TSTP Solution File: REL018-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL018-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 20:01:46 EDT 2022
% Result : Unsatisfiable 3.42s 3.59s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 15
% Syntax : Number of clauses : 125 ( 125 unt; 0 nHn; 125 RR)
% Number of literals : 125 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(composition(sk1,top),sk1),
file('REL018-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(composition(complement(sk1),top),complement(sk1)),
file('REL018-1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,v),join(v,u)),
file('REL018-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL018-1.p',unknown),
[] ).
cnf(5,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL018-1.p',unknown),
[] ).
cnf(6,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL018-1.p',unknown),
[] ).
cnf(7,axiom,
equal(composition(composition(u,v),w),composition(u,composition(v,w))),
file('REL018-1.p',unknown),
[] ).
cnf(8,axiom,
equal(composition(u,one),u),
file('REL018-1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL018-1.p',unknown),
[] ).
cnf(10,axiom,
equal(converse(converse(u)),u),
file('REL018-1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL018-1.p',unknown),
[] ).
cnf(12,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL018-1.p',unknown),
[] ).
cnf(13,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL018-1.p',unknown),
[] ).
cnf(14,axiom,
equal(join(u,complement(u)),top),
file('REL018-1.p',unknown),
[] ).
cnf(15,axiom,
equal(meet(u,complement(u)),zero),
file('REL018-1.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(39,plain,
equal(join(join(complement(u),complement(v)),meet(u,v)),top),
inference(spr,[status(thm),theory(equality)],[6,14]),
[iquote('0:SpR:6.0,14.0')] ).
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(46,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[15,43]),
[iquote('0:Rew:15.0,43.0')] ).
cnf(50,plain,
equal(join(meet(u,v),join(complement(u),complement(v))),top),
inference(rew,[status(thm),theory(equality)],[3,39]),
[iquote('0:Rew:3.0,39.0')] ).
cnf(55,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(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(78,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(79,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(80,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[6,73]),
[iquote('0:Rew:6.0,73.0')] ).
cnf(91,plain,
equal(complement(join(meet(top,u),complement(v))),meet(join(zero,complement(u)),v)),
inference(spr,[status(thm),theory(equality)],[55,6]),
[iquote('0:SpR:55.0,6.0')] ).
cnf(94,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,join(zero,complement(v)))),
inference(spr,[status(thm),theory(equality)],[55,6]),
[iquote('0:SpR:55.0,6.0')] ).
cnf(159,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(163,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(168,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(172,plain,
equal(join(complement(u),join(meet(v,u),complement(v))),top),
inference(rew,[status(thm),theory(equality)],[159,50]),
[iquote('0:Rew:159.0,50.0')] ).
cnf(178,plain,
equal(join(complement(u),join(complement(v),meet(v,u))),top),
inference(rew,[status(thm),theory(equality)],[3,172]),
[iquote('0:Rew:3.0,172.0')] ).
cnf(205,plain,
equal(join(complement(top),composition(converse(sk1),complement(sk1))),complement(top)),
inference(spr,[status(thm),theory(equality)],[1,16]),
[iquote('0:SpR:1.0,16.0')] ).
cnf(210,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(214,plain,
equal(join(zero,composition(converse(u),complement(composition(u,top)))),zero),
inference(spr,[status(thm),theory(equality)],[46,16]),
[iquote('0:SpR:46.0,16.0')] ).
cnf(215,plain,
equal(join(zero,composition(converse(sk1),complement(sk1))),zero),
inference(rew,[status(thm),theory(equality)],[46,205]),
[iquote('0:Rew:46.0,205.0')] ).
cnf(333,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(336,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[10,333]),
[iquote('0:Rew:10.0,333.0')] ).
cnf(345,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[336,8]),
[iquote('0:SpR:336.0,8.0')] ).
cnf(348,plain,
equal(join(u,composition(v,u)),composition(join(converse(one),v),u)),
inference(spr,[status(thm),theory(equality)],[336,9]),
[iquote('0:SpR:336.0,9.0')] ).
