TSTP Solution File: REL006-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL006-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 20:01:29 EDT 2022
% Result : Unsatisfiable 3.72s 3.90s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 13
% Syntax : Number of clauses : 158 ( 158 unt; 0 nHn; 158 RR)
% Number of literals : 158 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(meet(converse(sk1),sk2),zero),
file('REL006-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(meet(sk1,converse(sk2)),zero),
file('REL006-1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,v),join(v,u)),
file('REL006-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL006-1.p',unknown),
[] ).
cnf(5,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL006-1.p',unknown),
[] ).
cnf(6,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL006-1.p',unknown),
[] ).
cnf(8,axiom,
equal(composition(u,one),u),
file('REL006-1.p',unknown),
[] ).
cnf(10,axiom,
equal(converse(converse(u)),u),
file('REL006-1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL006-1.p',unknown),
[] ).
cnf(12,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL006-1.p',unknown),
[] ).
cnf(13,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL006-1.p',unknown),
[] ).
cnf(14,axiom,
equal(join(u,complement(u)),top),
file('REL006-1.p',unknown),
[] ).
cnf(15,axiom,
equal(meet(u,complement(u)),zero),
file('REL006-1.p',unknown),
[] ).
cnf(16,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[3,13]),
[iquote('0:Rew:3.0,13.0')] ).
cnf(17,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[6,5]),
[iquote('0:Rew:6.0,5.0')] ).
cnf(29,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[10,12]),
[iquote('0:SpR:10.0,12.0')] ).
cnf(34,plain,
equal(converse(join(u,converse(v))),join(converse(u),v)),
inference(spr,[status(thm),theory(equality)],[10,11]),
[iquote('0:SpR:10.0,11.0')] ).
cnf(35,plain,
equal(converse(join(converse(u),v)),join(u,converse(v))),
inference(spr,[status(thm),theory(equality)],[10,11]),
[iquote('0:SpR:10.0,11.0')] ).
cnf(40,plain,
equal(meet(join(complement(u),complement(v)),w),complement(join(meet(u,v),complement(w)))),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(43,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[14,6]),
[iquote('0:SpR:14.0,6.0')] ).
cnf(44,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(46,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[15,43]),
[iquote('0:Rew:15.0,43.0')] ).
cnf(47,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[6,44]),
[iquote('0:Rew:6.0,44.0')] ).
cnf(48,plain,
equal(meet(sk2,converse(sk1)),zero),
inference(rew,[status(thm),theory(equality)],[47,1]),
[iquote('0:Rew:47.0,1.0')] ).
cnf(54,plain,
equal(meet(top,zero),zero),
inference(spr,[status(thm),theory(equality)],[46,15]),
[iquote('0:SpR:46.0,15.0')] ).
cnf(56,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[46,6]),
[iquote('0:SpR:46.0,6.0')] ).
cnf(59,plain,
equal(meet(zero,top),zero),
inference(rew,[status(thm),theory(equality)],[47,54]),
[iquote('0:Rew:47.0,54.0')] ).
cnf(67,plain,
equal(join(meet(join(complement(u),complement(v)),w),complement(join(meet(u,v),w))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[6,17]),
[iquote('0:SpR:6.0,17.0')] ).
cnf(69,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[14,17]),
[iquote('0:SpR:14.0,17.0')] ).
cnf(70,plain,
equal(join(meet(u,v),complement(join(v,complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[3,17]),
[iquote('0:SpR:3.0,17.0')] ).
cnf(72,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[6,17]),
[iquote('0:SpR:6.0,17.0')] ).
cnf(73,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[15,17]),
[iquote('0:SpR:15.0,17.0')] ).
cnf(74,plain,
equal(join(zero,complement(join(complement(sk2),converse(sk1)))),sk2),
inference(spr,[status(thm),theory(equality)],[48,17]),
[iquote('0:SpR:48.0,17.0')] ).
cnf(75,plain,
equal(join(zero,complement(join(complement(zero),top))),zero),
inference(spr,[status(thm),theory(equality)],[59,17]),
[iquote('0:SpR:59.0,17.0')] ).
