TSTP Solution File: REL042+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL042+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 20:02:24 EDT 2022
% Result : Theorem 13.66s 13.88s
% Output : Refutation 14.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 15
% Syntax : Number of clauses : 130 ( 130 unt; 0 nHn; 130 RR)
% Number of literals : 130 ( 0 equ; 2 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 : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(composition(u,one),u),
file('REL042+2.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL042+2.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,complement(u)),top),
file('REL042+2.p',unknown),
[] ).
cnf(4,axiom,
equal(meet(u,complement(u)),zero),
file('REL042+2.p',unknown),
[] ).
cnf(5,axiom,
equal(join(u,v),join(v,u)),
file('REL042+2.p',unknown),
[] ).
cnf(6,axiom,
~ equal(join(composition(converse(skc1),skc1),one),one),
file('REL042+2.p',unknown),
[] ).
cnf(7,axiom,
equal(meet(composition(skc1,u),composition(skc1,complement(u))),zero),
file('REL042+2.p',unknown),
[] ).
cnf(8,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL042+2.p',unknown),
[] ).
cnf(9,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL042+2.p',unknown),
[] ).
cnf(10,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL042+2.p',unknown),
[] ).
cnf(11,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL042+2.p',unknown),
[] ).
cnf(13,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL042+2.p',unknown),
[] ).
cnf(14,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL042+2.p',unknown),
[] ).
cnf(15,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL042+2.p',unknown),
[] ).
cnf(17,axiom,
equal(join(meet(composition(u,v),w),meet(composition(u,meet(v,composition(converse(u),w))),w)),meet(composition(u,meet(v,composition(converse(u),w))),w)),
file('REL042+2.p',unknown),
[] ).
cnf(19,plain,
~ equal(join(one,composition(converse(skc1),skc1)),one),
inference(rew,[status(thm),theory(equality)],[5,6]),
[iquote('0:Rew:5.0,6.0')] ).
cnf(20,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[5,14]),
[iquote('0:Rew:5.0,14.0')] ).
cnf(21,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(32,plain,
equal(meet(skc1,composition(skc1,complement(one))),zero),
inference(spr,[status(thm),theory(equality)],[1,7]),
[iquote('0:SpR:1.0,7.0')] ).
cnf(35,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(40,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(41,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(84,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpR:3.0,8.0')] ).
cnf(85,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[5,8]),
[iquote('0:SpR:5.0,8.0')] ).
cnf(87,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[4,84]),
[iquote('0:Rew:4.0,84.0')] ).
cnf(88,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[8,85]),
[iquote('0:Rew:8.0,85.0')] ).
cnf(89,plain,
equal(join(meet(composition(u,v),w),meet(w,composition(u,meet(v,composition(converse(u),w))))),meet(w,composition(u,meet(v,composition(converse(u),w))))),
inference(rew,[status(thm),theory(equality)],[88,17]),
[iquote('0:Rew:88.0,17.0')] ).
cnf(97,plain,
equal(meet(top,zero),zero),
inference(spr,[status(thm),theory(equality)],[87,4]),
[iquote('0:SpR:87.0,4.0')] ).
cnf(100,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[87,8]),
[iquote('0:SpR:87.0,8.0')] ).
cnf(103,plain,
equal(meet(zero,top),zero),
inference(rew,[status(thm),theory(equality)],[88,97]),
[iquote('0:Rew:88.0,97.0')] ).
cnf(111,plain,
equal(join(meet(top,u),complement(join(zero,u))),top),
inference(spr,[status(thm),theory(equality)],[87,21]),
[iquote('0:SpR:87.0,21.0')] ).
cnf(112,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[3,21]),
[iquote('0:SpR:3.0,21.0')] ).
cnf(115,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[8,21]),
[iquote('0:SpR:8.0,21.0')] ).
cnf(116,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[4,21]),
[iquote('0:SpR:4.0,21.0')] ).
