TSTP Solution File: REL025+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : REL025+2 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 01:16:14 EST 2010
% Result : Theorem 2.27s
% Output : CNFRefutation 2.27s
% Verified :
% SZS Type : None (Could not find formula named 121or)
% Syntax : Number of formulae : 186
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/tmp/tmp-pLAWj/sel_REL025+2.p_1',converse_multiplicativity) ).
fof(2,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/tmp/tmp-pLAWj/sel_REL025+2.p_1',converse_idempotence) ).
fof(3,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/tmp/tmp-pLAWj/sel_REL025+2.p_1',composition_distributivity) ).
fof(4,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/tmp/tmp-pLAWj/sel_REL025+2.p_1',converse_additivity) ).
fof(5,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/tmp/tmp-pLAWj/sel_REL025+2.p_1',maddux1_join_commutativity) ).
fof(6,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/tmp/tmp-pLAWj/sel_REL025+2.p_1',composition_associativity) ).
fof(7,axiom,
! [X1] : composition(X1,one) = X1,
file('/tmp/tmp-pLAWj/sel_REL025+2.p_1',composition_identity) ).
fof(8,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/tmp/tmp-pLAWj/sel_REL025+2.p_1',converse_cancellativity) ).
fof(9,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/tmp/tmp-pLAWj/sel_REL025+2.p_1',maddux2_join_associativity) ).
fof(10,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/tmp/tmp-pLAWj/sel_REL025+2.p_1',maddux3_a_kind_of_de_Morgan) ).
fof(11,conjecture,
! [X1] :
( ( join(X1,one) = one
=> join(converse(X1),X1) = X1 )
& ( join(X1,one) = one
=> join(X1,converse(X1)) = converse(X1) ) ),
file('/tmp/tmp-pLAWj/sel_REL025+2.p_1',goals) ).
fof(12,negated_conjecture,
~ ! [X1] :
( ( join(X1,one) = one
=> join(converse(X1),X1) = X1 )
& ( join(X1,one) = one
=> join(X1,converse(X1)) = converse(X1) ) ),
inference(assume_negation,[status(cth)],[11]) ).
fof(13,plain,
! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
inference(variable_rename,[status(thm)],[1]) ).
cnf(14,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[13]) ).
fof(15,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(16,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[15]) ).
fof(17,plain,
! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(18,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[17]) ).
fof(19,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(20,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[19]) ).
fof(21,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(22,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,plain,
! [X4,X5,X6] : composition(X4,composition(X5,X6)) = composition(composition(X4,X5),X6),
inference(variable_rename,[status(thm)],[6]) ).
cnf(24,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[23]) ).
fof(25,plain,
! [X2] : composition(X2,one) = X2,
inference(variable_rename,[status(thm)],[7]) ).
cnf(26,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[25]) ).
fof(27,plain,
! [X3,X4] : join(composition(converse(X3),complement(composition(X3,X4))),complement(X4)) = complement(X4),
inference(variable_rename,[status(thm)],[8]) ).
cnf(28,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
inference(variable_rename,[status(thm)],[9]) ).
cnf(30,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X3,X4] : X3 = join(complement(join(complement(X3),complement(X4))),complement(join(complement(X3),X4))),
inference(variable_rename,[status(thm)],[10]) ).
cnf(32,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[31]) ).
fof(33,negated_conjecture,
? [X1] :
( ( join(X1,one) = one
& join(converse(X1),X1) != X1 )
| ( join(X1,one) = one
& join(X1,converse(X1)) != converse(X1) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(34,negated_conjecture,
? [X2] :
( ( join(X2,one) = one
& join(converse(X2),X2) != X2 )
| ( join(X2,one) = one
& join(X2,converse(X2)) != converse(X2) ) ),
inference(variable_rename,[status(thm)],[33]) ).
fof(35,negated_conjecture,
( ( join(esk1_0,one) = one
& join(converse(esk1_0),esk1_0) != esk1_0 )
| ( join(esk1_0,one) = one
& join(esk1_0,converse(esk1_0)) != converse(esk1_0) ) ),
inference(skolemize,[status(esa)],[34]) ).