cnf(76,plain,
equal(join(zero,complement(join(top,complement(zero)))),zero),
inference(rew,[status(thm),theory(equality)],[3,75]),
[iquote('0:Rew:3.0,75.0')] ).
cnf(77,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[3,69,46]),
[iquote('0:Rew:3.0,69.0,46.0,69.0')] ).
cnf(78,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[3,72]),
[iquote('0:Rew:3.0,72.0')] ).
cnf(79,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[6,73]),
[iquote('0:Rew:6.0,73.0')] ).
cnf(80,plain,
equal(join(zero,complement(join(converse(sk1),complement(sk2)))),sk2),
inference(rew,[status(thm),theory(equality)],[3,74]),
[iquote('0:Rew:3.0,74.0')] ).
cnf(81,plain,
equal(join(complement(join(meet(u,v),w)),meet(join(complement(u),complement(v)),w)),join(complement(u),complement(v))),
inference(rew,[status(thm),theory(equality)],[3,67]),
[iquote('0:Rew:3.0,67.0')] ).
cnf(82,plain,
equal(join(complement(join(meet(u,v),w)),complement(join(meet(u,v),complement(w)))),join(complement(u),complement(v))),
inference(rew,[status(thm),theory(equality)],[40,81]),
[iquote('0:Rew:40.0,81.0')] ).
cnf(95,plain,
equal(complement(join(meet(top,u),complement(v))),meet(join(zero,complement(u)),v)),
inference(spr,[status(thm),theory(equality)],[56,6]),
[iquote('0:SpR:56.0,6.0')] ).
cnf(98,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,join(zero,complement(v)))),
inference(spr,[status(thm),theory(equality)],[56,6]),
[iquote('0:SpR:56.0,6.0')] ).
cnf(101,plain,
equal(complement(join(zero,zero)),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[46,56]),
[iquote('0:SpR:46.0,56.0')] ).
cnf(117,plain,
equal(meet(join(zero,zero),meet(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[101,15]),
[iquote('0:SpR:101.0,15.0')] ).
cnf(126,plain,
equal(meet(meet(top,top),join(zero,zero)),zero),
inference(rew,[status(thm),theory(equality)],[47,117]),
[iquote('0:Rew:47.0,117.0')] ).
cnf(141,plain,
equal(join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[126,17]),
[iquote('0:SpR:126.0,17.0')] ).
cnf(147,plain,
equal(join(zero,complement(join(join(zero,zero),complement(meet(top,top))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[3,141]),
[iquote('0:Rew:3.0,141.0')] ).
cnf(148,plain,
equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[4,147]),
[iquote('0:Rew:4.0,147.0')] ).
cnf(150,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(154,plain,
equal(join(u,join(complement(u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[14,4]),
[iquote('0:SpR:14.0,4.0')] ).
cnf(160,plain,
equal(join(meet(u,v),join(complement(join(complement(u),v)),w)),join(u,w)),
inference(spr,[status(thm),theory(equality)],[17,4]),
[iquote('0:SpR:17.0,4.0')] ).
cnf(161,plain,
equal(join(zero,join(complement(join(top,complement(zero))),u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[76,4]),
[iquote('0:SpR:76.0,4.0')] ).
cnf(206,plain,
equal(join(complement(u),composition(v,complement(composition(converse(v),u)))),complement(u)),
inference(spr,[status(thm),theory(equality)],[10,16]),
[iquote('0:SpR:10.0,16.0')] ).
cnf(259,plain,
equal(meet(top,join(converse(sk1),complement(sk2))),complement(sk2)),
inference(spr,[status(thm),theory(equality)],[80,56]),
[iquote('0:SpR:80.0,56.0')] ).
cnf(316,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[8,29]),
[iquote('0:SpR:8.0,29.0')] ).
cnf(319,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[10,316]),
[iquote('0:Rew:10.0,316.0')] ).
cnf(328,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[319,8]),
[iquote('0:SpR:319.0,8.0')] ).
cnf(334,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[319,16]),
[iquote('0:SpR:319.0,16.0')] ).
cnf(338,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[328,319]),
[iquote('0:Rew:328.0,319.0')] ).