cnf(119,plain,
equal(join(zero,complement(join(complement(zero),top))),zero),
inference(spr,[status(thm),theory(equality)],[103,21]),
[iquote('0:SpR:103.0,21.0')] ).
cnf(120,plain,
equal(join(zero,complement(join(top,complement(zero)))),zero),
inference(rew,[status(thm),theory(equality)],[5,119]),
[iquote('0:Rew:5.0,119.0')] ).
cnf(121,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[5,112,87]),
[iquote('0:Rew:5.0,112.0,87.0,112.0')] ).
cnf(122,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[5,115]),
[iquote('0:Rew:5.0,115.0')] ).
cnf(123,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[8,116]),
[iquote('0:Rew:8.0,116.0')] ).
cnf(147,plain,
equal(meet(join(zero,complement(u)),meet(top,u)),zero),
inference(spr,[status(thm),theory(equality)],[100,4]),
[iquote('0:SpR:100.0,4.0')] ).
cnf(153,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,join(zero,complement(v)))),
inference(spr,[status(thm),theory(equality)],[100,8]),
[iquote('0:SpR:100.0,8.0')] ).
cnf(156,plain,
equal(complement(join(zero,zero)),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[87,100]),
[iquote('0:SpR:87.0,100.0')] ).
cnf(160,plain,
equal(meet(meet(top,u),join(zero,complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[88,147]),
[iquote('0:Rew:88.0,147.0')] ).
cnf(166,plain,
equal(meet(join(zero,zero),meet(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[156,4]),
[iquote('0:SpR:156.0,4.0')] ).
cnf(176,plain,
equal(meet(meet(top,top),join(zero,zero)),zero),
inference(rew,[status(thm),theory(equality)],[88,166]),
[iquote('0:Rew:88.0,166.0')] ).
cnf(189,plain,
equal(join(u,join(v,complement(join(u,v)))),top),
inference(spr,[status(thm),theory(equality)],[11,3]),
[iquote('0:SpR:11.0,3.0')] ).
cnf(190,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[11,5]),
[iquote('0:SpR:11.0,5.0')] ).
cnf(196,plain,
equal(join(u,join(complement(u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[3,11]),
[iquote('0:SpR:3.0,11.0')] ).
cnf(203,plain,
equal(join(zero,join(complement(join(top,complement(zero))),u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[120,11]),
[iquote('0:SpR:120.0,11.0')] ).
cnf(219,plain,
equal(join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[176,21]),
[iquote('0:SpR:176.0,21.0')] ).
cnf(225,plain,
equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[11,219,5]),
[iquote('0:Rew:11.0,219.0,5.0,219.0')] ).
cnf(252,plain,
equal(join(zero,composition(converse(u),complement(composition(u,top)))),zero),
inference(spr,[status(thm),theory(equality)],[87,20]),
[iquote('0:SpR:87.0,20.0')] ).
cnf(354,plain,
equal(join(meet(composition(converse(u),v),w),meet(w,composition(converse(u),meet(v,composition(u,w))))),meet(w,composition(converse(u),meet(v,composition(u,w))))),
inference(spr,[status(thm),theory(equality)],[2,89]),
[iquote('0:SpR:2.0,89.0')] ).
cnf(390,plain,
equal(meet(meet(u,top),join(zero,complement(u))),zero),
inference(spr,[status(thm),theory(equality)],[88,160]),
[iquote('0:SpR:88.0,160.0')] ).
cnf(567,plain,
equal(join(zero,complement(join(complement(meet(u,top)),join(zero,complement(u))))),meet(u,top)),
inference(spr,[status(thm),theory(equality)],[390,21]),
[iquote('0:SpR:390.0,21.0')] ).
cnf(590,plain,
equal(join(zero,complement(join(zero,join(complement(u),complement(meet(u,top)))))),meet(u,top)),
inference(rew,[status(thm),theory(equality)],[190,567]),
[iquote('0:Rew:190.0,567.0')] ).
cnf(655,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[1,35]),
[iquote('0:SpR:1.0,35.0')] ).
