TSTP Solution File: REL041+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL041+2 : 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 01:37:06 EST 2010
% Result : Theorem 11.39s
% Output : CNFRefutation 11.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 14
% Syntax : Number of formulae : 135 ( 130 unt; 0 def)
% Number of atoms : 140 ( 137 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 0 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 13 ( 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 : 209 ( 18 sgn 58 !; 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/tmpZUNTu3/sel_REL041+2.p_1',modular_law_1) ).
fof(3,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/tmp/tmpZUNTu3/sel_REL041+2.p_1',converse_multiplicativity) ).
fof(4,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmpZUNTu3/sel_REL041+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/tmpZUNTu3/sel_REL041+2.p_1',composition_distributivity) ).
fof(6,axiom,
! [X1] : composition(X1,one) = X1,
file('/tmp/tmpZUNTu3/sel_REL041+2.p_1',composition_identity) ).
fof(7,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmpZUNTu3/sel_REL041+2.p_1',converse_additivity) ).
fof(8,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmpZUNTu3/sel_REL041+2.p_1',maddux1_join_commutativity) ).
fof(9,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/tmp/tmpZUNTu3/sel_REL041+2.p_1',composition_associativity) ).
fof(11,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/tmp/tmpZUNTu3/sel_REL041+2.p_1',def_zero) ).
fof(12,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/tmp/tmpZUNTu3/sel_REL041+2.p_1',converse_cancellativity) ).
fof(13,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/tmp/tmpZUNTu3/sel_REL041+2.p_1',maddux4_definiton_of_meet) ).
fof(14,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmpZUNTu3/sel_REL041+2.p_1',maddux2_join_associativity) ).
fof(15,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/tmp/tmpZUNTu3/sel_REL041+2.p_1',maddux3_a_kind_of_de_Morgan) ).
fof(16,conjecture,
! [X1] :
( join(composition(converse(X1),X1),one) = one
=> ! [X2] : meet(composition(X1,X2),composition(X1,complement(X2))) = zero ),
file('/tmp/tmpZUNTu3/sel_REL041+2.p_1',goals) ).
fof(17,negated_conjecture,
~ ! [X1] :
( join(composition(converse(X1),X1),one) = one
=> ! [X2] : meet(composition(X1,X2),composition(X1,complement(X2))) = zero ),
inference(assume_negation,[status(cth)],[16]) ).
fof(20,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(21,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)],[20]) ).
fof(22,plain,
! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(23,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[4]) ).
cnf(25,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[24]) ).
fof(26,plain,
! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
inference(variable_rename,[status(thm)],[5]) ).
cnf(27,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[26]) ).
fof(28,plain,
! [X2] : composition(X2,one) = X2,
inference(variable_rename,[status(thm)],[6]) ).
cnf(29,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[28]) ).
fof(30,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[7]) ).
cnf(31,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[30]) ).
fof(32,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[8]) ).
cnf(33,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[32]) ).
fof(34,plain,
! [X4,X5,X6] : composition(X4,composition(X5,X6)) = composition(composition(X4,X5),X6),
inference(variable_rename,[status(thm)],[9]) ).
cnf(35,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[34]) ).
fof(38,plain,
! [X2] : zero = meet(X2,complement(X2)),
inference(variable_rename,[status(thm)],[11]) ).
cnf(39,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[38]) ).
fof(40,plain,
! [X3,X4] : join(composition(converse(X3),complement(composition(X3,X4))),complement(X4)) = complement(X4),
inference(variable_rename,[status(thm)],[12]) ).
cnf(41,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[40]) ).
fof(42,plain,
! [X3,X4] : meet(X3,X4) = complement(join(complement(X3),complement(X4))),
inference(variable_rename,[status(thm)],[13]) ).
cnf(43,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[42]) ).
fof(44,plain,
! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
inference(variable_rename,[status(thm)],[14]) ).
cnf(45,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[44]) ).
fof(46,plain,
! [X3,X4] : X3 = join(complement(join(complement(X3),complement(X4))),complement(join(complement(X3),X4))),
inference(variable_rename,[status(thm)],[15]) ).