fof(36,negated_conjecture,
( ( join(esk1_0,one) = one
| join(esk1_0,one) = one )
& ( join(esk1_0,converse(esk1_0)) != converse(esk1_0)
| join(esk1_0,one) = one )
& ( join(esk1_0,one) = one
| join(converse(esk1_0),esk1_0) != esk1_0 )
& ( join(esk1_0,converse(esk1_0)) != converse(esk1_0)
| join(converse(esk1_0),esk1_0) != esk1_0 ) ),
inference(distribute,[status(thm)],[35]) ).
cnf(37,negated_conjecture,
( join(converse(esk1_0),esk1_0) != esk1_0
| join(esk1_0,converse(esk1_0)) != converse(esk1_0) ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(40,negated_conjecture,
( join(esk1_0,one) = one
| join(esk1_0,one) = one ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(41,negated_conjecture,
( join(esk1_0,converse(esk1_0)) != converse(esk1_0)
| join(esk1_0,converse(esk1_0)) != esk1_0 ),
inference(rw,[status(thm)],[37,22,theory(equality)]) ).
cnf(43,plain,
composition(converse(X1),X2) = converse(composition(converse(X2),X1)),
inference(spm,[status(thm)],[14,16,theory(equality)]) ).
cnf(44,plain,
join(X1,converse(X2)) = converse(join(converse(X1),X2)),
inference(spm,[status(thm)],[20,16,theory(equality)]) ).
cnf(45,plain,
join(converse(X1),X2) = converse(join(X1,converse(X2))),
inference(spm,[status(thm)],[20,16,theory(equality)]) ).
cnf(60,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[22,30,theory(equality)]) ).
cnf(62,plain,
join(join(X2,X1),X3) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[30,22,theory(equality)]) ).
cnf(66,plain,
join(X2,join(X1,X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[62,30,theory(equality)]) ).
cnf(73,plain,
join(composition(X1,X2),composition(X3,composition(X4,X2))) = composition(join(X1,composition(X3,X4)),X2),
inference(spm,[status(thm)],[18,24,theory(equality)]) ).
cnf(86,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(rw,[status(thm)],[28,22,theory(equality)]) ).
cnf(88,plain,
join(complement(one),composition(converse(X1),complement(X1))) = complement(one),
inference(spm,[status(thm)],[86,26,theory(equality)]) ).
cnf(93,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[32,22,theory(equality)]) ).
cnf(94,plain,
join(X1,X3) = join(complement(join(complement(X1),X2)),join(complement(join(complement(X1),complement(X2))),X3)),
inference(spm,[status(thm)],[30,93,theory(equality)]) ).
cnf(96,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)],[93,93,theory(equality)]) ).
cnf(98,plain,
join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
inference(spm,[status(thm)],[93,22,theory(equality)]) ).
cnf(136,plain,
converse(converse(X1)) = composition(converse(one),X1),
inference(spm,[status(thm)],[43,26,theory(equality)]) ).
cnf(150,plain,
X1 = composition(converse(one),X1),
inference(rw,[status(thm)],[136,16,theory(equality)]) ).
cnf(162,plain,
one = converse(one),
inference(spm,[status(thm)],[26,150,theory(equality)]) ).
cnf(183,plain,
join(one,converse(X1)) = converse(join(one,X1)),
inference(spm,[status(thm)],[20,162,theory(equality)]) ).
cnf(184,plain,
join(converse(X1),one) = converse(join(X1,one)),
inference(spm,[status(thm)],[20,162,theory(equality)]) ).
cnf(188,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[150,162,theory(equality)]) ).
cnf(192,plain,
join(one,converse(X1)) = converse(join(X1,one)),
inference(rw,[status(thm)],[184,22,theory(equality)]) ).
cnf(196,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[18,188,theory(equality)]) ).
cnf(198,plain,
join(complement(X1),composition(converse(one),complement(X1))) = complement(X1),
inference(spm,[status(thm)],[86,188,theory(equality)]) ).