cnf(658,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[2,655]),
[iquote('0:Rew:2.0,655.0')] ).
cnf(669,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[658,1]),
[iquote('0:SpR:658.0,1.0')] ).
cnf(680,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[658,20]),
[iquote('0:SpR:658.0,20.0')] ).
cnf(687,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[669,658]),
[iquote('0:Rew:669.0,658.0')] ).
cnf(703,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[687,680]),
[iquote('0:Rew:687.0,680.0')] ).
cnf(776,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[703,8]),
[iquote('0:SpR:703.0,8.0')] ).
cnf(782,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[87,703]),
[iquote('0:SpR:87.0,703.0')] ).
cnf(787,plain,
equal(meet(top,top),complement(zero)),
inference(rew,[status(thm),theory(equality)],[782,156]),
[iquote('0:Rew:782.0,156.0')] ).
cnf(801,plain,
equal(join(zero,complement(join(zero,join(zero,complement(complement(zero)))))),complement(zero)),
inference(rew,[status(thm),theory(equality)],[787,225]),
[iquote('0:Rew:787.0,225.0')] ).
cnf(803,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[776,123]),
[iquote('0:Rew:776.0,123.0')] ).
cnf(833,plain,
equal(join(zero,complement(zero)),complement(zero)),
inference(rew,[status(thm),theory(equality)],[782,801,803]),
[iquote('0:Rew:782.0,801.0,803.0,801.0')] ).
cnf(834,plain,
equal(complement(zero),top),
inference(rew,[status(thm),theory(equality)],[3,833]),
[iquote('0:Rew:3.0,833.0')] ).
cnf(842,plain,
equal(join(zero,join(complement(join(top,top)),u)),join(zero,u)),
inference(rew,[status(thm),theory(equality)],[834,203]),
[iquote('0:Rew:834.0,203.0')] ).
cnf(861,plain,
equal(meet(top,complement(u)),complement(u)),
inference(spr,[status(thm),theory(equality)],[803,100]),
[iquote('0:SpR:803.0,100.0')] ).
cnf(867,plain,
equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[8,803]),
[iquote('0:SpR:8.0,803.0')] ).
cnf(888,plain,
equal(complement(join(top,complement(u))),meet(zero,u)),
inference(spr,[status(thm),theory(equality)],[834,8]),
[iquote('0:SpR:834.0,8.0')] ).
cnf(889,plain,
equal(join(meet(zero,u),complement(join(top,u))),zero),
inference(spr,[status(thm),theory(equality)],[834,21]),
[iquote('0:SpR:834.0,21.0')] ).
cnf(898,plain,
equal(join(top,top),top),
inference(spr,[status(thm),theory(equality)],[834,703]),
[iquote('0:SpR:834.0,703.0')] ).
cnf(907,plain,
equal(join(zero,join(complement(top),u)),join(zero,u)),
inference(rew,[status(thm),theory(equality)],[898,842]),
[iquote('0:Rew:898.0,842.0')] ).
cnf(931,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(rew,[status(thm),theory(equality)],[87,907]),
[iquote('0:Rew:87.0,907.0')] ).
cnf(952,plain,
equal(join(top,join(top,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[898,11]),
[iquote('0:SpR:898.0,11.0')] ).
cnf(963,plain,
equal(join(complement(u),complement(join(zero,complement(u)))),top),
inference(spr,[status(thm),theory(equality)],[861,111]),
[iquote('0:SpR:861.0,111.0')] ).
cnf(976,plain,
equal(join(complement(u),meet(top,u)),top),
inference(rew,[status(thm),theory(equality)],[100,963]),
[iquote('0:Rew:100.0,963.0')] ).
cnf(1059,plain,
equal(join(complement(u),meet(u,top)),top),
inference(spr,[status(thm),theory(equality)],[88,976]),
[iquote('0:SpR:88.0,976.0')] ).
