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 : n014.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 : Theorem 3.58s 3.78s
% Output : Refutation 3.72s
% 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(composition(u,one),u),
file('REL006+1.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL006+1.p',unknown),
[] ).
cnf(3,axiom,
equal(meet(converse(skc2),skc3),zero),
file('REL006+1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(u,complement(u)),top),
file('REL006+1.p',unknown),
[] ).
cnf(5,axiom,
equal(meet(u,complement(u)),zero),
file('REL006+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(meet(skc2,converse(skc3)),zero),
file('REL006+1.p',unknown),
[] ).
cnf(7,axiom,
equal(join(u,v),join(v,u)),
file('REL006+1.p',unknown),
[] ).
cnf(8,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL006+1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL006+1.p',unknown),
[] ).
cnf(10,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL006+1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL006+1.p',unknown),
[] ).
cnf(14,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL006+1.p',unknown),
[] ).
cnf(15,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
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)],[7,14]),
[iquote('0:Rew:7.0,14.0')] ).
cnf(17,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[8,15]),
[iquote('0:Rew:8.0,15.0')] ).
cnf(29,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[2,10]),
[iquote('0:SpR:2.0,10.0')] ).
cnf(34,plain,
equal(converse(join(u,converse(v))),join(converse(u),v)),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(35,plain,
equal(converse(join(converse(u),v)),join(u,converse(v))),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(40,plain,
equal(meet(join(complement(u),complement(v)),w),complement(join(meet(u,v),complement(w)))),
inference(spr,[status(thm),theory(equality)],[8]),
[iquote('0:SpR:8.0,8.0')] ).
cnf(43,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[4,8]),
[iquote('0:SpR:4.0,8.0')] ).
cnf(44,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[7,8]),
[iquote('0:SpR:7.0,8.0')] ).
cnf(46,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[5,43]),
[iquote('0:Rew:5.0,43.0')] ).
cnf(47,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[8,44]),
[iquote('0:Rew:8.0,44.0')] ).
cnf(48,plain,
equal(meet(skc3,converse(skc2)),zero),
inference(rew,[status(thm),theory(equality)],[47,3]),
[iquote('0:Rew:47.0,3.0')] ).
cnf(54,plain,
equal(meet(top,zero),zero),
inference(spr,[status(thm),theory(equality)],[46,5]),
[iquote('0:SpR:46.0,5.0')] ).
cnf(56,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[46,8]),
[iquote('0:SpR:46.0,8.0')] ).
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)],[8,17]),
[iquote('0:SpR:8.0,17.0')] ).
cnf(69,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[4,17]),
[iquote('0:SpR:4.0,17.0')] ).
cnf(70,plain,
equal(join(meet(u,v),complement(join(v,complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[7,17]),
[iquote('0:SpR:7.0,17.0')] ).
cnf(72,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[8,17]),
[iquote('0:SpR:8.0,17.0')] ).
cnf(73,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[5,17]),
[iquote('0:SpR:5.0,17.0')] ).
cnf(74,plain,
equal(join(zero,complement(join(complement(skc3),converse(skc2)))),skc3),
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)],[7,75]),
[iquote('0:Rew:7.0,75.0')] ).
cnf(77,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[7,69,46]),
[iquote('0:Rew:7.0,69.0,46.0,69.0')] ).
cnf(78,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[7,72]),
[iquote('0:Rew:7.0,72.0')] ).
cnf(79,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[8,73]),
[iquote('0:Rew:8.0,73.0')] ).
cnf(80,plain,
equal(join(zero,complement(join(converse(skc2),complement(skc3)))),skc3),
inference(rew,[status(thm),theory(equality)],[7,74]),
[iquote('0:Rew:7.0,74.0')] ).
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)],[7,67]),
[iquote('0:Rew:7.0,67.0')] ).