cnf(203,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[198,162,theory(equality)]),188,theory(equality)]) ).
cnf(222,negated_conjecture,
converse(one) = join(one,converse(esk1_0)),
inference(spm,[status(thm)],[192,40,theory(equality)]) ).
cnf(234,negated_conjecture,
one = join(one,converse(esk1_0)),
inference(rw,[status(thm)],[222,162,theory(equality)]) ).
cnf(239,negated_conjecture,
join(one,X1) = join(one,join(converse(esk1_0),X1)),
inference(spm,[status(thm)],[30,234,theory(equality)]) ).
cnf(245,plain,
join(complement(X1),X2) = join(complement(X1),join(complement(X1),X2)),
inference(spm,[status(thm)],[30,203,theory(equality)]) ).
cnf(351,negated_conjecture,
join(one,converse(join(esk1_0,X1))) = join(one,converse(X1)),
inference(spm,[status(thm)],[239,20,theory(equality)]) ).
cnf(851,plain,
join(complement(join(complement(X1),X2)),X1) = X1,
inference(spm,[status(thm)],[245,93,theory(equality)]) ).
cnf(867,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[851,22,theory(equality)]) ).
cnf(878,plain,
join(X1,complement(complement(X1))) = X1,
inference(spm,[status(thm)],[867,86,theory(equality)]) ).
cnf(894,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[867,22,theory(equality)]) ).
cnf(899,plain,
join(X1,complement(join(X2,join(X3,complement(X1))))) = X1,
inference(spm,[status(thm)],[867,60,theory(equality)]) ).
cnf(912,plain,
join(X1,X2) = join(X1,join(complement(complement(X1)),X2)),
inference(spm,[status(thm)],[30,878,theory(equality)]) ).
cnf(918,plain,
converse(converse(X1)) = join(X1,converse(complement(complement(converse(X1))))),
inference(spm,[status(thm)],[44,878,theory(equality)]) ).
cnf(920,negated_conjecture,
join(one,converse(esk1_0)) = join(one,converse(complement(complement(esk1_0)))),
inference(spm,[status(thm)],[351,878,theory(equality)]) ).
cnf(930,plain,
X1 = join(X1,converse(complement(complement(converse(X1))))),
inference(rw,[status(thm)],[918,16,theory(equality)]) ).
cnf(932,negated_conjecture,
one = join(one,converse(complement(complement(esk1_0)))),
inference(rw,[status(thm)],[920,234,theory(equality)]) ).
cnf(967,negated_conjecture,
converse(one) = join(one,converse(converse(complement(complement(esk1_0))))),
inference(spm,[status(thm)],[183,932,theory(equality)]) ).
cnf(973,negated_conjecture,
one = join(one,converse(converse(complement(complement(esk1_0))))),
inference(rw,[status(thm)],[967,162,theory(equality)]) ).
cnf(974,negated_conjecture,
one = join(one,complement(complement(esk1_0))),
inference(rw,[status(thm)],[973,16,theory(equality)]) ).
cnf(1012,negated_conjecture,
join(complement(esk1_0),complement(one)) = complement(esk1_0),
inference(spm,[status(thm)],[894,974,theory(equality)]) ).
cnf(1038,negated_conjecture,
join(complement(esk1_0),X1) = join(complement(esk1_0),join(complement(one),X1)),
inference(spm,[status(thm)],[30,1012,theory(equality)]) ).
cnf(1120,plain,
join(X1,complement(complement(X1))) = join(X1,complement(complement(complement(complement(X1))))),
inference(spm,[status(thm)],[912,878,theory(equality)]) ).
cnf(1151,plain,
X1 = join(X1,complement(complement(complement(complement(X1))))),
inference(rw,[status(thm)],[1120,878,theory(equality)]) ).
cnf(1171,plain,
join(complement(complement(complement(X1))),complement(X1)) = complement(complement(complement(X1))),
inference(spm,[status(thm)],[894,1151,theory(equality)]) ).
