TSTP Solution File: REL023+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL023+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 20:01:53 EDT 2022
% Result : Theorem 0.54s 0.75s
% Output : Refutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 15
% Syntax : Number of clauses : 131 ( 131 unt; 0 nHn; 131 RR)
% Number of literals : 131 ( 0 equ; 4 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 : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(composition(u,one),u),
file('REL023+2.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL023+2.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,complement(u)),top),
file('REL023+2.p',unknown),
[] ).
cnf(4,axiom,
equal(meet(u,complement(u)),zero),
file('REL023+2.p',unknown),
[] ).
cnf(5,axiom,
equal(join(u,v),join(v,u)),
file('REL023+2.p',unknown),
[] ).
cnf(6,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL023+2.p',unknown),
[] ).
cnf(7,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL023+2.p',unknown),
[] ).
cnf(8,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL023+2.p',unknown),
[] ).
cnf(9,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL023+2.p',unknown),
[] ).
cnf(10,axiom,
equal(composition(composition(u,v),w),composition(u,composition(v,w))),
file('REL023+2.p',unknown),
[] ).
cnf(11,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL023+2.p',unknown),
[] ).
cnf(12,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL023+2.p',unknown),
[] ).
cnf(13,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL023+2.p',unknown),
[] ).
cnf(14,axiom,
~ equal(join(composition(meet(skc5,converse(skc4)),meet(skc4,skc3)),composition(skc5,meet(skc4,skc3))),composition(skc5,meet(skc4,skc3))),
file('REL023+2.p',unknown),
[] ).
cnf(16,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('REL023+2.p',unknown),
[] ).
cnf(18,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[5,12]),
[iquote('0:Rew:5.0,12.0')] ).
cnf(19,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[6,13]),
[iquote('0:Rew:6.0,13.0')] ).
cnf(20,plain,
~ equal(composition(join(skc5,meet(skc5,converse(skc4))),meet(skc4,skc3)),composition(skc5,meet(skc4,skc3))),
inference(rew,[status(thm),theory(equality)],[5,14,11]),
[iquote('0:Rew:5.0,14.0,11.0,14.0')] ).
cnf(31,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(36,plain,
equal(converse(join(u,converse(v))),join(converse(u),v)),
inference(spr,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
cnf(37,plain,
equal(converse(join(converse(u),v)),join(u,converse(v))),
inference(spr,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
cnf(79,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(80,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[5,6]),
[iquote('0:SpR:5.0,6.0')] ).
cnf(82,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[4,79]),
[iquote('0:Rew:4.0,79.0')] ).
cnf(83,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[6,80]),
[iquote('0:Rew:6.0,80.0')] ).
cnf(84,plain,
~ equal(composition(join(skc5,meet(skc5,converse(skc4))),meet(skc3,skc4)),composition(skc5,meet(skc3,skc4))),
inference(rew,[status(thm),theory(equality)],[83,20]),
[iquote('0:Rew:83.0,20.0')] ).
cnf(85,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)],[83,16]),
[iquote('0:Rew:83.0,16.0')] ).
cnf(94,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[3,19]),
[iquote('0:SpR:3.0,19.0')] ).
cnf(97,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[6,19]),
[iquote('0:SpR:6.0,19.0')] ).
cnf(98,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[4,19]),
[iquote('0:SpR:4.0,19.0')] ).
cnf(99,plain,
equal(join(complement(top),meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[5,94]),
[iquote('0:Rew:5.0,94.0')] ).
cnf(100,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[82,99]),
[iquote('0:Rew:82.0,99.0')] ).
cnf(101,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[5,97]),
[iquote('0:Rew:5.0,97.0')] ).
cnf(102,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[6,98]),
[iquote('0:Rew:6.0,98.0')] ).
cnf(106,plain,
equal(join(top,zero),top),
inference(spr,[status(thm),theory(equality)],[82,3]),
[iquote('0:SpR:82.0,3.0')] ).