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)],[56,8]),
[iquote('0:SpR:56.0,8.0')] ).
cnf(98,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,join(zero,complement(v)))),
inference(spr,[status(thm),theory(equality)],[56,8]),
[iquote('0:SpR:56.0,8.0')] ).
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)],[101,5]),
[iquote('0:SpR:101.0,5.0')] ).
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)],[7,141]),
[iquote('0:Rew:7.0,141.0')] ).
cnf(148,plain,
equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[11,147]),
[iquote('0:Rew:11.0,147.0')] ).
cnf(150,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[11,7]),
[iquote('0:SpR:11.0,7.0')] ).
cnf(154,plain,
equal(join(u,join(complement(u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[4,11]),
[iquote('0:SpR:4.0,11.0')] ).
cnf(160,plain,
equal(join(meet(u,v),join(complement(join(complement(u),v)),w)),join(u,w)),
inference(spr,[status(thm),theory(equality)],[17,11]),
[iquote('0:SpR:17.0,11.0')] ).
cnf(161,plain,
equal(join(zero,join(complement(join(top,complement(zero))),u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[76,11]),
[iquote('0:SpR:76.0,11.0')] ).
cnf(206,plain,
equal(join(complement(u),composition(v,complement(composition(converse(v),u)))),complement(u)),
inference(spr,[status(thm),theory(equality)],[2,16]),
[iquote('0:SpR:2.0,16.0')] ).
cnf(259,plain,
equal(meet(top,join(converse(skc2),complement(skc3))),complement(skc3)),
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)],[1,29]),
[iquote('0:SpR:1.0,29.0')] ).
cnf(319,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[2,316]),
[iquote('0:Rew:2.0,316.0')] ).
cnf(328,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[319,1]),
[iquote('0:SpR:319.0,1.0')] ).
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)],[345,8]),
[iquote('0:SpR:345.0,8.0')] ).
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)],[4,424]),
[iquote('0:Rew:4.0,424.0')] ).
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)],[8,405]),
[iquote('0:SpR:8.0,405.0')] ).
cnf(449,plain,
equal(complement(join(top,complement(u))),meet(zero,u)),
inference(spr,[status(thm),theory(equality)],[425,8]),
[iquote('0:SpR:425.0,8.0')] ).
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)],[455,11]),
[iquote('0:SpR:455.0,11.0')] ).
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(skc2),complement(skc3)),complement(skc3)),
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(skc2,converse(complement(skc3))),converse(complement(skc3))),
inference(spr,[status(thm),theory(equality)],[732,35]),
[iquote('0:SpR:732.0,35.0')] ).
cnf(1009,plain,
equal(join(u,join(v,complement(u))),join(top,v)),
inference(spr,[status(thm),theory(equality)],[7,154]),
[iquote('0:SpR:7.0,154.0')] ).
cnf(1096,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(1104,plain,
equal(join(u,meet(u,zero)),u),
inference(rew,[status(thm),theory(equality)],[46,1096]),
[iquote('0:Rew:46.0,1096.0')] ).
cnf(1126,plain,
equal(join(u,complement(u)),join(top,meet(complement(u),zero))),
inference(spr,[status(thm),theory(equality)],[1104,154]),
[iquote('0:SpR:1104.0,154.0')] ).
cnf(1136,plain,
equal(join(top,complement(join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[4,1126,760,47]),
[iquote('0:Rew:4.0,1126.0,760.0,1126.0,47.0,1126.0')] ).
cnf(1137,plain,
equal(complement(meet(zero,join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[761,1136]),
[iquote('0:Rew:761.0,1136.0')] ).
cnf(1223,plain,
equal(meet(zero,join(top,u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[1137,704]),
[iquote('0:SpR:1137.0,704.0')] ).
cnf(1253,plain,
equal(meet(zero,join(top,u)),zero),
inference(rew,[status(thm),theory(equality)],[46,1223]),
[iquote('0:Rew:46.0,1223.0')] ).