cnf(47,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[46]) ).
fof(48,negated_conjecture,
? [X1] :
( join(composition(converse(X1),X1),one) = one
& ? [X2] : meet(composition(X1,X2),composition(X1,complement(X2))) != zero ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(49,negated_conjecture,
? [X3] :
( join(composition(converse(X3),X3),one) = one
& ? [X4] : meet(composition(X3,X4),composition(X3,complement(X4))) != zero ),
inference(variable_rename,[status(thm)],[48]) ).
fof(50,negated_conjecture,
( join(composition(converse(esk1_0),esk1_0),one) = one
& meet(composition(esk1_0,esk2_0),composition(esk1_0,complement(esk2_0))) != zero ),
inference(skolemize,[status(esa)],[49]) ).
cnf(51,negated_conjecture,
meet(composition(esk1_0,esk2_0),composition(esk1_0,complement(esk2_0))) != zero,
inference(split_conjunct,[status(thm)],[50]) ).
cnf(52,negated_conjecture,
join(composition(converse(esk1_0),esk1_0),one) = one,
inference(split_conjunct,[status(thm)],[50]) ).
cnf(53,plain,
complement(join(complement(X1),complement(complement(X1)))) = zero,
inference(rw,[status(thm)],[39,43,theory(equality)]),
[unfolding] ).
cnf(54,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)],[21,43,theory(equality)]),43,theory(equality)]),43,theory(equality)]),43,theory(equality)]),43,theory(equality)]),
[unfolding] ).
cnf(57,negated_conjecture,
complement(join(complement(composition(esk1_0,esk2_0)),complement(composition(esk1_0,complement(esk2_0))))) != zero,
inference(rw,[status(thm)],[51,43,theory(equality)]),
[unfolding] ).
cnf(58,negated_conjecture,
join(one,composition(converse(esk1_0),esk1_0)) = one,
inference(rw,[status(thm)],[52,33,theory(equality)]) ).
cnf(61,plain,
composition(converse(X1),X2) = converse(composition(converse(X2),X1)),
inference(spm,[status(thm)],[23,25,theory(equality)]) ).
cnf(62,plain,
join(X1,converse(X2)) = converse(join(converse(X1),X2)),
inference(spm,[status(thm)],[31,25,theory(equality)]) ).
cnf(63,plain,
join(converse(X1),X2) = converse(join(X1,converse(X2))),
inference(spm,[status(thm)],[31,25,theory(equality)]) ).
cnf(78,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[33,45,theory(equality)]) ).
cnf(80,plain,
join(join(X2,X1),X3) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[45,33,theory(equality)]) ).
cnf(84,plain,
join(X2,join(X1,X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[80,45,theory(equality)]) ).
cnf(88,plain,
join(converse(composition(X2,X1)),composition(X3,converse(X2))) = composition(join(converse(X1),X3),converse(X2)),
inference(spm,[status(thm)],[27,23,theory(equality)]) ).
cnf(101,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(rw,[status(thm)],[41,33,theory(equality)]) ).
cnf(109,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[47,33,theory(equality)]) ).
cnf(118,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[109,33,theory(equality)]) ).
cnf(125,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)],[54,33,theory(equality)]) ).
cnf(126,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)],[125,33,theory(equality)]) ).
cnf(139,plain,
join(complement(join(complement(join(complement(composition(X1,X2)),complement(X3))),join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3))))))))),complement(complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))))))) = join(complement(composition(X1,X2)),complement(X3)),
inference(spm,[status(thm)],[109,126,theory(equality)]) ).
cnf(151,plain,
join(complement(complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3))))))))),complement(join(complement(join(complement(composition(X1,X2)),complement(X3))),join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))))))) = join(complement(composition(X1,X2)),complement(X3)),
inference(rw,[status(thm)],[139,33,theory(equality)]) ).
cnf(275,plain,
converse(converse(X1)) = composition(converse(one),X1),
inference(spm,[status(thm)],[61,29,theory(equality)]) ).
cnf(293,plain,
X1 = composition(converse(one),X1),
inference(rw,[status(thm)],[275,25,theory(equality)]) ).