cnf(351,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[336,16]),
[iquote('0:SpR:336.0,16.0')] ).
cnf(355,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[345,336]),
[iquote('0:Rew:345.0,336.0')] ).
cnf(362,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[355,351]),
[iquote('0:Rew:355.0,351.0')] ).
cnf(363,plain,
equal(join(u,composition(v,u)),composition(join(one,v),u)),
inference(rew,[status(thm),theory(equality)],[345,348]),
[iquote('0:Rew:345.0,348.0')] ).
cnf(398,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[362,6]),
[iquote('0:SpR:362.0,6.0')] ).
cnf(404,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[46,362]),
[iquote('0:SpR:46.0,362.0')] ).
cnf(421,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[398,80]),
[iquote('0:Rew:398.0,80.0')] ).
cnf(449,plain,
equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[6,421]),
[iquote('0:SpR:6.0,421.0')] ).
cnf(460,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[404,4]),
[iquote('0:SpR:404.0,4.0')] ).
cnf(635,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[78,460]),
[iquote('0:SpR:78.0,460.0')] ).
cnf(640,plain,
equal(composition(converse(sk1),complement(sk1)),zero),
inference(rew,[status(thm),theory(equality)],[635,215]),
[iquote('0:Rew:635.0,215.0')] ).
cnf(642,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[635,421]),
[iquote('0:Rew:635.0,421.0')] ).
cnf(643,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[635,55]),
[iquote('0:Rew:635.0,55.0')] ).
cnf(645,plain,
equal(composition(converse(u),complement(composition(u,top))),zero),
inference(rew,[status(thm),theory(equality)],[635,214]),
[iquote('0:Rew:635.0,214.0')] ).
cnf(650,plain,
equal(join(complement(u),complement(v)),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[635,449]),
[iquote('0:Rew:635.0,449.0')] ).
cnf(652,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[635,94]),
[iquote('0:Rew:635.0,94.0')] ).
cnf(655,plain,
equal(complement(join(meet(top,u),complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[635,91]),
[iquote('0:Rew:635.0,91.0')] ).
cnf(663,plain,
equal(meet(u,u),u),
inference(rew,[status(thm),theory(equality)],[642,398]),
[iquote('0:Rew:642.0,398.0')] ).
cnf(670,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[642,643]),
[iquote('0:Rew:642.0,643.0')] ).
cnf(698,plain,
equal(complement(join(complement(u),v)),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[670,652]),
[iquote('0:Rew:670.0,652.0')] ).
cnf(701,plain,
equal(join(meet(u,v),join(meet(u,complement(v)),w)),join(u,w)),
inference(rew,[status(thm),theory(equality)],[698,168]),
[iquote('0:Rew:698.0,168.0')] ).
cnf(702,plain,
equal(complement(join(u,complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[670,655]),
[iquote('0:Rew:670.0,655.0')] ).
cnf(703,plain,
equal(join(meet(u,v),meet(complement(v),u)),u),
inference(rew,[status(thm),theory(equality)],[702,70]),
[iquote('0:Rew:702.0,70.0')] ).
cnf(712,plain,
equal(complement(zero),top),
inference(spr,[status(thm),theory(equality)],[635,14]),
[iquote('0:SpR:635.0,14.0')] ).
cnf(713,plain,
equal(join(u,zero),u),
inference(spr,[status(thm),theory(equality)],[635,3]),
[iquote('0:SpR:635.0,3.0')] ).
cnf(717,plain,
equal(join(converse(zero),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[635,34]),
[iquote('0:SpR:635.0,34.0')] ).
cnf(727,plain,
equal(join(converse(zero),u),u),
inference(rew,[status(thm),theory(equality)],[10,717]),
[iquote('0:Rew:10.0,717.0')] ).
cnf(750,plain,
equal(join(complement(complement(sk1)),composition(converse(converse(sk1)),complement(zero))),complement(complement(sk1))),
inference(spr,[status(thm),theory(equality)],[640,16]),
[iquote('0:SpR:640.0,16.0')] ).