cnf(1265,plain,
equal(join(zero,meet(zero,complement(join(top,u)))),zero),
inference(spr,[status(thm),theory(equality)],[1253,78]),
[iquote('0:SpR:1253.0,78.0')] ).
cnf(1285,plain,
equal(complement(join(top,u)),zero),
inference(rew,[status(thm),theory(equality)],[698,1265,487,760]),
[iquote('0:Rew:698.0,1265.0,487.0,1265.0,760.0,1265.0')] ).
cnf(1368,plain,
equal(join(top,u),complement(zero)),
inference(spr,[status(thm),theory(equality)],[1285,704]),
[iquote('0:SpR:1285.0,704.0')] ).
cnf(1385,plain,
equal(join(top,u),top),
inference(rew,[status(thm),theory(equality)],[425,1368]),
[iquote('0:Rew:425.0,1368.0')] ).
cnf(1389,plain,
equal(join(u,join(v,complement(u))),top),
inference(rew,[status(thm),theory(equality)],[1385,1009]),
[iquote('0:Rew:1385.0,1009.0')] ).
cnf(1418,plain,
equal(join(converse(top),u),converse(top)),
inference(spr,[status(thm),theory(equality)],[1385,34]),
[iquote('0:SpR:1385.0,34.0')] ).
cnf(1469,plain,
equal(converse(top),top),
inference(spr,[status(thm),theory(equality)],[1418,4]),
[iquote('0:SpR:1418.0,4.0')] ).
cnf(1729,plain,
equal(join(u,join(v,w)),join(w,join(v,u))),
inference(spr,[status(thm),theory(equality)],[7,150]),
[iquote('0:SpR:7.0,150.0')] ).
cnf(2495,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(2898,plain,
equal(join(u,complement(meet(v,u))),top),
inference(spr,[status(thm),theory(equality)],[713,1389]),
[iquote('0:SpR:713.0,1389.0')] ).
cnf(2906,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(2909,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(2946,plain,
equal(complement(meet(u,meet(v,complement(u)))),top),
inference(spr,[status(thm),theory(equality)],[2898,713]),
[iquote('0:SpR:2898.0,713.0')] ).
cnf(3135,plain,
equal(meet(u,meet(v,complement(u))),complement(top)),
inference(spr,[status(thm),theory(equality)],[2946,704]),
[iquote('0:SpR:2946.0,704.0')] ).
cnf(3171,plain,
equal(meet(u,meet(v,complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[46,3135]),
[iquote('0:Rew:46.0,3135.0')] ).
cnf(3265,plain,
equal(join(zero,meet(u,complement(meet(v,complement(u))))),u),
inference(spr,[status(thm),theory(equality)],[3171,78]),
[iquote('0:SpR:3171.0,78.0')] ).
cnf(3277,plain,
equal(meet(complement(u),meet(v,u)),zero),
inference(spr,[status(thm),theory(equality)],[704,3171]),
[iquote('0:SpR:704.0,3171.0')] ).
cnf(3291,plain,
equal(meet(u,complement(meet(v,complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[698,3265]),
[iquote('0:Rew:698.0,3265.0')] ).
cnf(3292,plain,
equal(meet(u,join(complement(v),u)),u),
inference(rew,[status(thm),theory(equality)],[2906,3291]),
[iquote('0:Rew:2906.0,3291.0')] ).
cnf(3618,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[704,3292]),
[iquote('0:SpR:704.0,3292.0')] ).
cnf(3680,plain,
equal(meet(u,join(u,v)),u),
inference(spr,[status(thm),theory(equality)],[7,3618]),
[iquote('0:SpR:7.0,3618.0')] ).
cnf(3740,plain,
equal(meet(complement(join(u,v)),u),zero),
inference(spr,[status(thm),theory(equality)],[3680,3277]),
[iquote('0:SpR:3680.0,3277.0')] ).