cnf(309,plain,
one = converse(one),
inference(spm,[status(thm)],[29,293,theory(equality)]) ).
cnf(346,plain,
join(one,converse(X1)) = converse(join(one,X1)),
inference(spm,[status(thm)],[31,309,theory(equality)]) ).
cnf(355,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[293,309,theory(equality)]) ).
cnf(367,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[27,355,theory(equality)]) ).
cnf(369,plain,
join(complement(X1),composition(converse(one),complement(X1))) = complement(X1),
inference(spm,[status(thm)],[101,355,theory(equality)]) ).
cnf(380,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[369,309,theory(equality)]),355,theory(equality)]) ).
cnf(423,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[380,53,theory(equality)]) ).
cnf(425,plain,
join(complement(complement(X1)),complement(join(complement(X1),complement(complement(X1))))) = X1,
inference(spm,[status(thm)],[109,380,theory(equality)]) ).
cnf(437,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[425,53,theory(equality)]),33,theory(equality)]) ).
cnf(451,plain,
join(zero,X1) = join(zero,join(zero,X1)),
inference(spm,[status(thm)],[45,423,theory(equality)]) ).
cnf(556,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[451,437,theory(equality)]) ).
cnf(566,plain,
converse(converse(X1)) = join(converse(zero),X1),
inference(spm,[status(thm)],[63,556,theory(equality)]) ).
cnf(572,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[437,556,theory(equality)]) ).
cnf(577,plain,
X1 = join(converse(zero),X1),
inference(rw,[status(thm)],[566,25,theory(equality)]) ).
cnf(620,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[380,572,theory(equality)]) ).
cnf(622,plain,
complement(join(X1,complement(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[53,572,theory(equality)]),33,theory(equality)]) ).
cnf(642,plain,
complement(zero) = join(X1,complement(X1)),
inference(spm,[status(thm)],[572,622,theory(equality)]) ).
cnf(688,plain,
join(X1,X2) = join(X1,join(X1,X2)),
inference(spm,[status(thm)],[45,620,theory(equality)]) ).
cnf(747,plain,
complement(complement(converse(zero))) = zero,
inference(spm,[status(thm)],[622,577,theory(equality)]) ).
cnf(758,plain,
converse(zero) = zero,
inference(rw,[status(thm)],[747,572,theory(equality)]) ).
cnf(760,plain,
composition(zero,converse(X1)) = converse(composition(X1,zero)),
inference(spm,[status(thm)],[23,758,theory(equality)]) ).
cnf(820,plain,
converse(zero) = composition(zero,converse(one)),
inference(spm,[status(thm)],[760,355,theory(equality)]) ).
cnf(835,plain,
zero = composition(zero,converse(one)),
inference(rw,[status(thm)],[820,758,theory(equality)]) ).
cnf(836,plain,
zero = composition(zero,one),
inference(rw,[status(thm)],[835,309,theory(equality)]) ).
cnf(982,plain,
join(complement(join(complement(X1),X2)),X1) = X1,
inference(spm,[status(thm)],[688,109,theory(equality)]) ).
cnf(991,plain,
join(X1,complement(zero)) = complement(zero),
inference(spm,[status(thm)],[688,642,theory(equality)]) ).
cnf(994,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[688,33,theory(equality)]) ).
cnf(1005,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[982,33,theory(equality)]) ).
cnf(1024,plain,
converse(complement(zero)) = join(X1,converse(complement(zero))),
inference(spm,[status(thm)],[62,991,theory(equality)]) ).
cnf(1027,plain,
complement(zero) = join(complement(zero),X1),
inference(spm,[status(thm)],[33,991,theory(equality)]) ).
cnf(1168,plain,
converse(complement(zero)) = complement(zero),
inference(spm,[status(thm)],[1027,1024,theory(equality)]) ).
cnf(1184,plain,
composition(complement(zero),converse(X1)) = converse(composition(X1,complement(zero))),
inference(spm,[status(thm)],[23,1168,theory(equality)]) ).