cnf(753,plain,
equal(composition(converse(complement(sk1)),sk1),converse(zero)),
inference(spr,[status(thm),theory(equality)],[640,29]),
[iquote('0:SpR:640.0,29.0')] ).
cnf(755,plain,
equal(join(sk1,sk1),sk1),
inference(rew,[status(thm),theory(equality)],[1,750,10,712,642]),
[iquote('0:Rew:1.0,750.0,10.0,750.0,712.0,750.0,642.0,750.0')] ).
cnf(759,plain,
equal(join(sk1,join(sk1,u)),join(sk1,u)),
inference(spr,[status(thm),theory(equality)],[755,4]),
[iquote('0:SpR:755.0,4.0')] ).
cnf(815,plain,
equal(join(u,converse(complement(converse(u)))),converse(top)),
inference(spr,[status(thm),theory(equality)],[14,35]),
[iquote('0:SpR:14.0,35.0')] ).
cnf(844,plain,
equal(converse(zero),zero),
inference(spr,[status(thm),theory(equality)],[727,713]),
[iquote('0:SpR:727.0,713.0')] ).
cnf(851,plain,
equal(composition(converse(complement(sk1)),sk1),zero),
inference(rew,[status(thm),theory(equality)],[844,753]),
[iquote('0:Rew:844.0,753.0')] ).
cnf(880,plain,
equal(join(complement(sk1),composition(converse(converse(complement(sk1))),complement(zero))),complement(sk1)),
inference(spr,[status(thm),theory(equality)],[851,16]),
[iquote('0:SpR:851.0,16.0')] ).
cnf(886,plain,
equal(join(complement(sk1),composition(complement(sk1),top)),complement(sk1)),
inference(rew,[status(thm),theory(equality)],[10,880,712]),
[iquote('0:Rew:10.0,880.0,712.0,880.0')] ).
cnf(1027,plain,
equal(join(sk1,converse(top)),converse(top)),
inference(spr,[status(thm),theory(equality)],[815,759]),
[iquote('0:SpR:815.0,759.0')] ).
cnf(1028,plain,
equal(join(top,converse(complement(converse(complement(u))))),join(u,converse(top))),
inference(spr,[status(thm),theory(equality)],[815,163]),
[iquote('0:SpR:815.0,163.0')] ).
cnf(1481,plain,
equal(join(complement(u),join(complement(u),u)),top),
inference(spr,[status(thm),theory(equality)],[663,178]),
[iquote('0:SpR:663.0,178.0')] ).
cnf(1493,plain,
equal(join(top,complement(u)),top),
inference(rew,[status(thm),theory(equality)],[3,1481,14]),
[iquote('0:Rew:3.0,1481.0,14.0,1481.0,3.0,1481.0')] ).
cnf(1509,plain,
equal(join(top,u),top),
inference(spr,[status(thm),theory(equality)],[642,1493]),
[iquote('0:SpR:642.0,1493.0')] ).
cnf(1515,plain,
equal(join(u,converse(top)),top),
inference(rew,[status(thm),theory(equality)],[1509,1028]),
[iquote('0:Rew:1509.0,1028.0')] ).
cnf(1523,plain,
equal(converse(top),top),
inference(rew,[status(thm),theory(equality)],[1515,1027]),
[iquote('0:Rew:1515.0,1027.0')] ).
cnf(1539,plain,
equal(composition(top,converse(u)),converse(composition(u,top))),
inference(spr,[status(thm),theory(equality)],[1523,12]),
[iquote('0:SpR:1523.0,12.0')] ).
cnf(1544,plain,
equal(composition(top,complement(composition(top,top))),zero),
inference(spr,[status(thm),theory(equality)],[1523,645]),
[iquote('0:SpR:1523.0,645.0')] ).
cnf(1551,plain,
equal(join(complement(u),composition(top,complement(composition(top,u)))),complement(u)),
inference(spr,[status(thm),theory(equality)],[1523,16]),
[iquote('0:SpR:1523.0,16.0')] ).