cnf(107,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[82,6]),
[iquote('0:SpR:82.0,6.0')] ).
cnf(108,plain,
equal(join(meet(top,u),complement(join(zero,u))),top),
inference(spr,[status(thm),theory(equality)],[82,19]),
[iquote('0:SpR:82.0,19.0')] ).
cnf(136,plain,
equal(meet(join(zero,complement(u)),meet(top,u)),zero),
inference(spr,[status(thm),theory(equality)],[107,4]),
[iquote('0:SpR:107.0,4.0')] ).
cnf(144,plain,
equal(complement(join(zero,zero)),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[82,107]),
[iquote('0:SpR:82.0,107.0')] ).
cnf(150,plain,
equal(meet(meet(top,u),join(zero,complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[83,136]),
[iquote('0:Rew:83.0,136.0')] ).
cnf(160,plain,
equal(join(u,join(v,complement(join(u,v)))),top),
inference(spr,[status(thm),theory(equality)],[9,3]),
[iquote('0:SpR:9.0,3.0')] ).
cnf(161,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(167,plain,
equal(join(u,join(complement(u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[3,9]),
[iquote('0:SpR:3.0,9.0')] ).
cnf(172,plain,
equal(join(top,join(zero,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[106,9]),
[iquote('0:SpR:106.0,9.0')] ).
cnf(183,plain,
equal(meet(join(zero,zero),meet(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[144,4]),
[iquote('0:SpR:144.0,4.0')] ).
cnf(192,plain,
equal(meet(meet(top,top),join(zero,zero)),zero),
inference(rew,[status(thm),theory(equality)],[83,183]),
[iquote('0:Rew:83.0,183.0')] ).
cnf(199,plain,
equal(join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[192,19]),
[iquote('0:SpR:192.0,19.0')] ).
cnf(205,plain,
equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[9,199,5]),
[iquote('0:Rew:9.0,199.0,5.0,199.0')] ).
cnf(211,plain,
equal(join(top,meet(u,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[102,172]),
[iquote('0:SpR:102.0,172.0')] ).
cnf(228,plain,
equal(join(zero,composition(converse(u),complement(composition(u,top)))),zero),
inference(spr,[status(thm),theory(equality)],[82,18]),
[iquote('0:SpR:82.0,18.0')] ).
cnf(343,plain,
equal(meet(meet(u,top),join(zero,complement(u))),zero),
inference(spr,[status(thm),theory(equality)],[83,150]),
[iquote('0:SpR:83.0,150.0')] ).
cnf(453,plain,
equal(join(zero,complement(join(complement(meet(u,top)),join(zero,complement(u))))),meet(u,top)),
inference(spr,[status(thm),theory(equality)],[343,19]),
[iquote('0:SpR:343.0,19.0')] ).
cnf(472,plain,
equal(join(zero,complement(join(zero,join(complement(u),complement(meet(u,top)))))),meet(u,top)),
inference(rew,[status(thm),theory(equality)],[161,453]),
[iquote('0:Rew:161.0,453.0')] ).
cnf(566,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[1,31]),
[iquote('0:SpR:1.0,31.0')] ).
cnf(569,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[2,566]),
[iquote('0:Rew:2.0,566.0')] ).
cnf(611,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[569,1]),
[iquote('0:SpR:569.0,1.0')] ).
cnf(614,plain,
equal(join(u,composition(v,u)),composition(join(converse(one),v),u)),
inference(spr,[status(thm),theory(equality)],[569,11]),
[iquote('0:SpR:569.0,11.0')] ).
cnf(623,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[569,18]),
[iquote('0:SpR:569.0,18.0')] ).
cnf(629,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[611,569]),
[iquote('0:Rew:611.0,569.0')] ).
cnf(644,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[629,623]),
[iquote('0:Rew:629.0,623.0')] ).
