11,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmpfNXo0l/sel_REL042+1.p_1',maddux2_join_associativity) ).
fof(12,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/tmp/tmpfNXo0l/sel_REL042+1.p_1',maddux3_a_kind_of_de_Morgan) ).
fof(13,conjecture,
! [X1] :
( ! [X2] : meet(composition(X1,X2),composition(X1,complement(X2))) = zero
=> join(composition(converse(X1),X1),one) = one ),
file('/tmp/tmpfNXo0l/sel_REL042+1.p_1',goals) ).
fof(14,negated_conjecture,
~ ! [X1] :
( ! [X2] : meet(composition(X1,X2),composition(X1,complement(X2))) = zero
=> join(composition(converse(X1),X1),one) = one ),
inference(assume_negation,[status(cth)],[13]) ).
fof(15,plain,
! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
inference(variable_rename,[status(thm)],[1]) ).
cnf(16,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[15]) ).
fof(17,plain,
! [X3,X4] : meet(X3,X4) = complement(join(complement(X3),complement(X4))),
inference(variable_rename,[status(thm)],[2]) ).
cnf(18,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[17]) ).
fof(19,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[3]) ).
cnf(20,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[19]) ).
fof(21,plain,
! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(22,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[5]) ).
cnf(24,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[23]) ).
fof(25,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[6]) ).
cnf(26,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[25]) ).
fof(27,plain,
! [X4,X5,X6] : composition(X4,composition(X5,X6)) = composition(composition(X4,X5),X6),
inference(variable_rename,[status(thm)],[7]) ).
cnf(28,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X2] : zero = meet(X2,complement(X2)),
inference(variable_rename,[status(thm)],[8]) ).
cnf(30,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X2] : composition(X2,one) = X2,
inference(variable_rename,[status(thm)],[9]) ).
cnf(32,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[31]) ).
fof(33,plain,
! [X3,X4] : join(composition(converse(X3),complement(composition(X3,X4))),complement(X4)) = complement(X4),
inference(variable_rename,[status(thm)],[10]) ).
cnf(34,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[33]) ).
fof(35,plain,
! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
inference(variable_rename,[status(thm)],[11]) ).
cnf(36,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X3,X4] : X3 = join(complement(join(complement(X3),complement(X4))),complement(join(complement(X3),X4))),
inference(variable_rename,[status(thm)],[12]) ).
cnf(38,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,negated_conjecture,
? [X1] :
( ! [X2] : meet(composition(X1,X2),composition(X1,complement(X2))) = zero
& join(composition(converse(X1),X1),one) != one ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(40,negated_conjecture,
? [X3] :
( ! [X4] : meet(composition(X3,X4),composition(X3,complement(X4))) = zero
& join(composition(converse(X3),X3),one) != one ),
inference(variable_rename,[status(thm)],[39]) ).
fof(41,negated_conjecture,
( ! [X4] : meet(composition(esk1_0,X4),composition(esk1_0,complement(X4))) = zero
& join(composition(converse(esk1_0),esk1_0),one) != one ),
inference(skolemize,[status(esa)],[40]) ).
fof(42,negated_conjecture,
! [X4] :
( meet(composition(esk1_0,X4),composition(esk1_0,complement(X4))) = zero
& join(composition(converse(esk1_0),esk1_0),one) != one ),
inference(shift_quantors,[status(thm)],[41]) ).
cnf(43,negated_conjecture,
join(composition(converse(esk1_0),esk1_0),one) != one,
inference(split_conjunct,[status(thm)],[42]) ).
cnf(44,negated_conjecture,
meet(composition(esk1_0,X1),composition(esk1_0,complement(X1))) = zero,
inference(split_conjunct,[status(thm)],[42]) ).
cnf(45,plain,
complement(join(complement(X1),complement(complement(X1)))) = zero,
inference(rw,[status(thm)],[30,18,theory(equality)]),
[unfolding] ).
cnf(46,negated_conjecture,
complement(join(complement(composition(esk1_0,X1)),complement(composition(esk1_0,complement(X1))))) = zero,
inference(rw,[status(thm)],[44,18,theory(equality)]),
[unfolding] ).
cnf(47,negated_conjecture,
join(one,composition(converse(esk1_0),esk1_0)) != one,
inference(rw,[status(thm)],[43,26,theory(equality)]) ).