cnf(1185,plain,
complement(X1) = complement(complement(complement(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1171,22,theory(equality)]),878,theory(equality)]) ).
cnf(1189,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = complement(complement(X1)),
inference(spm,[status(thm)],[93,1185,theory(equality)]) ).
cnf(1203,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[1189,93,theory(equality)]) ).
cnf(1216,plain,
join(complement(one),composition(converse(complement(X1)),X1)) = complement(one),
inference(spm,[status(thm)],[88,1203,theory(equality)]) ).
cnf(1219,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[894,1203,theory(equality)]) ).
cnf(1221,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(rw,[status(thm)],[912,1203,theory(equality)]) ).
cnf(1222,plain,
join(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[930,1203,theory(equality)]),16,theory(equality)]) ).
cnf(1277,plain,
join(X1,X2) = join(X2,join(X1,X2)),
inference(spm,[status(thm)],[60,1222,theory(equality)]) ).
cnf(1540,plain,
join(X1,join(X2,X3)) = join(join(X2,X3),join(X1,X2)),
inference(spm,[status(thm)],[60,1221,theory(equality)]) ).
cnf(1595,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,join(X1,X2))),
inference(rw,[status(thm)],[1540,30,theory(equality)]) ).
cnf(4799,plain,
join(complement(one),converse(complement(one))) = complement(one),
inference(spm,[status(thm)],[1216,26,theory(equality)]) ).
cnf(4841,plain,
converse(complement(one)) = join(converse(complement(one)),complement(one)),
inference(spm,[status(thm)],[45,4799,theory(equality)]) ).
cnf(4860,plain,
converse(complement(one)) = complement(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[4841,22,theory(equality)]),4799,theory(equality)]) ).
cnf(4880,plain,
join(converse(X1),complement(one)) = converse(join(X1,complement(one))),
inference(spm,[status(thm)],[20,4860,theory(equality)]) ).
cnf(5130,negated_conjecture,
converse(complement(esk1_0)) = join(converse(complement(esk1_0)),complement(one)),
inference(spm,[status(thm)],[4880,1012,theory(equality)]) ).
cnf(5165,negated_conjecture,
converse(complement(esk1_0)) = join(complement(one),converse(complement(esk1_0))),
inference(rw,[status(thm)],[5130,22,theory(equality)]) ).
cnf(8207,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)],[96,1203,theory(equality)]),22,theory(equality)]),30,theory(equality)]),1219,theory(equality)]) ).
cnf(8213,plain,
join(complement(X1),complement(complement(X1))) = join(complement(X1),join(complement(complement(X1)),X2)),
inference(spm,[status(thm)],[8207,867,theory(equality)]) ).
cnf(8217,negated_conjecture,
join(complement(esk1_0),complement(complement(esk1_0))) = join(complement(esk1_0),one),
inference(spm,[status(thm)],[8207,1012,theory(equality)]) ).
cnf(8218,plain,
join(X1,complement(join(X1,complement(X2)))) = join(X1,X2),
inference(spm,[status(thm)],[8207,1203,theory(equality)]) ).
cnf(8264,plain,
join(X1,complement(X1)) = join(complement(X1),join(complement(complement(X1)),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[8213,1203,theory(equality)]),22,theory(equality)]) ).
cnf(8265,plain,
join(X1,complement(X1)) = join(X1,join(complement(X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[8264,1203,theory(equality)]),66,theory(equality)]) ).
cnf(8270,negated_conjecture,
join(esk1_0,complement(esk1_0)) = join(complement(esk1_0),one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[8217,1203,theory(equality)]),22,theory(equality)]) ).
cnf(8271,negated_conjecture,
join(esk1_0,complement(esk1_0)) = join(one,complement(esk1_0)),
inference(rw,[status(thm)],[8270,22,theory(equality)]) ).
cnf(8459,plain,
join(X1,join(X2,complement(X2))) = join(complement(X2),join(X1,X2)),
inference(spm,[status(thm)],[1595,8265,theory(equality)]) ).
cnf(8476,negated_conjecture,
join(one,converse(complement(esk1_0))) = join(one,complement(one)),
inference(spm,[status(thm)],[8265,5165,theory(equality)]) ).