cnf(345,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[338,334]),
[iquote('0:Rew:338.0,334.0')] ).
cnf(382,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[345,6]),
[iquote('0:SpR:345.0,6.0')] ).
cnf(388,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[46,345]),
[iquote('0:SpR:46.0,345.0')] ).
cnf(393,plain,
equal(meet(top,top),complement(zero)),
inference(rew,[status(thm),theory(equality)],[388,101]),
[iquote('0:Rew:388.0,101.0')] ).
cnf(404,plain,
equal(join(zero,complement(join(zero,join(zero,complement(complement(zero)))))),complement(zero)),
inference(rew,[status(thm),theory(equality)],[393,148]),
[iquote('0:Rew:393.0,148.0')] ).
cnf(405,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[382,79]),
[iquote('0:Rew:382.0,79.0')] ).
cnf(424,plain,
equal(join(zero,complement(zero)),complement(zero)),
inference(rew,[status(thm),theory(equality)],[388,404,405]),
[iquote('0:Rew:388.0,404.0,405.0,404.0')] ).
cnf(425,plain,
equal(complement(zero),top),
inference(rew,[status(thm),theory(equality)],[14,424]),
[iquote('0:Rew:14.0,424.0')] ).
cnf(431,plain,
equal(join(zero,join(complement(join(top,top)),u)),join(zero,u)),
inference(rew,[status(thm),theory(equality)],[425,161]),
[iquote('0:Rew:425.0,161.0')] ).
cnf(442,plain,
equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[6,405]),
[iquote('0:SpR:6.0,405.0')] ).
cnf(449,plain,
equal(complement(join(top,complement(u))),meet(zero,u)),
inference(spr,[status(thm),theory(equality)],[425,6]),
[iquote('0:SpR:425.0,6.0')] ).
cnf(455,plain,
equal(join(top,top),top),
inference(spr,[status(thm),theory(equality)],[425,345]),
[iquote('0:SpR:425.0,345.0')] ).
cnf(463,plain,
equal(join(zero,join(complement(top),u)),join(zero,u)),
inference(rew,[status(thm),theory(equality)],[455,431]),
[iquote('0:Rew:455.0,431.0')] ).
cnf(476,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(rew,[status(thm),theory(equality)],[46,463]),
[iquote('0:Rew:46.0,463.0')] ).
cnf(487,plain,
equal(join(top,join(top,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[455,4]),
[iquote('0:SpR:455.0,4.0')] ).
cnf(661,plain,
equal(meet(top,join(top,complement(u))),complement(join(zero,meet(zero,u)))),
inference(spr,[status(thm),theory(equality)],[449,56]),
[iquote('0:SpR:449.0,56.0')] ).
cnf(673,plain,
equal(meet(zero,join(zero,complement(u))),complement(join(top,meet(top,u)))),
inference(spr,[status(thm),theory(equality)],[56,449]),
[iquote('0:SpR:56.0,449.0')] ).
cnf(698,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[77,476]),
[iquote('0:SpR:77.0,476.0')] ).
cnf(704,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[698,405]),
[iquote('0:Rew:698.0,405.0')] ).
cnf(705,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[698,56]),
[iquote('0:Rew:698.0,56.0')] ).
cnf(713,plain,
equal(join(complement(u),complement(v)),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[698,442]),
[iquote('0:Rew:698.0,442.0')] ).
cnf(714,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[698,98]),
[iquote('0:Rew:698.0,98.0')] ).
cnf(717,plain,
equal(complement(join(meet(top,u),complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[698,95]),
[iquote('0:Rew:698.0,95.0')] ).
cnf(721,plain,
equal(complement(join(top,meet(top,u))),meet(zero,complement(u))),
inference(rew,[status(thm),theory(equality)],[698,673]),
[iquote('0:Rew:698.0,673.0')] ).
cnf(727,plain,
equal(meet(top,join(top,complement(u))),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[698,661]),
[iquote('0:Rew:698.0,661.0')] ).
cnf(731,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[704,705]),
[iquote('0:Rew:704.0,705.0')] ).