cnf(49,plain,
composition(X1,converse(X2)) = converse(composition(X2,converse(X1))),
inference(spm,[status(thm)],[16,20,theory(equality)]) ).
cnf(50,plain,
composition(converse(X1),X2) = converse(composition(converse(X2),X1)),
inference(spm,[status(thm)],[16,20,theory(equality)]) ).
cnf(51,plain,
join(X1,converse(X2)) = converse(join(converse(X1),X2)),
inference(spm,[status(thm)],[24,20,theory(equality)]) ).
cnf(52,plain,
join(converse(X1),X2) = converse(join(X1,converse(X2))),
inference(spm,[status(thm)],[24,20,theory(equality)]) ).
cnf(59,plain,
composition(converse(composition(X2,X1)),X3) = composition(converse(X1),composition(converse(X2),X3)),
inference(spm,[status(thm)],[28,16,theory(equality)]) ).
cnf(66,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[26,36,theory(equality)]) ).
cnf(77,plain,
join(composition(X1,converse(X2)),converse(composition(X2,X3))) = composition(join(X1,converse(X3)),converse(X2)),
inference(spm,[status(thm)],[22,16,theory(equality)]) ).
cnf(89,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(rw,[status(thm)],[34,26,theory(equality)]) ).
cnf(93,plain,
join(complement(converse(X1)),composition(converse(converse(X2)),complement(converse(composition(X1,X2))))) = complement(converse(X1)),
inference(spm,[status(thm)],[89,16,theory(equality)]) ).
cnf(96,plain,
join(complement(converse(X1)),composition(X2,complement(converse(composition(X1,X2))))) = complement(converse(X1)),
inference(rw,[status(thm)],[93,20,theory(equality)]) ).
cnf(97,negated_conjecture,
complement(join(complement(esk1_0),complement(composition(esk1_0,complement(one))))) = zero,
inference(spm,[status(thm)],[46,32,theory(equality)]) ).
cnf(104,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[38,26,theory(equality)]) ).
cnf(115,plain,
join(complement(X1),complement(join(complement(join(complement(X1),X2)),complement(complement(join(complement(X1),complement(X2))))))) = join(complement(X1),X2),
inference(spm,[status(thm)],[104,104,theory(equality)]) ).
cnf(117,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[104,26,theory(equality)]) ).
cnf(118,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[104,26,theory(equality)]) ).
cnf(180,plain,
converse(converse(X1)) = composition(converse(one),X1),
inference(spm,[status(thm)],[50,32,theory(equality)]) ).
cnf(194,plain,
X1 = composition(converse(one),X1),
inference(rw,[status(thm)],[180,20,theory(equality)]) ).
cnf(206,plain,
one = converse(one),
inference(spm,[status(thm)],[32,194,theory(equality)]) ).
cnf(232,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[194,206,theory(equality)]) ).
cnf(240,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[22,232,theory(equality)]) ).
cnf(242,plain,
join(complement(X1),composition(converse(one),complement(X1))) = complement(X1),
inference(spm,[status(thm)],[89,232,theory(equality)]) ).
cnf(247,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[242,206,theory(equality)]),232,theory(equality)]) ).
cnf(277,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[247,45,theory(equality)]) ).
cnf(280,plain,
join(complement(complement(X1)),complement(join(complement(X1),complement(complement(X1))))) = X1,
inference(spm,[status(thm)],[104,247,theory(equality)]) ).
cnf(286,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[280,45,theory(equality)]),26,theory(equality)]) ).
cnf(290,plain,
join(zero,X1) = join(zero,join(zero,X1)),
inference(spm,[status(thm)],[36,277,theory(equality)]) ).
cnf(383,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[290,286,theory(equality)]) ).
cnf(398,plain,
join(complement(composition(converse(X1),X2)),composition(converse(converse(X3)),complement(composition(converse(composition(X1,X3)),X2)))) = complement(composition(converse(X1),X2)),
inference(spm,[status(thm)],[89,59,theory(equality)]) ).
cnf(422,plain,
join(complement(composition(converse(X1),X2)),composition(X3,complement(composition(converse(composition(X1,X3)),X2)))) = complement(composition(converse(X1),X2)),
inference(rw,[status(thm)],[398,20,theory(equality)]) ).
cnf(438,plain,
converse(converse(X1)) = join(converse(zero),X1),
inference(spm,[status(thm)],[52,383,theory(equality)]) ).