cnf(645,plain,
equal(join(u,composition(v,u)),composition(join(one,v),u)),
inference(rew,[status(thm),theory(equality)],[611,614]),
[iquote('0:Rew:611.0,614.0')] ).
cnf(716,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[644,6]),
[iquote('0:SpR:644.0,6.0')] ).
cnf(722,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[82,644]),
[iquote('0:SpR:82.0,644.0')] ).
cnf(728,plain,
equal(meet(top,top),complement(zero)),
inference(rew,[status(thm),theory(equality)],[722,144]),
[iquote('0:Rew:722.0,144.0')] ).
cnf(741,plain,
equal(join(zero,complement(join(zero,join(zero,complement(complement(zero)))))),complement(zero)),
inference(rew,[status(thm),theory(equality)],[728,205]),
[iquote('0:Rew:728.0,205.0')] ).
cnf(744,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[716,102]),
[iquote('0:Rew:716.0,102.0')] ).
cnf(745,plain,
equal(join(top,complement(complement(u))),join(top,u)),
inference(rew,[status(thm),theory(equality)],[716,211]),
[iquote('0:Rew:716.0,211.0')] ).
cnf(773,plain,
equal(join(zero,complement(zero)),complement(zero)),
inference(rew,[status(thm),theory(equality)],[722,741,744]),
[iquote('0:Rew:722.0,741.0,744.0,741.0')] ).
cnf(774,plain,
equal(complement(zero),top),
inference(rew,[status(thm),theory(equality)],[3,773]),
[iquote('0:Rew:3.0,773.0')] ).
cnf(797,plain,
equal(meet(top,complement(u)),complement(u)),
inference(spr,[status(thm),theory(equality)],[744,107]),
[iquote('0:SpR:744.0,107.0')] ).
cnf(804,plain,
equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[6,744]),
[iquote('0:SpR:6.0,744.0')] ).
cnf(823,plain,
equal(complement(join(top,complement(u))),meet(zero,u)),
inference(spr,[status(thm),theory(equality)],[774,6]),
[iquote('0:SpR:774.0,6.0')] ).
cnf(833,plain,
equal(join(top,top),top),
inference(spr,[status(thm),theory(equality)],[774,644]),
[iquote('0:SpR:774.0,644.0')] ).
cnf(852,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[722,9]),
[iquote('0:SpR:722.0,9.0')] ).
cnf(870,plain,
equal(join(top,join(top,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[833,9]),
[iquote('0:SpR:833.0,9.0')] ).
cnf(880,plain,
equal(join(complement(u),complement(join(zero,complement(u)))),top),
inference(spr,[status(thm),theory(equality)],[797,108]),
[iquote('0:SpR:797.0,108.0')] ).
cnf(891,plain,
equal(join(complement(u),meet(top,u)),top),
inference(rew,[status(thm),theory(equality)],[107,880]),
[iquote('0:Rew:107.0,880.0')] ).
cnf(976,plain,
equal(join(complement(u),meet(u,top)),top),
inference(spr,[status(thm),theory(equality)],[83,891]),
[iquote('0:SpR:83.0,891.0')] ).
cnf(1003,plain,
equal(join(meet(u,meet(u,top)),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[976,19]),
[iquote('0:SpR:976.0,19.0')] ).
cnf(1015,plain,
equal(join(zero,meet(u,meet(u,top))),u),
inference(rew,[status(thm),theory(equality)],[5,1003,82]),
[iquote('0:Rew:5.0,1003.0,82.0,1003.0')] ).
cnf(1114,plain,
equal(meet(top,join(top,complement(u))),complement(join(zero,meet(zero,u)))),
inference(spr,[status(thm),theory(equality)],[823,107]),
[iquote('0:SpR:823.0,107.0')] ).
cnf(1133,plain,
equal(meet(zero,complement(u)),complement(join(top,u))),
inference(spr,[status(thm),theory(equality)],[745,823]),
[iquote('0:SpR:745.0,823.0')] ).