cnf(732,plain,
equal(join(converse(sk1),complement(sk2)),complement(sk2)),
inference(rew,[status(thm),theory(equality)],[731,259]),
[iquote('0:Rew:731.0,259.0')] ).
cnf(750,plain,
equal(complement(meet(join(meet(u,v),w),join(meet(u,v),complement(w)))),join(complement(u),complement(v))),
inference(rew,[status(thm),theory(equality)],[713,82]),
[iquote('0:Rew:713.0,82.0')] ).
cnf(760,plain,
equal(meet(zero,complement(u)),complement(join(top,u))),
inference(rew,[status(thm),theory(equality)],[731,721]),
[iquote('0:Rew:731.0,721.0')] ).
cnf(761,plain,
equal(join(top,complement(u)),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[731,727]),
[iquote('0:Rew:731.0,727.0')] ).
cnf(770,plain,
equal(complement(join(complement(u),v)),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[731,714]),
[iquote('0:Rew:731.0,714.0')] ).
cnf(772,plain,
equal(join(meet(u,v),join(meet(u,complement(v)),w)),join(u,w)),
inference(rew,[status(thm),theory(equality)],[770,160]),
[iquote('0:Rew:770.0,160.0')] ).
cnf(774,plain,
equal(complement(join(u,complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[731,717]),
[iquote('0:Rew:731.0,717.0')] ).
cnf(775,plain,
equal(join(meet(u,v),meet(complement(v),u)),u),
inference(rew,[status(thm),theory(equality)],[774,70]),
[iquote('0:Rew:774.0,70.0')] ).
cnf(784,plain,
equal(complement(meet(join(meet(u,v),w),join(meet(u,v),complement(w)))),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[713,750]),
[iquote('0:Rew:713.0,750.0')] ).
cnf(809,plain,
equal(meet(u,top),u),
inference(spr,[status(thm),theory(equality)],[731,47]),
[iquote('0:SpR:731.0,47.0')] ).
cnf(921,plain,
equal(join(sk1,converse(complement(sk2))),converse(complement(sk2))),
inference(spr,[status(thm),theory(equality)],[732,35]),
[iquote('0:SpR:732.0,35.0')] ).
cnf(1008,plain,
equal(join(u,join(v,complement(u))),join(top,v)),
inference(spr,[status(thm),theory(equality)],[3,154]),
[iquote('0:SpR:3.0,154.0')] ).
cnf(1095,plain,
equal(join(u,meet(u,complement(top))),u),
inference(spr,[status(thm),theory(equality)],[809,78]),
[iquote('0:SpR:809.0,78.0')] ).
cnf(1103,plain,
equal(join(u,meet(u,zero)),u),
inference(rew,[status(thm),theory(equality)],[46,1095]),
[iquote('0:Rew:46.0,1095.0')] ).
cnf(1125,plain,
equal(join(u,complement(u)),join(top,meet(complement(u),zero))),
inference(spr,[status(thm),theory(equality)],[1103,154]),
[iquote('0:SpR:1103.0,154.0')] ).
cnf(1135,plain,
equal(join(top,complement(join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[14,1125,760,47]),
[iquote('0:Rew:14.0,1125.0,760.0,1125.0,47.0,1125.0')] ).
cnf(1136,plain,
equal(complement(meet(zero,join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[761,1135]),
[iquote('0:Rew:761.0,1135.0')] ).
cnf(1222,plain,
equal(meet(zero,join(top,u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[1136,704]),
[iquote('0:SpR:1136.0,704.0')] ).
cnf(1250,plain,
equal(meet(zero,join(top,u)),zero),
inference(rew,[status(thm),theory(equality)],[46,1222]),
[iquote('0:Rew:46.0,1222.0')] ).
cnf(1262,plain,
equal(join(zero,meet(zero,complement(join(top,u)))),zero),
inference(spr,[status(thm),theory(equality)],[1250,78]),
[iquote('0:SpR:1250.0,78.0')] ).
cnf(1281,plain,
equal(complement(join(top,u)),zero),
inference(rew,[status(thm),theory(equality)],[698,1262,487,760]),
[iquote('0:Rew:698.0,1262.0,487.0,1262.0,760.0,1262.0')] ).