cnf(440,plain,
X1 = join(X1,zero),
inference(spm,[status(thm)],[26,383,theory(equality)]) ).
cnf(445,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[286,383,theory(equality)]) ).
cnf(449,plain,
X1 = join(converse(zero),X1),
inference(rw,[status(thm)],[438,20,theory(equality)]) ).
cnf(451,plain,
join(X1,composition(converse(X2),complement(composition(X2,complement(X1))))) = X1,
inference(spm,[status(thm)],[89,445,theory(equality)]) ).
cnf(456,negated_conjecture,
complement(zero) = join(complement(esk1_0),complement(composition(esk1_0,complement(one)))),
inference(spm,[status(thm)],[445,97,theory(equality)]) ).
cnf(457,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[247,445,theory(equality)]) ).
cnf(458,plain,
complement(join(X1,complement(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[45,445,theory(equality)]),26,theory(equality)]) ).
cnf(496,plain,
complement(zero) = join(X1,complement(X1)),
inference(spm,[status(thm)],[445,458,theory(equality)]) ).
cnf(565,plain,
join(X1,X2) = join(X1,join(X1,X2)),
inference(spm,[status(thm)],[36,457,theory(equality)]) ).
cnf(599,plain,
zero = converse(zero),
inference(spm,[status(thm)],[440,449,theory(equality)]) ).
cnf(653,plain,
converse(complement(zero)) = join(X1,converse(complement(converse(X1)))),
inference(spm,[status(thm)],[51,496,theory(equality)]) ).
cnf(708,plain,
join(X1,X2) = join(X2,join(X1,X2)),
inference(spm,[status(thm)],[66,457,theory(equality)]) ).
cnf(842,plain,
join(complement(join(complement(X1),X2)),X1) = X1,
inference(spm,[status(thm)],[565,104,theory(equality)]) ).
cnf(851,plain,
join(X1,complement(zero)) = complement(zero),
inference(spm,[status(thm)],[565,496,theory(equality)]) ).
cnf(870,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[842,26,theory(equality)]) ).
cnf(890,plain,
converse(complement(zero)) = join(X1,converse(complement(zero))),
inference(spm,[status(thm)],[51,851,theory(equality)]) ).
cnf(894,plain,
complement(zero) = join(complement(zero),X1),
inference(spm,[status(thm)],[26,851,theory(equality)]) ).
cnf(1153,plain,
converse(complement(zero)) = complement(zero),
inference(spm,[status(thm)],[894,890,theory(equality)]) ).
cnf(1182,plain,
composition(converse(X1),complement(zero)) = converse(composition(complement(zero),X1)),
inference(spm,[status(thm)],[16,1153,theory(equality)]) ).
cnf(1250,negated_conjecture,
join(complement(complement(zero)),complement(join(complement(esk1_0),complement(complement(composition(esk1_0,complement(one))))))) = esk1_0,
inference(spm,[status(thm)],[104,456,theory(equality)]) ).
cnf(1261,negated_conjecture,
complement(join(complement(esk1_0),composition(esk1_0,complement(one)))) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1250,445,theory(equality)]),445,theory(equality)]),383,theory(equality)]) ).
cnf(1281,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(spm,[status(thm)],[870,445,theory(equality)]) ).
cnf(1291,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[870,708,theory(equality)]) ).
cnf(1336,negated_conjecture,
complement(esk1_0) = join(complement(esk1_0),composition(esk1_0,complement(one))),
inference(spm,[status(thm)],[445,1261,theory(equality)]) ).
cnf(2069,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[1291,445,theory(equality)]) ).
cnf(2420,plain,
join(X1,converse(complement(converse(X1)))) = complement(zero),
inference(rw,[status(thm)],[653,1153,theory(equality)]) ).
cnf(3167,plain,
join(complement(converse(X1)),complement(converse(join(X1,X2)))) = complement(converse(X1)),
inference(spm,[status(thm)],[1281,24,theory(equality)]) ).
cnf(3413,plain,
join(complement(complement(zero)),composition(X1,complement(converse(composition(complement(zero),X1))))) = complement(complement(zero)),
inference(spm,[status(thm)],[96,1153,theory(equality)]) ).
cnf(3451,plain,
composition(X1,complement(composition(converse(X1),complement(zero)))) = complement(complement(zero)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[3413,445,theory(equality)]),1182,theory(equality)]),383,theory(equality)]) ).