cnf(3779,plain,
equal(meet(skc2,converse(complement(skc3))),skc2),
inference(spr,[status(thm),theory(equality)],[921,3680]),
[iquote('0:SpR:921.0,3680.0')] ).
cnf(3787,plain,
equal(meet(u,complement(join(u,v))),zero),
inference(rew,[status(thm),theory(equality)],[47,3740]),
[iquote('0:Rew:47.0,3740.0')] ).
cnf(3840,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(3880,plain,
equal(join(u,meet(v,u)),join(u,meet(u,v))),
inference(rew,[status(thm),theory(equality)],[704,3840,7]),
[iquote('0:Rew:704.0,3840.0,7.0,3840.0')] ).
cnf(3940,plain,
equal(join(converse(complement(skc3)),complement(skc2)),top),
inference(spr,[status(thm),theory(equality)],[3779,2898]),
[iquote('0:SpR:3779.0,2898.0')] ).
cnf(3944,plain,
equal(join(complement(skc2),converse(complement(skc3))),top),
inference(rew,[status(thm),theory(equality)],[7,3940]),
[iquote('0:Rew:7.0,3940.0')] ).
cnf(3979,plain,
equal(join(converse(complement(skc2)),complement(skc3)),converse(top)),
inference(spr,[status(thm),theory(equality)],[3944,34]),
[iquote('0:SpR:3944.0,34.0')] ).
cnf(3985,plain,
equal(join(complement(skc3),converse(complement(skc2))),top),
inference(rew,[status(thm),theory(equality)],[7,3979,1469]),
[iquote('0:Rew:7.0,3979.0,1469.0,3979.0')] ).
cnf(6834,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(6853,plain,
equal(complement(meet(u,join(complement(u),join(v,meet(u,v))))),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[1729,6834,2909]),
[iquote('0:Rew:1729.0,6834.0,2909.0,6834.0')] ).
cnf(12257,plain,
equal(converse(join(converse(u),meet(converse(u),v))),join(u,converse(meet(v,converse(u))))),
inference(spr,[status(thm),theory(equality)],[3880,35]),
[iquote('0:SpR:3880.0,35.0')] ).
cnf(12372,plain,
equal(join(u,converse(meet(converse(u),v))),join(u,converse(meet(v,converse(u))))),
inference(rew,[status(thm),theory(equality)],[35,12257]),
[iquote('0:Rew:35.0,12257.0')] ).
cnf(17095,plain,
equal(join(u,complement(composition(converse(one),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[338,2495]),
[iquote('0:SpR:338.0,2495.0')] ).
cnf(17105,plain,
equal(join(u,u),u),
inference(rew,[status(thm),theory(equality)],[704,17095,338,328]),
[iquote('0:Rew:704.0,17095.0,338.0,17095.0,328.0,17095.0')] ).
cnf(17324,plain,
equal(join(meet(u,v),meet(u,complement(v))),join(u,meet(u,complement(v)))),
inference(spr,[status(thm),theory(equality)],[17105,772]),
[iquote('0:SpR:17105.0,772.0')] ).
cnf(17377,plain,
equal(join(u,meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[78,17324]),
[iquote('0:Rew:78.0,17324.0')] ).
cnf(17444,plain,
equal(join(u,meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[704,17377]),
[iquote('0:SpR:704.0,17377.0')] ).
cnf(17477,plain,
equal(join(u,meet(v,u)),u),
inference(rew,[status(thm),theory(equality)],[17444,3880]),
[iquote('0:Rew:17444.0,3880.0')] ).
cnf(17492,plain,
equal(complement(meet(u,join(complement(u),v))),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[17477,6853]),
[iquote('0:Rew:17477.0,6853.0')] ).
cnf(17548,plain,
equal(join(u,converse(meet(converse(u),v))),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[17444,35]),
[iquote('0:SpR:17444.0,35.0')] ).
cnf(17665,plain,
equal(join(u,converse(meet(converse(u),v))),u),
inference(rew,[status(thm),theory(equality)],[2,17548]),
[iquote('0:Rew:2.0,17548.0')] ).