cnf(8483,plain,
join(complement(join(complement(X1),X2)),join(complement(join(complement(X1),complement(X2))),complement(complement(join(complement(X1),complement(X2)))))) = join(X1,join(complement(complement(join(complement(X1),complement(X2)))),X3)),
inference(spm,[status(thm)],[94,8265,theory(equality)]) ).
cnf(8495,plain,
join(X1,complement(join(X2,complement(X2)))) = X1,
inference(spm,[status(thm)],[899,8265,theory(equality)]) ).
cnf(8544,plain,
join(X1,join(X2,complement(X2))) = join(X2,complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[8459,60,theory(equality)]),8265,theory(equality)]) ).
cnf(8564,plain,
join(X2,complement(X2)) = join(X1,join(complement(complement(join(complement(X1),complement(X2)))),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[8483,1203,theory(equality)]),60,theory(equality)]),22,theory(equality)]),8207,theory(equality)]),60,theory(equality)]),8265,theory(equality)]),60,theory(equality)]),22,theory(equality)]),66,theory(equality)]),1219,theory(equality)]) ).
cnf(8565,plain,
join(X2,complement(X2)) = join(X1,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[8564,1203,theory(equality)]),30,theory(equality)]),8265,theory(equality)]) ).
cnf(8629,negated_conjecture,
converse(join(one,complement(one))) = join(one,converse(converse(complement(esk1_0)))),
inference(spm,[status(thm)],[183,8476,theory(equality)]) ).
cnf(8660,negated_conjecture,
join(one,complement(one)) = join(one,converse(converse(complement(esk1_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[8629,183,theory(equality)]),4860,theory(equality)]) ).
cnf(8661,negated_conjecture,
join(one,complement(one)) = join(esk1_0,complement(esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[8660,16,theory(equality)]),8271,theory(equality)]) ).
cnf(8769,plain,
join(complement(join(X1,complement(X1))),X2) = X2,
inference(spm,[status(thm)],[1277,8495,theory(equality)]) ).
cnf(9586,plain,
converse(join(X1,complement(X1))) = join(one,converse(complement(one))),
inference(spm,[status(thm)],[183,8565,theory(equality)]) ).
cnf(9716,plain,
converse(join(X1,complement(X1))) = join(esk1_0,complement(esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[9586,4860,theory(equality)]),8661,theory(equality)]) ).
cnf(10118,plain,
join(esk1_0,complement(esk1_0)) = join(X1,converse(complement(converse(X1)))),
inference(spm,[status(thm)],[44,9716,theory(equality)]) ).
cnf(11154,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[8218,1203,theory(equality)]) ).
cnf(11863,plain,
join(X1,complement(join(esk1_0,complement(esk1_0)))) = join(X1,complement(converse(complement(converse(X1))))),
inference(spm,[status(thm)],[11154,10118,theory(equality)]) ).
cnf(11941,plain,
X1 = join(X1,complement(converse(complement(converse(X1))))),
inference(rw,[status(thm)],[11863,8495,theory(equality)]) ).
cnf(11963,plain,
converse(converse(X1)) = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(spm,[status(thm)],[44,11941,theory(equality)]) ).
cnf(12035,plain,
X1 = join(X1,converse(complement(converse(complement(converse(converse(X1))))))),
inference(rw,[status(thm)],[11963,16,theory(equality)]) ).
cnf(12036,plain,
X1 = join(X1,converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[12035,16,theory(equality)]) ).
cnf(12115,plain,
join(complement(converse(complement(converse(complement(X1))))),complement(X1)) = complement(converse(complement(converse(complement(X1))))),
inference(spm,[status(thm)],[1219,12036,theory(equality)]) ).
cnf(12176,plain,
complement(X1) = complement(converse(complement(converse(complement(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[12115,22,theory(equality)]),11941,theory(equality)]) ).
cnf(12221,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = converse(complement(converse(complement(X1)))),
inference(spm,[status(thm)],[93,12176,theory(equality)]) ).