cnf(1080,plain,
equal(join(meet(u,meet(u,top)),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[1059,21]),
[iquote('0:SpR:1059.0,21.0')] ).
cnf(1094,plain,
equal(join(zero,meet(u,meet(u,top))),u),
inference(rew,[status(thm),theory(equality)],[5,1080,87]),
[iquote('0:Rew:5.0,1080.0,87.0,1080.0')] ).
cnf(1183,plain,
equal(meet(top,join(top,complement(u))),complement(join(zero,meet(zero,u)))),
inference(spr,[status(thm),theory(equality)],[888,100]),
[iquote('0:SpR:888.0,100.0')] ).
cnf(1197,plain,
equal(meet(zero,join(zero,complement(u))),complement(join(top,meet(top,u)))),
inference(spr,[status(thm),theory(equality)],[100,888]),
[iquote('0:SpR:100.0,888.0')] ).
cnf(1229,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[121,931]),
[iquote('0:SpR:121.0,931.0')] ).
cnf(1236,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[1229,803]),
[iquote('0:Rew:1229.0,803.0')] ).
cnf(1237,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[1229,100]),
[iquote('0:Rew:1229.0,100.0')] ).
cnf(1242,plain,
equal(complement(join(zero,join(complement(u),complement(meet(u,top))))),meet(u,top)),
inference(rew,[status(thm),theory(equality)],[1229,590]),
[iquote('0:Rew:1229.0,590.0')] ).
cnf(1244,plain,
equal(join(complement(u),complement(v)),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[1229,867]),
[iquote('0:Rew:1229.0,867.0')] ).
cnf(1245,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[1229,153]),
[iquote('0:Rew:1229.0,153.0')] ).
cnf(1252,plain,
equal(complement(join(top,meet(top,u))),meet(zero,complement(u))),
inference(rew,[status(thm),theory(equality)],[1229,1197]),
[iquote('0:Rew:1229.0,1197.0')] ).
cnf(1254,plain,
equal(composition(converse(u),complement(composition(u,top))),zero),
inference(rew,[status(thm),theory(equality)],[1229,252]),
[iquote('0:Rew:1229.0,252.0')] ).
cnf(1258,plain,
equal(meet(u,meet(u,top)),u),
inference(rew,[status(thm),theory(equality)],[1229,1094]),
[iquote('0:Rew:1229.0,1094.0')] ).
cnf(1261,plain,
equal(meet(top,join(top,complement(u))),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[1229,1183]),
[iquote('0:Rew:1229.0,1183.0')] ).
cnf(1276,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[1236,1237]),
[iquote('0:Rew:1236.0,1237.0')] ).
cnf(1306,plain,
equal(meet(zero,complement(u)),complement(join(top,u))),
inference(rew,[status(thm),theory(equality)],[1276,1252]),
[iquote('0:Rew:1276.0,1252.0')] ).
cnf(1308,plain,
equal(join(top,complement(u)),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[1276,1261]),
[iquote('0:Rew:1276.0,1261.0')] ).
cnf(1323,plain,
equal(complement(join(complement(u),v)),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[1276,1245]),
[iquote('0:Rew:1276.0,1245.0')] ).
cnf(1340,plain,
equal(meet(u,top),u),
inference(rew,[status(thm),theory(equality)],[1236,1242,1229,1258,1244]),
[iquote('0:Rew:1236.0,1242.0,1229.0,1242.0,1258.0,1242.0,1244.0,1242.0')] ).
cnf(1468,plain,
equal(join(u,converse(complement(converse(u)))),converse(top)),
inference(spr,[status(thm),theory(equality)],[3,41]),
[iquote('0:SpR:3.0,41.0')] ).
cnf(1690,plain,
equal(join(u,complement(meet(zero,join(u,top)))),top),
inference(spr,[status(thm),theory(equality)],[1308,189]),
[iquote('0:SpR:1308.0,189.0')] ).
cnf(1712,plain,
equal(join(top,converse(top)),converse(top)),
inference(spr,[status(thm),theory(equality)],[1468,952]),
[iquote('0:SpR:1468.0,952.0')] ).