cnf(1364,plain,
equal(join(top,u),complement(zero)),
inference(spr,[status(thm),theory(equality)],[1281,704]),
[iquote('0:SpR:1281.0,704.0')] ).
cnf(1380,plain,
equal(join(top,u),top),
inference(rew,[status(thm),theory(equality)],[425,1364]),
[iquote('0:Rew:425.0,1364.0')] ).
cnf(1384,plain,
equal(join(u,join(v,complement(u))),top),
inference(rew,[status(thm),theory(equality)],[1380,1008]),
[iquote('0:Rew:1380.0,1008.0')] ).
cnf(1413,plain,
equal(join(converse(top),u),converse(top)),
inference(spr,[status(thm),theory(equality)],[1380,34]),
[iquote('0:SpR:1380.0,34.0')] ).
cnf(1464,plain,
equal(converse(top),top),
inference(spr,[status(thm),theory(equality)],[1413,14]),
[iquote('0:SpR:1413.0,14.0')] ).
cnf(1724,plain,
equal(join(u,join(v,w)),join(w,join(v,u))),
inference(spr,[status(thm),theory(equality)],[3,150]),
[iquote('0:SpR:3.0,150.0')] ).
cnf(2490,plain,
equal(join(u,composition(v,complement(composition(converse(v),complement(u))))),u),
inference(spr,[status(thm),theory(equality)],[704,206]),
[iquote('0:SpR:704.0,206.0')] ).
cnf(2893,plain,
equal(join(u,complement(meet(v,u))),top),
inference(spr,[status(thm),theory(equality)],[713,1384]),
[iquote('0:SpR:713.0,1384.0')] ).
cnf(2901,plain,
equal(complement(meet(u,complement(v))),join(complement(u),v)),
inference(spr,[status(thm),theory(equality)],[704,713]),
[iquote('0:SpR:704.0,713.0')] ).
cnf(2904,plain,
equal(complement(meet(complement(u),v)),join(u,complement(v))),
inference(spr,[status(thm),theory(equality)],[704,713]),
[iquote('0:SpR:704.0,713.0')] ).
cnf(2941,plain,
equal(complement(meet(u,meet(v,complement(u)))),top),
inference(spr,[status(thm),theory(equality)],[2893,713]),
[iquote('0:SpR:2893.0,713.0')] ).
cnf(3130,plain,
equal(meet(u,meet(v,complement(u))),complement(top)),
inference(spr,[status(thm),theory(equality)],[2941,704]),
[iquote('0:SpR:2941.0,704.0')] ).
cnf(3166,plain,
equal(meet(u,meet(v,complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[46,3130]),
[iquote('0:Rew:46.0,3130.0')] ).
cnf(3260,plain,
equal(join(zero,meet(u,complement(meet(v,complement(u))))),u),
inference(spr,[status(thm),theory(equality)],[3166,78]),
[iquote('0:SpR:3166.0,78.0')] ).
cnf(3272,plain,
equal(meet(complement(u),meet(v,u)),zero),
inference(spr,[status(thm),theory(equality)],[704,3166]),
[iquote('0:SpR:704.0,3166.0')] ).
cnf(3286,plain,
equal(meet(u,complement(meet(v,complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[698,3260]),
[iquote('0:Rew:698.0,3260.0')] ).
cnf(3287,plain,
equal(meet(u,join(complement(v),u)),u),
inference(rew,[status(thm),theory(equality)],[2901,3286]),
[iquote('0:Rew:2901.0,3286.0')] ).
cnf(3613,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[704,3287]),
[iquote('0:SpR:704.0,3287.0')] ).
cnf(3675,plain,
equal(meet(u,join(u,v)),u),
inference(spr,[status(thm),theory(equality)],[3,3613]),
[iquote('0:SpR:3.0,3613.0')] ).
cnf(3735,plain,
equal(meet(complement(join(u,v)),u),zero),
inference(spr,[status(thm),theory(equality)],[3675,3272]),
[iquote('0:SpR:3675.0,3272.0')] ).