cnf(3452,plain,
composition(X1,complement(composition(converse(X1),complement(zero)))) = zero,
inference(rw,[status(thm)],[3451,445,theory(equality)]) ).
cnf(3500,negated_conjecture,
join(complement(composition(esk1_0,complement(one))),complement(complement(esk1_0))) = complement(composition(esk1_0,complement(one))),
inference(spm,[status(thm)],[2069,1336,theory(equality)]) ).
cnf(3563,negated_conjecture,
join(esk1_0,complement(composition(esk1_0,complement(one)))) = complement(composition(esk1_0,complement(one))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3500,445,theory(equality)]),26,theory(equality)]) ).
cnf(4262,plain,
join(composition(X1,converse(X2)),converse(zero)) = composition(join(X1,converse(complement(composition(converse(X2),complement(zero))))),converse(X2)),
inference(spm,[status(thm)],[77,3452,theory(equality)]) ).
cnf(4301,plain,
composition(X1,converse(X2)) = composition(join(X1,converse(complement(composition(converse(X2),complement(zero))))),converse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[4262,599,theory(equality)]),440,theory(equality)]) ).
cnf(5139,plain,
join(X1,composition(complement(one),X1)) = composition(complement(zero),X1),
inference(spm,[status(thm)],[240,496,theory(equality)]) ).
cnf(5728,plain,
join(complement(X1),complement(join(complement(X1),complement(X2)))) = join(complement(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[115,445,theory(equality)]),26,theory(equality)]),36,theory(equality)]),2069,theory(equality)]) ).
cnf(5733,plain,
join(X1,complement(join(X1,complement(X2)))) = join(X1,X2),
inference(spm,[status(thm)],[5728,445,theory(equality)]) ).
cnf(6098,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[5733,445,theory(equality)]) ).
cnf(6252,plain,
join(X1,complement(complement(zero))) = join(X1,complement(converse(complement(converse(X1))))),
inference(spm,[status(thm)],[6098,2420,theory(equality)]) ).
cnf(6348,plain,
X1 = join(X1,complement(converse(complement(converse(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[6252,445,theory(equality)]),440,theory(equality)]) ).
cnf(6548,plain,
join(complement(join(X1,X2)),complement(join(X2,complement(X1)))) = complement(X2),
inference(spm,[status(thm)],[117,445,theory(equality)]) ).
cnf(6663,plain,
converse(converse(X1)) = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(spm,[status(thm)],[51,6348,theory(equality)]) ).
cnf(6706,plain,
X1 = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(rw,[status(thm)],[6663,20,theory(equality)]) ).
cnf(6707,plain,
X1 = join(X1,converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[6706,20,theory(equality)]) ).
cnf(6768,plain,
join(complement(converse(complement(converse(complement(X1))))),complement(X1)) = complement(converse(complement(converse(complement(X1))))),
inference(spm,[status(thm)],[2069,6707,theory(equality)]) ).
cnf(6802,plain,
complement(X1) = complement(converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[6768,26,theory(equality)]),6348,theory(equality)]) ).
cnf(6817,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = converse(complement(converse(complement(X1)))),
inference(spm,[status(thm)],[104,6802,theory(equality)]) ).
cnf(6852,plain,
X1 = converse(complement(converse(complement(X1)))),
inference(rw,[status(thm)],[6817,104,theory(equality)]) ).
cnf(6877,plain,
converse(X1) = complement(converse(complement(X1))),
inference(spm,[status(thm)],[20,6852,theory(equality)]) ).
cnf(6922,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[445,6877,theory(equality)]) ).
cnf(6972,plain,
composition(complement(converse(X1)),converse(X2)) = converse(composition(X2,complement(X1))),
inference(spm,[status(thm)],[16,6922,theory(equality)]) ).
cnf(6977,plain,
converse(composition(X1,complement(converse(X2)))) = composition(complement(X2),converse(X1)),
inference(spm,[status(thm)],[49,6922,theory(equality)]) ).
cnf(12420,plain,
composition(complement(one),converse(X1)) = converse(composition(X1,complement(one))),
inference(spm,[status(thm)],[6972,206,theory(equality)]) ).
cnf(23658,plain,
converse(converse(X1)) = join(X1,converse(composition(converse(X2),complement(composition(X2,complement(converse(X1))))))),
inference(spm,[status(thm)],[51,451,theory(equality)]) ).