cnf(1745,plain,
equal(join(converse(top),top),converse(converse(top))),
inference(spr,[status(thm),theory(equality)],[1712,40]),
[iquote('0:SpR:1712.0,40.0')] ).
cnf(1748,plain,
equal(converse(top),top),
inference(rew,[status(thm),theory(equality)],[1712,1745,5,2]),
[iquote('0:Rew:1712.0,1745.0,5.0,1745.0,2.0,1745.0')] ).
cnf(1770,plain,
equal(composition(top,complement(composition(top,top))),zero),
inference(spr,[status(thm),theory(equality)],[1748,1254]),
[iquote('0:SpR:1748.0,1254.0')] ).
cnf(1808,plain,
equal(join(u,meet(u,complement(top))),u),
inference(spr,[status(thm),theory(equality)],[1340,122]),
[iquote('0:SpR:1340.0,122.0')] ).
cnf(1819,plain,
equal(join(u,meet(u,zero)),u),
inference(rew,[status(thm),theory(equality)],[87,1808]),
[iquote('0:Rew:87.0,1808.0')] ).
cnf(1840,plain,
equal(join(u,complement(u)),join(top,meet(complement(u),zero))),
inference(spr,[status(thm),theory(equality)],[1819,196]),
[iquote('0:SpR:1819.0,196.0')] ).
cnf(1850,plain,
equal(complement(meet(zero,join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[3,1840,1308,1306,88]),
[iquote('0:Rew:3.0,1840.0,1308.0,1840.0,1306.0,1840.0,88.0,1840.0')] ).
cnf(1967,plain,
equal(join(composition(u,complement(composition(top,top))),zero),composition(join(u,top),complement(composition(top,top)))),
inference(spr,[status(thm),theory(equality)],[1770,13]),
[iquote('0:SpR:1770.0,13.0')] ).
cnf(1971,plain,
equal(composition(join(u,top),complement(composition(top,top))),composition(u,complement(composition(top,top)))),
inference(rew,[status(thm),theory(equality)],[1229,1967,5]),
[iquote('0:Rew:1229.0,1967.0,5.0,1967.0')] ).
cnf(1987,plain,
equal(complement(meet(zero,join(u,top))),top),
inference(spr,[status(thm),theory(equality)],[5,1850]),
[iquote('0:SpR:5.0,1850.0')] ).
cnf(2009,plain,
equal(join(u,top),top),
inference(rew,[status(thm),theory(equality)],[1987,1690]),
[iquote('0:Rew:1987.0,1690.0')] ).
cnf(2023,plain,
equal(composition(top,complement(composition(top,top))),composition(u,complement(composition(top,top)))),
inference(rew,[status(thm),theory(equality)],[2009,1971]),
[iquote('0:Rew:2009.0,1971.0')] ).
cnf(2044,plain,
equal(composition(u,complement(composition(top,top))),zero),
inference(rew,[status(thm),theory(equality)],[1770,2023]),
[iquote('0:Rew:1770.0,2023.0')] ).
cnf(2049,plain,
equal(join(top,u),top),
inference(spr,[status(thm),theory(equality)],[2009,5]),
[iquote('0:SpR:2009.0,5.0')] ).
cnf(2070,plain,
equal(join(meet(zero,u),complement(top)),zero),
inference(rew,[status(thm),theory(equality)],[2049,889]),
[iquote('0:Rew:2049.0,889.0')] ).
cnf(2091,plain,
equal(meet(zero,u),zero),
inference(rew,[status(thm),theory(equality)],[1229,2070,5,87]),
[iquote('0:Rew:1229.0,2070.0,5.0,2070.0,87.0,2070.0')] ).
cnf(2225,plain,
equal(complement(composition(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[2044,687]),
[iquote('0:SpR:2044.0,687.0')] ).