cnf(3774,plain,
equal(meet(sk1,converse(complement(sk2))),sk1),
inference(spr,[status(thm),theory(equality)],[921,3675]),
[iquote('0:SpR:921.0,3675.0')] ).
cnf(3782,plain,
equal(meet(u,complement(join(u,v))),zero),
inference(rew,[status(thm),theory(equality)],[47,3735]),
[iquote('0:Rew:47.0,3735.0')] ).
cnf(3835,plain,
equal(join(u,meet(complement(complement(v)),u)),join(meet(u,v),u)),
inference(spr,[status(thm),theory(equality)],[775,772]),
[iquote('0:SpR:775.0,772.0')] ).
cnf(3875,plain,
equal(join(u,meet(v,u)),join(u,meet(u,v))),
inference(rew,[status(thm),theory(equality)],[704,3835,3]),
[iquote('0:Rew:704.0,3835.0,3.0,3835.0')] ).
cnf(3935,plain,
equal(join(converse(complement(sk2)),complement(sk1)),top),
inference(spr,[status(thm),theory(equality)],[3774,2893]),
[iquote('0:SpR:3774.0,2893.0')] ).
cnf(3939,plain,
equal(join(complement(sk1),converse(complement(sk2))),top),
inference(rew,[status(thm),theory(equality)],[3,3935]),
[iquote('0:Rew:3.0,3935.0')] ).
cnf(3974,plain,
equal(join(converse(complement(sk1)),complement(sk2)),converse(top)),
inference(spr,[status(thm),theory(equality)],[3939,34]),
[iquote('0:SpR:3939.0,34.0')] ).
cnf(3980,plain,
equal(join(complement(sk2),converse(complement(sk1))),top),
inference(rew,[status(thm),theory(equality)],[3,3974,1464]),
[iquote('0:Rew:3.0,3974.0,1464.0,3974.0')] ).
cnf(6829,plain,
equal(complement(meet(u,join(meet(u,v),complement(meet(complement(v),u))))),complement(meet(u,v))),
inference(spr,[status(thm),theory(equality)],[775,784]),
[iquote('0:SpR:775.0,784.0')] ).
cnf(6848,plain,
equal(complement(meet(u,join(complement(u),join(v,meet(u,v))))),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[1724,6829,2904]),
[iquote('0:Rew:1724.0,6829.0,2904.0,6829.0')] ).
cnf(12252,plain,
equal(converse(join(converse(u),meet(converse(u),v))),join(u,converse(meet(v,converse(u))))),
inference(spr,[status(thm),theory(equality)],[3875,35]),
[iquote('0:SpR:3875.0,35.0')] ).
cnf(12367,plain,
equal(join(u,converse(meet(converse(u),v))),join(u,converse(meet(v,converse(u))))),
inference(rew,[status(thm),theory(equality)],[35,12252]),
[iquote('0:Rew:35.0,12252.0')] ).
cnf(17090,plain,
equal(join(u,complement(composition(converse(one),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[338,2490]),
[iquote('0:SpR:338.0,2490.0')] ).
cnf(17100,plain,
equal(join(u,u),u),
inference(rew,[status(thm),theory(equality)],[704,17090,338,328]),
[iquote('0:Rew:704.0,17090.0,338.0,17090.0,328.0,17090.0')] ).
cnf(17319,plain,
equal(join(meet(u,v),meet(u,complement(v))),join(u,meet(u,complement(v)))),
inference(spr,[status(thm),theory(equality)],[17100,772]),
[iquote('0:SpR:17100.0,772.0')] ).
cnf(17372,plain,
equal(join(u,meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[78,17319]),
[iquote('0:Rew:78.0,17319.0')] ).
cnf(17439,plain,
equal(join(u,meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[704,17372]),
[iquote('0:SpR:704.0,17372.0')] ).
cnf(17472,plain,
equal(join(u,meet(v,u)),u),
inference(rew,[status(thm),theory(equality)],[17439,3875]),
[iquote('0:Rew:17439.0,3875.0')] ).
cnf(17487,plain,
equal(complement(meet(u,join(complement(u),v))),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[17472,6848]),
[iquote('0:Rew:17472.0,6848.0')] ).