cnf(17666,plain,
equal(join(u,converse(meet(v,converse(u)))),u),
inference(rew,[status(thm),theory(equality)],[17665,12372]),
[iquote('0:Rew:17665.0,12372.0')] ).
cnf(20032,plain,
equal(complement(meet(skc3,converse(complement(skc2)))),complement(meet(skc3,top))),
inference(spr,[status(thm),theory(equality)],[3985,17492]),
[iquote('0:SpR:3985.0,17492.0')] ).
cnf(20091,plain,
equal(complement(meet(skc3,converse(complement(skc2)))),complement(skc3)),
inference(rew,[status(thm),theory(equality)],[731,20032,47]),
[iquote('0:Rew:731.0,20032.0,47.0,20032.0')] ).
cnf(21570,plain,
equal(meet(skc3,converse(complement(skc2))),complement(complement(skc3))),
inference(spr,[status(thm),theory(equality)],[20091,704]),
[iquote('0:SpR:20091.0,704.0')] ).
cnf(21622,plain,
equal(meet(skc3,converse(complement(skc2))),skc3),
inference(rew,[status(thm),theory(equality)],[704,21570]),
[iquote('0:Rew:704.0,21570.0')] ).
cnf(21716,plain,
equal(join(complement(skc2),converse(skc3)),complement(skc2)),
inference(spr,[status(thm),theory(equality)],[21622,17666]),
[iquote('0:SpR:21622.0,17666.0')] ).
cnf(21734,plain,
equal(join(converse(skc3),complement(skc2)),complement(skc2)),
inference(rew,[status(thm),theory(equality)],[7,21716]),
[iquote('0:Rew:7.0,21716.0')] ).
cnf(22059,plain,
equal(meet(converse(skc3),complement(complement(skc2))),zero),
inference(spr,[status(thm),theory(equality)],[21734,3787]),
[iquote('0:SpR:21734.0,3787.0')] ).
cnf(22085,plain,
equal(meet(skc2,converse(skc3)),zero),
inference(rew,[status(thm),theory(equality)],[47,22059,704]),
[iquote('0:Rew:47.0,22059.0,704.0,22059.0')] ).
cnf(22086,plain,
$false,
inference(mrr,[status(thm)],[22085,6]),
[iquote('0:MRR:22085.0,6.0')] ).
%------------------------------------------------------------------------------
%----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
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 8 11:29:51 EDT 2022
% 0.14/0.34 % CPUTime :
% 3.58/3.78
% 3.58/3.78 SPASS V 3.9
% 3.58/3.78 SPASS beiseite: Proof found.
% 3.58/3.78 % SZS status Theorem
% 3.58/3.78 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.58/3.78 SPASS derived 13608 clauses, backtracked 0 clauses, performed 0 splits and kept 1950 clauses.
% 3.58/3.78 SPASS allocated 104705 KBytes.
% 3.58/3.78 SPASS spent 0:00:03.41 on the problem.
% 3.58/3.78 0:00:00.04 for the input.
% 3.58/3.78 0:00:00.02 for the FLOTTER CNF translation.
% 3.58/3.78 0:00:00.10 for inferences.
% 3.58/3.78 0:00:00.00 for the backtracking.
% 3.58/3.78 0:00:03.21 for the reduction.
% 3.58/3.78
% 3.58/3.78
% 3.58/3.78 Here is a proof with depth 15, length 158 :
% 3.58/3.78 % SZS output start Refutation
% See solution above
% 3.72/3.92 Formulae used in the proof : composition_identity converse_idempotence goals def_top def_zero maddux1_join_commutativity maddux4_definiton_of_meet converse_additivity converse_multiplicativity maddux2_join_associativity converse_cancellativity maddux3_a_kind_of_de_Morgan
% 3.72/3.92
%------------------------------------------------------------------------------