cnf(2226,plain,
equal(composition(u,zero),zero),
inference(rew,[status(thm),theory(equality)],[2225,2044]),
[iquote('0:Rew:2225.0,2044.0')] ).
cnf(10742,plain,
equal(join(meet(composition(converse(skc1),skc1),complement(one)),meet(complement(one),composition(converse(skc1),zero))),meet(complement(one),composition(converse(skc1),zero))),
inference(spr,[status(thm),theory(equality)],[32,354]),
[iquote('0:SpR:32.0,354.0')] ).
cnf(10801,plain,
equal(meet(complement(one),composition(converse(skc1),skc1)),zero),
inference(rew,[status(thm),theory(equality)],[1229,10742,5,88,2091,2226]),
[iquote('0:Rew:1229.0,10742.0,5.0,10742.0,88.0,10742.0,2091.0,10742.0,88.0,10742.0,2226.0,10742.0')] ).
cnf(10843,plain,
equal(join(zero,meet(complement(one),complement(composition(converse(skc1),skc1)))),complement(one)),
inference(spr,[status(thm),theory(equality)],[10801,122]),
[iquote('0:SpR:10801.0,122.0')] ).
cnf(10882,plain,
equal(meet(complement(one),complement(composition(converse(skc1),skc1))),complement(one)),
inference(rew,[status(thm),theory(equality)],[1229,10843]),
[iquote('0:Rew:1229.0,10843.0')] ).
cnf(34061,plain,
equal(meet(complement(u),complement(v)),complement(join(u,v))),
inference(spr,[status(thm),theory(equality)],[1236,1323]),
[iquote('0:SpR:1236.0,1323.0')] ).
cnf(34181,plain,
equal(complement(join(one,composition(converse(skc1),skc1))),complement(one)),
inference(rew,[status(thm),theory(equality)],[34061,10882]),
[iquote('0:Rew:34061.0,10882.0')] ).
cnf(34348,plain,
equal(join(one,composition(converse(skc1),skc1)),complement(complement(one))),
inference(spr,[status(thm),theory(equality)],[34181,1236]),
[iquote('0:SpR:34181.0,1236.0')] ).
cnf(34406,plain,
equal(join(one,composition(converse(skc1),skc1)),one),
inference(rew,[status(thm),theory(equality)],[1236,34348]),
[iquote('0:Rew:1236.0,34348.0')] ).
cnf(34407,plain,
$false,
inference(mrr,[status(thm)],[34406,19]),
[iquote('0:MRR:34406.0,19.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : REL042+2 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Fri Jul 8 11:15:31 EDT 2022
% 0.14/0.36 % CPUTime :
% 13.66/13.88
% 13.66/13.88 SPASS V 3.9
% 13.66/13.88 SPASS beiseite: Proof found.
% 13.66/13.88 % SZS status Theorem
% 13.66/13.88 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.66/13.88 SPASS derived 21189 clauses, backtracked 0 clauses, performed 0 splits and kept 4109 clauses.
% 13.66/13.88 SPASS allocated 128341 KBytes.
% 13.66/13.88 SPASS spent 0:0:13.47 on the problem.
% 13.66/13.88 0:00:00.03 for the input.
% 13.66/13.88 0:00:00.03 for the FLOTTER CNF translation.
% 13.66/13.88 0:00:00.19 for inferences.
% 13.66/13.88 0:00:00.00 for the backtracking.
% 13.66/13.88 0:0:13.16 for the reduction.
% 13.66/13.88
% 13.66/13.88
% 13.66/13.88 Here is a proof with depth 12, length 130 :
% 13.66/13.88 % SZS output start Refutation
% See solution above
% 14.09/14.29 Formulae used in the proof : composition_identity converse_idempotence def_top def_zero maddux1_join_commutativity goals maddux4_definiton_of_meet converse_additivity converse_multiplicativity maddux2_join_associativity composition_distributivity converse_cancellativity maddux3_a_kind_of_de_Morgan modular_law_1
% 14.09/14.29
%------------------------------------------------------------------------------