cnf(1161,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[100,852]),
[iquote('0:SpR:100.0,852.0')] ).
cnf(1168,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[1161,744]),
[iquote('0:Rew:1161.0,744.0')] ).
cnf(1169,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[1161,107]),
[iquote('0:Rew:1161.0,107.0')] ).
cnf(1176,plain,
equal(composition(converse(u),complement(composition(u,top))),zero),
inference(rew,[status(thm),theory(equality)],[1161,228]),
[iquote('0:Rew:1161.0,228.0')] ).
cnf(1179,plain,
equal(join(zero,complement(join(complement(u),complement(meet(u,top))))),meet(u,top)),
inference(rew,[status(thm),theory(equality)],[1161,472]),
[iquote('0:Rew:1161.0,472.0')] ).
cnf(1182,plain,
equal(meet(u,meet(u,top)),u),
inference(rew,[status(thm),theory(equality)],[1161,1015]),
[iquote('0:Rew:1161.0,1015.0')] ).
cnf(1186,plain,
equal(meet(top,join(top,complement(u))),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[1161,1114]),
[iquote('0:Rew:1161.0,1114.0')] ).
cnf(1188,plain,
equal(join(complement(u),complement(v)),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[1161,804]),
[iquote('0:Rew:1161.0,804.0')] ).
cnf(1208,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[1168,1169]),
[iquote('0:Rew:1168.0,1169.0')] ).
cnf(1240,plain,
equal(join(top,complement(u)),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[1208,1186]),
[iquote('0:Rew:1208.0,1186.0')] ).
cnf(1267,plain,
equal(meet(u,top),u),
inference(rew,[status(thm),theory(equality)],[1161,1179,1168,1182,1188]),
[iquote('0:Rew:1161.0,1179.0,1168.0,1179.0,1182.0,1179.0,1188.0,1179.0')] ).
cnf(1378,plain,
equal(join(u,converse(complement(converse(u)))),converse(top)),
inference(spr,[status(thm),theory(equality)],[3,37]),
[iquote('0:SpR:3.0,37.0')] ).
cnf(1617,plain,
equal(join(u,complement(meet(zero,join(u,top)))),top),
inference(spr,[status(thm),theory(equality)],[1240,160]),
[iquote('0:SpR:1240.0,160.0')] ).
cnf(1639,plain,
equal(join(top,converse(top)),converse(top)),
inference(spr,[status(thm),theory(equality)],[1378,870]),
[iquote('0:SpR:1378.0,870.0')] ).
cnf(1672,plain,
equal(join(converse(top),top),converse(converse(top))),
inference(spr,[status(thm),theory(equality)],[1639,36]),
[iquote('0:SpR:1639.0,36.0')] ).
cnf(1675,plain,
equal(converse(top),top),
inference(rew,[status(thm),theory(equality)],[1639,1672,5,2]),
[iquote('0:Rew:1639.0,1672.0,5.0,1672.0,2.0,1672.0')] ).
cnf(1697,plain,
equal(composition(top,complement(composition(top,top))),zero),
inference(spr,[status(thm),theory(equality)],[1675,1176]),
[iquote('0:SpR:1675.0,1176.0')] ).
cnf(1700,plain,
equal(join(complement(u),composition(top,complement(composition(top,u)))),complement(u)),
inference(spr,[status(thm),theory(equality)],[1675,18]),
[iquote('0:SpR:1675.0,18.0')] ).
cnf(1734,plain,
equal(join(u,meet(u,complement(top))),u),
inference(spr,[status(thm),theory(equality)],[1267,101]),
[iquote('0:SpR:1267.0,101.0')] ).
cnf(1741,plain,
equal(join(u,meet(u,zero)),u),
inference(rew,[status(thm),theory(equality)],[82,1734]),
[iquote('0:Rew:82.0,1734.0')] ).