cnf(1330,plain,
join(X1,X3) = join(X1,join(complement(join(complement(X1),X2)),X3)),
inference(spm,[status(thm)],[45,1005,theory(equality)]) ).
cnf(1355,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[1005,994,theory(equality)]) ).
cnf(1492,plain,
join(X1,complement(join(X2,join(X3,complement(X1))))) = X1,
inference(spm,[status(thm)],[1005,78,theory(equality)]) ).
cnf(1955,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[1355,572,theory(equality)]) ).
cnf(2166,plain,
join(converse(zero),composition(X1,converse(zero))) = composition(join(converse(one),X1),converse(zero)),
inference(spm,[status(thm)],[88,836,theory(equality)]) ).
cnf(2203,plain,
composition(X1,zero) = composition(join(converse(one),X1),converse(zero)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[2166,758,theory(equality)]),758,theory(equality)]),556,theory(equality)]) ).
cnf(2204,plain,
composition(X1,zero) = composition(join(one,X1),zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2203,309,theory(equality)]),758,theory(equality)]) ).
cnf(3607,plain,
converse(complement(zero)) = composition(complement(zero),converse(one)),
inference(spm,[status(thm)],[1184,355,theory(equality)]) ).
cnf(3633,plain,
complement(zero) = composition(complement(zero),converse(one)),
inference(rw,[status(thm)],[3607,1168,theory(equality)]) ).
cnf(3634,plain,
complement(zero) = composition(complement(zero),one),
inference(rw,[status(thm)],[3633,309,theory(equality)]) ).
cnf(3655,plain,
join(converse(complement(zero)),composition(X1,converse(complement(zero)))) = composition(join(converse(one),X1),converse(complement(zero))),
inference(spm,[status(thm)],[88,3634,theory(equality)]) ).
cnf(3675,plain,
complement(zero) = composition(join(converse(one),X1),converse(complement(zero))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[3655,1168,theory(equality)]),1168,theory(equality)]),1027,theory(equality)]) ).
cnf(3676,plain,
complement(zero) = composition(join(one,X1),complement(zero)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3675,309,theory(equality)]),1168,theory(equality)]) ).
cnf(3692,plain,
join(complement(complement(zero)),composition(converse(join(one,X1)),complement(complement(zero)))) = complement(complement(zero)),
inference(spm,[status(thm)],[101,3676,theory(equality)]) ).
cnf(3735,plain,
composition(converse(X1),zero) = complement(complement(zero)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[3692,572,theory(equality)]),346,theory(equality)]),572,theory(equality)]),2204,theory(equality)]),556,theory(equality)]) ).
cnf(3736,plain,
composition(converse(X1),zero) = zero,
inference(rw,[status(thm)],[3735,572,theory(equality)]) ).
cnf(3766,plain,
composition(X1,zero) = zero,
inference(spm,[status(thm)],[3736,25,theory(equality)]) ).
cnf(7919,negated_conjecture,
join(X1,composition(composition(converse(esk1_0),esk1_0),X1)) = composition(one,X1),
inference(spm,[status(thm)],[367,58,theory(equality)]) ).
cnf(8015,negated_conjecture,
join(X1,composition(converse(esk1_0),composition(esk1_0,X1))) = composition(one,X1),
inference(rw,[status(thm)],[7919,35,theory(equality)]) ).
cnf(8016,negated_conjecture,
join(X1,composition(converse(esk1_0),composition(esk1_0,X1))) = X1,
inference(rw,[status(thm)],[8015,355,theory(equality)]) ).
cnf(14864,plain,
join(complement(complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3))))))))),complement(join(complement(X3),join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))))))) = join(complement(composition(X1,X2)),complement(X3)),
inference(rw,[status(thm)],[151,84,theory(equality)]) ).
cnf(15718,plain,
join(complement(join(join(X1,join(X2,complement(complement(X3)))),complement(X3))),complement(complement(X3))) = X3,
inference(spm,[status(thm)],[118,1492,theory(equality)]) ).
cnf(15854,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)],[15718,45,theory(equality)]),45,theory(equality)]),33,theory(equality)]),642,theory(equality)]),991,theory(equality)]),991,theory(equality)]),572,theory(equality)]),556,theory(equality)]) ).