cnf(12264,plain,
X1 = converse(complement(converse(complement(X1)))),
inference(rw,[status(thm)],[12221,93,theory(equality)]) ).
cnf(12297,plain,
converse(X1) = complement(converse(complement(X1))),
inference(spm,[status(thm)],[16,12264,theory(equality)]) ).
cnf(19348,negated_conjecture,
join(X1,composition(converse(esk1_0),X1)) = composition(one,X1),
inference(spm,[status(thm)],[196,234,theory(equality)]) ).
cnf(19494,negated_conjecture,
join(X1,composition(converse(esk1_0),X1)) = X1,
inference(rw,[status(thm)],[19348,188,theory(equality)]) ).
cnf(19580,negated_conjecture,
converse(converse(X1)) = join(X1,converse(composition(converse(esk1_0),converse(X1)))),
inference(spm,[status(thm)],[44,19494,theory(equality)]) ).
cnf(19646,negated_conjecture,
X1 = join(X1,converse(composition(converse(esk1_0),converse(X1)))),
inference(rw,[status(thm)],[19580,16,theory(equality)]) ).
cnf(19647,negated_conjecture,
X1 = join(X1,composition(X1,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[19646,14,theory(equality)]),16,theory(equality)]) ).
cnf(19734,negated_conjecture,
join(complement(esk1_0),complement(one)) = join(complement(esk1_0),composition(complement(one),esk1_0)),
inference(spm,[status(thm)],[1038,19647,theory(equality)]) ).
cnf(19759,negated_conjecture,
join(X1,complement(X1)) = join(X1,complement(composition(X1,esk1_0))),
inference(spm,[status(thm)],[11154,19647,theory(equality)]) ).
cnf(19770,negated_conjecture,
join(X1,X2) = join(X2,join(X1,composition(X2,esk1_0))),
inference(spm,[status(thm)],[66,19647,theory(equality)]) ).
cnf(19774,negated_conjecture,
join(X1,composition(composition(one,esk1_0),X1)) = composition(one,X1),
inference(spm,[status(thm)],[196,19647,theory(equality)]) ).
cnf(19793,negated_conjecture,
complement(esk1_0) = join(complement(esk1_0),composition(complement(one),esk1_0)),
inference(rw,[status(thm)],[19734,1012,theory(equality)]) ).
cnf(19834,negated_conjecture,
join(X1,composition(esk1_0,X1)) = composition(one,X1),
inference(rw,[status(thm)],[19774,188,theory(equality)]) ).
cnf(19835,negated_conjecture,
join(X1,composition(esk1_0,X1)) = X1,
inference(rw,[status(thm)],[19834,188,theory(equality)]) ).
cnf(19854,negated_conjecture,
join(complement(composition(esk1_0,X1)),complement(X1)) = complement(composition(esk1_0,X1)),
inference(spm,[status(thm)],[1219,19835,theory(equality)]) ).
cnf(19913,negated_conjecture,
join(complement(X1),complement(composition(esk1_0,X1))) = complement(composition(esk1_0,X1)),
inference(rw,[status(thm)],[19854,22,theory(equality)]) ).
cnf(21720,negated_conjecture,
join(complement(composition(complement(one),esk1_0)),complement(complement(esk1_0))) = complement(composition(complement(one),esk1_0)),
inference(spm,[status(thm)],[1219,19793,theory(equality)]) ).
cnf(21744,negated_conjecture,
join(esk1_0,complement(composition(complement(one),esk1_0))) = complement(composition(complement(one),esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[21720,1203,theory(equality)]),22,theory(equality)]) ).
cnf(21963,negated_conjecture,
join(X1,composition(join(X2,X1),esk1_0)) = join(composition(X2,esk1_0),X1),
inference(spm,[status(thm)],[19770,18,theory(equality)]) ).
cnf(37909,negated_conjecture,
join(complement(esk1_0),composition(join(esk1_0,complement(esk1_0)),esk1_0)) = join(composition(one,esk1_0),complement(esk1_0)),
inference(spm,[status(thm)],[21963,8271,theory(equality)]) ).