cnf(1756,plain,
equal(join(u,complement(u)),join(top,meet(complement(u),zero))),
inference(spr,[status(thm),theory(equality)],[1741,167]),
[iquote('0:SpR:1741.0,167.0')] ).
cnf(1767,plain,
equal(complement(meet(zero,join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[3,1756,1240,1133,83]),
[iquote('0:Rew:3.0,1756.0,1240.0,1756.0,1133.0,1756.0,83.0,1756.0')] ).
cnf(1876,plain,
equal(join(composition(u,complement(composition(top,top))),zero),composition(join(u,top),complement(composition(top,top)))),
inference(spr,[status(thm),theory(equality)],[1697,11]),
[iquote('0:SpR:1697.0,11.0')] ).
cnf(1880,plain,
equal(composition(join(u,top),complement(composition(top,top))),composition(u,complement(composition(top,top)))),
inference(rew,[status(thm),theory(equality)],[1161,1876,5]),
[iquote('0:Rew:1161.0,1876.0,5.0,1876.0')] ).
cnf(1895,plain,
equal(complement(meet(zero,join(u,top))),top),
inference(spr,[status(thm),theory(equality)],[5,1767]),
[iquote('0:SpR:5.0,1767.0')] ).
cnf(1917,plain,
equal(join(u,top),top),
inference(rew,[status(thm),theory(equality)],[1895,1617]),
[iquote('0:Rew:1895.0,1617.0')] ).
cnf(1931,plain,
equal(composition(top,complement(composition(top,top))),composition(u,complement(composition(top,top)))),
inference(rew,[status(thm),theory(equality)],[1917,1880]),
[iquote('0:Rew:1917.0,1880.0')] ).
cnf(1950,plain,
equal(composition(u,complement(composition(top,top))),zero),
inference(rew,[status(thm),theory(equality)],[1697,1931]),
[iquote('0:Rew:1697.0,1931.0')] ).
cnf(2129,plain,
equal(complement(composition(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[1950,629]),
[iquote('0:SpR:1950.0,629.0')] ).
cnf(2272,plain,
equal(composition(top,top),complement(zero)),
inference(spr,[status(thm),theory(equality)],[2129,1168]),
[iquote('0:SpR:2129.0,1168.0')] ).
cnf(2280,plain,
equal(composition(top,top),top),
inference(rew,[status(thm),theory(equality)],[774,2272]),
[iquote('0:Rew:774.0,2272.0')] ).
cnf(2293,plain,
equal(composition(top,composition(top,u)),composition(top,u)),
inference(spr,[status(thm),theory(equality)],[2280,10]),
[iquote('0:SpR:2280.0,10.0')] ).
cnf(2295,plain,
equal(join(meet(top,u),meet(u,composition(top,meet(top,composition(converse(top),u))))),meet(u,composition(top,meet(top,composition(converse(top),u))))),
inference(spr,[status(thm),theory(equality)],[2280,85]),
[iquote('0:SpR:2280.0,85.0')] ).
cnf(2307,plain,
equal(join(u,meet(u,composition(top,composition(top,u)))),meet(u,composition(top,composition(top,u)))),
inference(rew,[status(thm),theory(equality)],[1208,2295,1675]),
[iquote('0:Rew:1208.0,2295.0,1208.0,2295.0,1675.0,2295.0')] ).
cnf(2308,plain,
equal(join(u,meet(u,composition(top,u))),meet(u,composition(top,u))),
inference(rew,[status(thm),theory(equality)],[2293,2307]),
[iquote('0:Rew:2293.0,2307.0')] ).
cnf(2756,plain,
equal(join(complement(composition(top,u)),composition(converse(top),complement(composition(top,u)))),complement(composition(top,u))),
inference(spr,[status(thm),theory(equality)],[2293,18]),
[iquote('0:SpR:2293.0,18.0')] ).