cnf(16225,plain,
join(join(complement(X1),complement(composition(X2,complement(join(complement(X3),complement(composition(converse(X2),X1))))))),complement(join(complement(X1),join(complement(join(complement(composition(X2,X3)),complement(X1))),complement(composition(X2,complement(join(complement(X3),complement(composition(converse(X2),X1)))))))))) = join(complement(composition(X2,X3)),complement(X1)),
inference(rw,[status(thm)],[14864,15854,theory(equality)]) ).
cnf(16226,plain,
join(complement(X1),join(complement(composition(X2,complement(join(complement(X3),complement(composition(converse(X2),X1)))))),complement(join(complement(X1),join(complement(join(complement(composition(X2,X3)),complement(X1))),complement(composition(X2,complement(join(complement(X3),complement(composition(converse(X2),X1))))))))))) = join(complement(composition(X2,X3)),complement(X1)),
inference(rw,[status(thm)],[16225,45,theory(equality)]) ).
cnf(143860,plain,
join(X1,X2) = join(X1,complement(join(complement(X2),complement(complement(X1))))),
inference(spm,[status(thm)],[1330,118,theory(equality)]) ).
cnf(144392,plain,
join(X1,X2) = join(X1,complement(join(complement(X2),X1))),
inference(rw,[status(thm)],[143860,572,theory(equality)]) ).
cnf(145207,plain,
join(complement(join(X1,X2)),complement(join(complement(join(complement(X2),X1)),complement(X1)))) = join(complement(X2),X1),
inference(spm,[status(thm)],[118,144392,theory(equality)]) ).
cnf(145671,plain,
join(X1,complement(join(X1,X2))) = join(complement(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[145207,33,theory(equality)]),1955,theory(equality)]),572,theory(equality)]),33,theory(equality)]) ).
cnf(146948,negated_conjecture,
join(X1,complement(X1)) = join(complement(composition(converse(esk1_0),composition(esk1_0,X1))),X1),
inference(spm,[status(thm)],[145671,8016,theory(equality)]) ).
cnf(147479,negated_conjecture,
complement(zero) = join(complement(composition(converse(esk1_0),composition(esk1_0,X1))),X1),
inference(rw,[status(thm)],[146948,642,theory(equality)]) ).
cnf(147480,negated_conjecture,
complement(zero) = join(X1,complement(composition(converse(esk1_0),composition(esk1_0,X1)))),
inference(rw,[status(thm)],[147479,33,theory(equality)]) ).
cnf(149463,negated_conjecture,
join(complement(composition(esk1_0,complement(X1))),join(complement(composition(esk1_0,complement(complement(zero)))),complement(join(complement(composition(esk1_0,complement(X1))),join(complement(join(complement(composition(esk1_0,X1)),complement(composition(esk1_0,complement(X1))))),complement(composition(esk1_0,complement(complement(zero))))))))) = join(complement(composition(esk1_0,X1)),complement(composition(esk1_0,complement(X1)))),
inference(spm,[status(thm)],[16226,147480,theory(equality)]) ).
cnf(149733,negated_conjecture,
complement(zero) = join(complement(composition(esk1_0,X1)),complement(composition(esk1_0,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[149463,572,theory(equality)]),3766,theory(equality)]),572,theory(equality)]),3766,theory(equality)]),991,theory(equality)]),991,theory(equality)]),572,theory(equality)]),33,theory(equality)]),556,theory(equality)]),991,theory(equality)]) ).
cnf(261413,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[57,149733,theory(equality)]),572,theory(equality)]) ).
cnf(261414,negated_conjecture,
$false,
inference(cn,[status(thm)],[261413,theory(equality)]) ).
cnf(261415,negated_conjecture,
$false,
261414,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL041+2.p
% --creating new selector for [REL001+0.ax, REL001+1.ax]
% -running prover on /tmp/tmpZUNTu3/sel_REL041+2.p_1 with time limit 29
% -prover status Theorem
% Problem REL041+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL041+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL041+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
%
%------------------------------------------------------------------------------