cnf(38210,negated_conjecture,
join(composition(esk1_0,esk1_0),complement(esk1_0)) = join(composition(one,esk1_0),complement(esk1_0)),
inference(rw,[status(thm)],[37909,21963,theory(equality)]) ).
cnf(38211,negated_conjecture,
join(composition(esk1_0,esk1_0),complement(esk1_0)) = join(esk1_0,complement(esk1_0)),
inference(rw,[status(thm)],[38210,188,theory(equality)]) ).
cnf(39635,negated_conjecture,
join(complement(join(esk1_0,complement(esk1_0))),complement(join(complement(esk1_0),complement(composition(esk1_0,esk1_0))))) = esk1_0,
inference(spm,[status(thm)],[98,38211,theory(equality)]) ).
cnf(39672,negated_conjecture,
composition(esk1_0,esk1_0) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[39635,19913,theory(equality)]),1203,theory(equality)]),8769,theory(equality)]) ).
cnf(39703,negated_conjecture,
join(esk1_0,composition(X1,esk1_0)) = composition(join(esk1_0,X1),esk1_0),
inference(spm,[status(thm)],[18,39672,theory(equality)]) ).
cnf(39709,negated_conjecture,
join(composition(X1,esk1_0),composition(X2,esk1_0)) = composition(join(X1,composition(X2,esk1_0)),esk1_0),
inference(spm,[status(thm)],[73,39672,theory(equality)]) ).
cnf(39773,negated_conjecture,
composition(join(X1,X2),esk1_0) = composition(join(X1,composition(X2,esk1_0)),esk1_0),
inference(rw,[status(thm)],[39709,18,theory(equality)]) ).
cnf(39978,negated_conjecture,
composition(join(X1,complement(X1)),esk1_0) = join(esk1_0,composition(complement(esk1_0),esk1_0)),
inference(spm,[status(thm)],[39703,8565,theory(equality)]) ).
cnf(40615,negated_conjecture,
join(esk1_0,composition(complement(one),esk1_0)) = join(esk1_0,composition(complement(esk1_0),esk1_0)),
inference(spm,[status(thm)],[196,39978,theory(equality)]) ).
cnf(40761,negated_conjecture,
join(esk1_0,complement(join(esk1_0,composition(complement(esk1_0),esk1_0)))) = join(esk1_0,complement(composition(complement(one),esk1_0))),
inference(spm,[status(thm)],[11154,40615,theory(equality)]) ).
cnf(40787,negated_conjecture,
join(esk1_0,complement(composition(complement(esk1_0),esk1_0))) = join(esk1_0,complement(composition(complement(one),esk1_0))),
inference(rw,[status(thm)],[40761,11154,theory(equality)]) ).
cnf(40788,negated_conjecture,
join(esk1_0,complement(composition(complement(esk1_0),esk1_0))) = complement(composition(complement(one),esk1_0)),
inference(rw,[status(thm)],[40787,21744,theory(equality)]) ).
cnf(40891,negated_conjecture,
join(complement(complement(composition(complement(one),esk1_0))),complement(join(complement(composition(complement(esk1_0),esk1_0)),complement(esk1_0)))) = composition(complement(esk1_0),esk1_0),
inference(spm,[status(thm)],[98,40788,theory(equality)]) ).
cnf(40920,negated_conjecture,
composition(complement(one),esk1_0) = composition(complement(esk1_0),esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[40891,1203,theory(equality)]),22,theory(equality)]),19759,theory(equality)]),1203,theory(equality)]),22,theory(equality)]),8495,theory(equality)]) ).
cnf(68373,negated_conjecture,
composition(complement(one),esk1_0) = composition(join(complement(one),converse(complement(esk1_0))),esk1_0),
inference(spm,[status(thm)],[39773,1216,theory(equality)]) ).
cnf(68477,negated_conjecture,
composition(complement(esk1_0),esk1_0) = composition(join(complement(one),converse(complement(esk1_0))),esk1_0),
inference(rw,[status(thm)],[68373,40920,theory(equality)]) ).