cnf(2773,plain,
equal(join(complement(composition(top,u)),composition(top,complement(composition(top,u)))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[1675,2756]),
[iquote('0:Rew:1675.0,2756.0')] ).
cnf(2774,plain,
equal(composition(join(one,top),complement(composition(top,u))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[645,2773]),
[iquote('0:Rew:645.0,2773.0')] ).
cnf(2775,plain,
equal(composition(top,complement(composition(top,u))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[1917,2774]),
[iquote('0:Rew:1917.0,2774.0')] ).
cnf(2776,plain,
equal(join(complement(u),complement(composition(top,u))),complement(u)),
inference(rew,[status(thm),theory(equality)],[2775,1700]),
[iquote('0:Rew:2775.0,1700.0')] ).
cnf(2777,plain,
equal(complement(meet(u,composition(top,u))),complement(u)),
inference(rew,[status(thm),theory(equality)],[1188,2776]),
[iquote('0:Rew:1188.0,2776.0')] ).
cnf(2973,plain,
equal(meet(u,composition(top,u)),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[2777,1168]),
[iquote('0:SpR:2777.0,1168.0')] ).
cnf(2995,plain,
equal(meet(u,composition(top,u)),u),
inference(rew,[status(thm),theory(equality)],[1168,2973]),
[iquote('0:Rew:1168.0,2973.0')] ).
cnf(2997,plain,
equal(join(u,u),u),
inference(rew,[status(thm),theory(equality)],[2995,2308]),
[iquote('0:Rew:2995.0,2308.0')] ).
cnf(3062,plain,
equal(join(u,join(u,v)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[2997,9]),
[iquote('0:SpR:2997.0,9.0')] ).
cnf(3266,plain,
equal(join(meet(u,v),u),u),
inference(spr,[status(thm),theory(equality)],[101,3062]),
[iquote('0:SpR:101.0,3062.0')] ).
cnf(3273,plain,
equal(join(u,meet(u,v)),u),
inference(rew,[status(thm),theory(equality)],[5,3266]),
[iquote('0:Rew:5.0,3266.0')] ).
cnf(3274,plain,
~ equal(composition(skc5,meet(skc3,skc4)),composition(skc5,meet(skc3,skc4))),
inference(rew,[status(thm),theory(equality)],[3273,84]),
[iquote('0:Rew:3273.0,84.0')] ).
cnf(3290,plain,
$false,
inference(obv,[status(thm),theory(equality)],[3274]),
[iquote('0:Obv:3274.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL023+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n024.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 11:50:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.54/0.75
% 0.54/0.75 SPASS V 3.9
% 0.54/0.75 SPASS beiseite: Proof found.
% 0.54/0.75 % SZS status Theorem
% 0.54/0.75 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.54/0.75 SPASS derived 2080 clauses, backtracked 0 clauses, performed 0 splits and kept 628 clauses.
% 0.54/0.75 SPASS allocated 88955 KBytes.
% 0.54/0.75 SPASS spent 0:00:00.41 on the problem.
% 0.54/0.75 0:00:00.04 for the input.
% 0.54/0.75 0:00:00.02 for the FLOTTER CNF translation.
% 0.54/0.75 0:00:00.02 for inferences.
% 0.54/0.75 0:00:00.00 for the backtracking.
% 0.54/0.75 0:00:00.31 for the reduction.
% 0.54/0.75
% 0.54/0.75
% 0.54/0.75 Here is a proof with depth 16, length 131 :
% 0.54/0.75 % SZS output start Refutation
% See solution above
% 0.54/0.78 Formulae used in the proof : composition_identity converse_idempotence def_top def_zero maddux1_join_commutativity maddux4_definiton_of_meet converse_additivity converse_multiplicativity maddux2_join_associativity composition_associativity composition_distributivity converse_cancellativity maddux3_a_kind_of_de_Morgan goals modular_law_1
% 0.54/0.78
%------------------------------------------------------------------------------