cnf(23765,plain,
X1 = join(X1,converse(composition(converse(X2),complement(composition(X2,complement(converse(X1))))))),
inference(rw,[status(thm)],[23658,20,theory(equality)]) ).
cnf(23766,plain,
X1 = join(X1,composition(complement(composition(complement(X1),converse(X2))),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[23765,50,theory(equality)]),6922,theory(equality)]),6977,theory(equality)]) ).
cnf(28745,plain,
join(complement(complement(composition(converse(X1),X2))),complement(join(complement(composition(converse(X1),X2)),complement(composition(X3,complement(composition(converse(composition(X1,X3)),X2))))))) = composition(converse(X1),X2),
inference(spm,[status(thm)],[104,422,theory(equality)]) ).
cnf(28874,plain,
complement(complement(composition(converse(X1),X2))) = composition(converse(X1),X2),
inference(rw,[status(thm)],[28745,1281,theory(equality)]) ).
cnf(29035,plain,
complement(complement(composition(X1,X2))) = composition(X1,X2),
inference(spm,[status(thm)],[28874,20,theory(equality)]) ).
cnf(79854,negated_conjecture,
join(complement(converse(esk1_0)),complement(converse(complement(composition(esk1_0,complement(one)))))) = complement(converse(esk1_0)),
inference(spm,[status(thm)],[3167,3563,theory(equality)]) ).
cnf(80186,negated_conjecture,
join(complement(converse(esk1_0)),composition(complement(one),converse(esk1_0))) = complement(converse(esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[79854,6922,theory(equality)]),12420,theory(equality)]),29035,theory(equality)]) ).
cnf(80529,negated_conjecture,
join(complement(complement(converse(esk1_0))),complement(join(complement(composition(complement(one),converse(esk1_0))),complement(converse(esk1_0))))) = converse(esk1_0),
inference(spm,[status(thm)],[118,80186,theory(equality)]) ).
cnf(80569,negated_conjecture,
complement(complement(converse(esk1_0))) = converse(esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[80529,26,theory(equality)]),1281,theory(equality)]) ).
cnf(94579,negated_conjecture,
join(complement(complement(converse(esk1_0))),complement(join(composition(complement(one),converse(esk1_0)),complement(complement(converse(esk1_0)))))) = complement(composition(complement(one),converse(esk1_0))),
inference(spm,[status(thm)],[6548,80186,theory(equality)]) ).
cnf(95054,negated_conjecture,
join(converse(esk1_0),complement(composition(complement(zero),converse(esk1_0)))) = complement(composition(complement(one),converse(esk1_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[94579,80569,theory(equality)]),80569,theory(equality)]),26,theory(equality)]),5139,theory(equality)]) ).
cnf(386445,plain,
composition(join(X1,complement(composition(complement(zero),X2))),converse(X2)) = composition(X1,converse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[4301,6922,theory(equality)]),50,theory(equality)]),6922,theory(equality)]),599,theory(equality)]) ).
cnf(386587,negated_conjecture,
composition(complement(composition(complement(one),converse(esk1_0))),converse(converse(esk1_0))) = composition(converse(esk1_0),converse(converse(esk1_0))),
inference(spm,[status(thm)],[386445,95054,theory(equality)]) ).
cnf(386870,negated_conjecture,
composition(complement(composition(complement(one),converse(esk1_0))),esk1_0) = composition(converse(esk1_0),converse(converse(esk1_0))),
inference(rw,[status(thm)],[386587,20,theory(equality)]) ).
cnf(386871,negated_conjecture,
composition(complement(composition(complement(one),converse(esk1_0))),esk1_0) = composition(converse(esk1_0),esk1_0),
inference(rw,[status(thm)],[386870,20,theory(equality)]) ).
cnf(388300,negated_conjecture,
join(one,composition(converse(esk1_0),esk1_0)) = one,
inference(spm,[status(thm)],[23766,386871,theory(equality)]) ).
cnf(388427,negated_conjecture,
$false,
inference(sr,[status(thm)],[388300,47,theory(equality)]) ).
cnf(388428,negated_conjecture,
$false,
388427,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL042+1.p
% --creating new selector for [REL001+0.ax]
% -running prover on /tmp/tmpfNXo0l/sel_REL042+1.p_1 with time limit 29
% -prover status Theorem
% Problem REL042+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL042+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL042+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
%
%------------------------------------------------------------------------------