cnf(68478,negated_conjecture,
composition(complement(esk1_0),esk1_0) = composition(converse(complement(esk1_0)),esk1_0),
inference(rw,[status(thm)],[68477,5165,theory(equality)]) ).
cnf(68587,negated_conjecture,
join(composition(complement(esk1_0),esk1_0),composition(X1,esk1_0)) = composition(join(converse(complement(esk1_0)),X1),esk1_0),
inference(spm,[status(thm)],[18,68478,theory(equality)]) ).
cnf(68636,negated_conjecture,
composition(join(complement(esk1_0),X1),esk1_0) = composition(join(converse(complement(esk1_0)),X1),esk1_0),
inference(rw,[status(thm)],[68587,18,theory(equality)]) ).
cnf(68966,negated_conjecture,
composition(join(complement(esk1_0),complement(converse(complement(esk1_0)))),esk1_0) = join(esk1_0,composition(complement(esk1_0),esk1_0)),
inference(spm,[status(thm)],[39978,68636,theory(equality)]) ).
cnf(69142,negated_conjecture,
composition(join(converse(esk1_0),complement(esk1_0)),esk1_0) = join(esk1_0,composition(complement(esk1_0),esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[68966,12297,theory(equality)]),22,theory(equality)]) ).
cnf(69234,negated_conjecture,
join(join(converse(esk1_0),complement(esk1_0)),join(esk1_0,composition(complement(esk1_0),esk1_0))) = join(converse(esk1_0),complement(esk1_0)),
inference(spm,[status(thm)],[19647,69142,theory(equality)]) ).
cnf(69272,negated_conjecture,
join(esk1_0,complement(esk1_0)) = join(converse(esk1_0),complement(esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[69234,30,theory(equality)]),19770,theory(equality)]),8544,theory(equality)]) ).
cnf(69317,negated_conjecture,
join(converse(esk1_0),complement(join(esk1_0,complement(esk1_0)))) = join(converse(esk1_0),complement(complement(esk1_0))),
inference(spm,[status(thm)],[11154,69272,theory(equality)]) ).
cnf(69375,negated_conjecture,
converse(esk1_0) = join(converse(esk1_0),complement(complement(esk1_0))),
inference(rw,[status(thm)],[69317,8495,theory(equality)]) ).
cnf(69376,negated_conjecture,
converse(esk1_0) = join(esk1_0,converse(esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[69375,1203,theory(equality)]),22,theory(equality)]) ).
cnf(70015,negated_conjecture,
converse(converse(esk1_0)) = join(converse(esk1_0),esk1_0),
inference(spm,[status(thm)],[45,69376,theory(equality)]) ).
cnf(70049,negated_conjecture,
( $false
| join(esk1_0,converse(esk1_0)) != esk1_0 ),
inference(rw,[status(thm)],[41,69376,theory(equality)]) ).
cnf(70050,negated_conjecture,
( $false
| converse(esk1_0) != esk1_0 ),
inference(rw,[status(thm)],[70049,69376,theory(equality)]) ).
cnf(70051,negated_conjecture,
converse(esk1_0) != esk1_0,
inference(cn,[status(thm)],[70050,theory(equality)]) ).
cnf(70052,negated_conjecture,
esk1_0 = join(converse(esk1_0),esk1_0),
inference(rw,[status(thm)],[70015,16,theory(equality)]) ).
cnf(70053,negated_conjecture,
esk1_0 = converse(esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[70052,22,theory(equality)]),69376,theory(equality)]) ).
cnf(70095,negated_conjecture,
$false,
inference(sr,[status(thm)],[70053,70051,theory(equality)]) ).
cnf(70096,negated_conjecture,
$false,
70095,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL025+2.p
% --creating new selector for [REL001+0.ax]
% -running prover on /tmp/tmp-pLAWj/sel_REL025+2.p_1 with time limit 29
% -prover status Theorem
% Problem REL025+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL025+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL025+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
%
%------------------------------------------------------------------------------