cnf(1648,plain,
equal(join(zero,composition(u,complement(composition(top,top)))),composition(join(top,u),complement(composition(top,top)))),
inference(spr,[status(thm),theory(equality)],[1544,9]),
[iquote('0:SpR:1544.0,9.0')] ).
cnf(1653,plain,
equal(composition(u,complement(composition(top,top))),zero),
inference(rew,[status(thm),theory(equality)],[635,1648,1544,1509]),
[iquote('0:Rew:635.0,1648.0,1544.0,1648.0,1509.0,1648.0')] ).
cnf(1901,plain,
equal(complement(composition(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[1653,355]),
[iquote('0:SpR:1653.0,355.0')] ).
cnf(2073,plain,
equal(composition(top,top),complement(zero)),
inference(spr,[status(thm),theory(equality)],[1901,642]),
[iquote('0:SpR:1901.0,642.0')] ).
cnf(2084,plain,
equal(composition(top,top),top),
inference(rew,[status(thm),theory(equality)],[712,2073]),
[iquote('0:Rew:712.0,2073.0')] ).
cnf(2255,plain,
equal(composition(top,composition(top,u)),composition(top,u)),
inference(spr,[status(thm),theory(equality)],[2084,7]),
[iquote('0:SpR:2084.0,7.0')] ).
cnf(2566,plain,
equal(join(u,composition(v,complement(composition(converse(v),complement(u))))),u),
inference(spr,[status(thm),theory(equality)],[642,210]),
[iquote('0:SpR:642.0,210.0')] ).
cnf(3006,plain,
equal(join(complement(composition(top,u)),composition(converse(top),complement(composition(top,u)))),complement(composition(top,u))),
inference(spr,[status(thm),theory(equality)],[2255,16]),
[iquote('0:SpR:2255.0,16.0')] ).
cnf(3027,plain,
equal(join(complement(composition(top,u)),composition(top,complement(composition(top,u)))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[1523,3006]),
[iquote('0:Rew:1523.0,3006.0')] ).
cnf(3028,plain,
equal(composition(join(one,top),complement(composition(top,u))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[363,3027]),
[iquote('0:Rew:363.0,3027.0')] ).
cnf(3029,plain,
equal(composition(top,complement(composition(top,u))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[1509,3028,3]),
[iquote('0:Rew:1509.0,3028.0,3.0,3028.0')] ).
cnf(3030,plain,
equal(join(complement(u),complement(composition(top,u))),complement(u)),
inference(rew,[status(thm),theory(equality)],[3029,1551]),
[iquote('0:Rew:3029.0,1551.0')] ).
cnf(3032,plain,
equal(complement(meet(u,composition(top,u))),complement(u)),
inference(rew,[status(thm),theory(equality)],[650,3030]),
[iquote('0:Rew:650.0,3030.0')] ).
cnf(3298,plain,
equal(join(u,meet(complement(complement(v)),u)),join(meet(u,v),u)),
inference(spr,[status(thm),theory(equality)],[703,701]),
[iquote('0:SpR:703.0,701.0')] ).
cnf(3333,plain,
equal(join(u,meet(v,u)),join(u,meet(u,v))),
inference(rew,[status(thm),theory(equality)],[642,3298,3]),
[iquote('0:Rew:642.0,3298.0,3.0,3298.0')] ).
cnf(3709,plain,
equal(meet(u,composition(top,u)),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[3032,642]),
[iquote('0:SpR:3032.0,642.0')] ).
cnf(3737,plain,
equal(meet(u,composition(top,u)),u),
inference(rew,[status(thm),theory(equality)],[642,3709]),
[iquote('0:Rew:642.0,3709.0')] ).
cnf(3916,plain,
equal(meet(converse(u),converse(composition(u,top))),converse(u)),
inference(spr,[status(thm),theory(equality)],[1539,3737]),
[iquote('0:SpR:1539.0,3737.0')] ).
cnf(13139,plain,
equal(converse(join(converse(u),meet(converse(u),v))),join(u,converse(meet(v,converse(u))))),
inference(spr,[status(thm),theory(equality)],[3333,35]),
[iquote('0:SpR:3333.0,35.0')] ).