cnf(17543,plain,
equal(join(u,converse(meet(converse(u),v))),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[17439,35]),
[iquote('0:SpR:17439.0,35.0')] ).
cnf(17660,plain,
equal(join(u,converse(meet(converse(u),v))),u),
inference(rew,[status(thm),theory(equality)],[10,17543]),
[iquote('0:Rew:10.0,17543.0')] ).
cnf(17661,plain,
equal(join(u,converse(meet(v,converse(u)))),u),
inference(rew,[status(thm),theory(equality)],[17660,12367]),
[iquote('0:Rew:17660.0,12367.0')] ).
cnf(20027,plain,
equal(complement(meet(sk2,converse(complement(sk1)))),complement(meet(sk2,top))),
inference(spr,[status(thm),theory(equality)],[3980,17487]),
[iquote('0:SpR:3980.0,17487.0')] ).
cnf(20086,plain,
equal(complement(meet(sk2,converse(complement(sk1)))),complement(sk2)),
inference(rew,[status(thm),theory(equality)],[809,20027]),
[iquote('0:Rew:809.0,20027.0')] ).
cnf(21565,plain,
equal(meet(sk2,converse(complement(sk1))),complement(complement(sk2))),
inference(spr,[status(thm),theory(equality)],[20086,704]),
[iquote('0:SpR:20086.0,704.0')] ).
cnf(21617,plain,
equal(meet(sk2,converse(complement(sk1))),sk2),
inference(rew,[status(thm),theory(equality)],[704,21565]),
[iquote('0:Rew:704.0,21565.0')] ).
cnf(21711,plain,
equal(join(complement(sk1),converse(sk2)),complement(sk1)),
inference(spr,[status(thm),theory(equality)],[21617,17661]),
[iquote('0:SpR:21617.0,17661.0')] ).
cnf(21729,plain,
equal(join(converse(sk2),complement(sk1)),complement(sk1)),
inference(rew,[status(thm),theory(equality)],[3,21711]),
[iquote('0:Rew:3.0,21711.0')] ).
cnf(22054,plain,
equal(meet(converse(sk2),complement(complement(sk1))),zero),
inference(spr,[status(thm),theory(equality)],[21729,3782]),
[iquote('0:SpR:21729.0,3782.0')] ).
cnf(22080,plain,
equal(meet(sk1,converse(sk2)),zero),
inference(rew,[status(thm),theory(equality)],[47,22054,704]),
[iquote('0:Rew:47.0,22054.0,704.0,22054.0')] ).
cnf(22081,plain,
$false,
inference(mrr,[status(thm)],[22080,2]),
[iquote('0:MRR:22080.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : REL006-1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 09:58:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.72/3.90
% 3.72/3.90 SPASS V 3.9
% 3.72/3.90 SPASS beiseite: Proof found.
% 3.72/3.90 % SZS status Theorem
% 3.72/3.90 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.72/3.90 SPASS derived 13604 clauses, backtracked 0 clauses, performed 0 splits and kept 1950 clauses.
% 3.72/3.90 SPASS allocated 82730 KBytes.
% 3.72/3.90 SPASS spent 0:00:03.54 on the problem.
% 3.72/3.90 0:00:00.03 for the input.
% 3.72/3.90 0:00:00.00 for the FLOTTER CNF translation.
% 3.72/3.90 0:00:00.11 for inferences.
% 3.72/3.90 0:00:00.00 for the backtracking.
% 3.72/3.90 0:00:03.36 for the reduction.
% 3.72/3.90
% 3.72/3.90
% 3.72/3.90 Here is a proof with depth 15, length 158 :
% 3.72/3.90 % SZS output start Refutation
% See solution above
% 3.89/4.06 Formulae used in the proof : goals_14 goals_15 maddux1_join_commutativity_1 maddux2_join_associativity_2 maddux3_a_kind_of_de_Morgan_3 maddux4_definiton_of_meet_4 composition_identity_6 converse_idempotence_8 converse_additivity_9 converse_multiplicativity_10 converse_cancellativity_11 def_top_12 def_zero_13
% 3.89/4.06
%------------------------------------------------------------------------------