cnf(13265,plain,
equal(join(u,converse(meet(converse(u),v))),join(u,converse(meet(v,converse(u))))),
inference(rew,[status(thm),theory(equality)],[35,13139]),
[iquote('0:Rew:35.0,13139.0')] ).
cnf(18952,plain,
equal(join(u,complement(composition(converse(one),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[355,2566]),
[iquote('0:SpR:355.0,2566.0')] ).
cnf(18968,plain,
equal(join(u,u),u),
inference(rew,[status(thm),theory(equality)],[642,18952,355,345]),
[iquote('0:Rew:642.0,18952.0,355.0,18952.0,345.0,18952.0')] ).
cnf(19159,plain,
equal(join(meet(u,v),meet(u,complement(v))),join(u,meet(u,complement(v)))),
inference(spr,[status(thm),theory(equality)],[18968,701]),
[iquote('0:SpR:18968.0,701.0')] ).
cnf(19284,plain,
equal(join(u,meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[79,19159]),
[iquote('0:Rew:79.0,19159.0')] ).
cnf(19355,plain,
equal(join(u,meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[642,19284]),
[iquote('0:SpR:642.0,19284.0')] ).
cnf(19464,plain,
equal(join(u,converse(meet(converse(u),v))),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[19355,35]),
[iquote('0:SpR:19355.0,35.0')] ).
cnf(19580,plain,
equal(join(u,converse(meet(converse(u),v))),u),
inference(rew,[status(thm),theory(equality)],[10,19464]),
[iquote('0:Rew:10.0,19464.0')] ).
cnf(19581,plain,
equal(join(u,converse(meet(v,converse(u)))),u),
inference(rew,[status(thm),theory(equality)],[19580,13265]),
[iquote('0:Rew:19580.0,13265.0')] ).
cnf(21649,plain,
equal(join(composition(u,top),converse(converse(u))),composition(u,top)),
inference(spr,[status(thm),theory(equality)],[3916,19581]),
[iquote('0:SpR:3916.0,19581.0')] ).
cnf(21678,plain,
equal(join(u,composition(u,top)),composition(u,top)),
inference(rew,[status(thm),theory(equality)],[3,21649,10]),
[iquote('0:Rew:3.0,21649.0,10.0,21649.0')] ).
cnf(21679,plain,
equal(composition(complement(sk1),top),complement(sk1)),
inference(rew,[status(thm),theory(equality)],[21678,886]),
[iquote('0:Rew:21678.0,886.0')] ).
cnf(21682,plain,
$false,
inference(mrr,[status(thm)],[21679,2]),
[iquote('0:MRR:21679.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : REL018-1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 15:56:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.42/3.59
% 3.42/3.59 SPASS V 3.9
% 3.42/3.59 SPASS beiseite: Proof found.
% 3.42/3.59 % SZS status Theorem
% 3.42/3.59 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.42/3.59 SPASS derived 13428 clauses, backtracked 0 clauses, performed 0 splits and kept 2104 clauses.
% 3.42/3.59 SPASS allocated 82421 KBytes.
% 3.42/3.59 SPASS spent 0:00:03.24 on the problem.
% 3.42/3.59 0:00:00.03 for the input.
% 3.42/3.59 0:00:00.00 for the FLOTTER CNF translation.
% 3.42/3.59 0:00:00.09 for inferences.
% 3.42/3.59 0:00:00.00 for the backtracking.
% 3.42/3.59 0:00:03.07 for the reduction.
% 3.42/3.59
% 3.42/3.59
% 3.42/3.59 Here is a proof with depth 10, length 125 :
% 3.42/3.59 % SZS output start Refutation
% See solution above
% 3.55/3.74 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_associativity_5 composition_identity_6 composition_distributivity_7 converse_idempotence_8 converse_additivity_9 converse_multiplicativity_10 converse_cancellativity_11 def_top_12 def_zero_13
% 3.55/3.74
%------------------------------------------------------------------------------