%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL024+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 20:01:55 EDT 2022
% Result : Theorem 86.93s 87.08s
% Output : Refutation 89.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 15
% Syntax : Number of clauses : 141 ( 141 unt; 0 nHn; 141 RR)
% Number of literals : 141 ( 0 equ; 5 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('REL024+2.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL024+2.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,complement(u)),top),
file('REL024+2.p',unknown),
[] ).
cnf(4,axiom,
equal(meet(u,complement(u)),zero),
file('REL024+2.p',unknown),
[] ).
cnf(5,axiom,
equal(join(u,v),join(v,u)),
file('REL024+2.p',unknown),
[] ).
cnf(6,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL024+2.p',unknown),
[] ).
cnf(7,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL024+2.p',unknown),
[] ).
cnf(8,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL024+2.p',unknown),
[] ).
cnf(9,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL024+2.p',unknown),
[] ).
cnf(10,axiom,
equal(composition(composition(u,v),w),composition(u,composition(v,w))),
file('REL024+2.p',unknown),
[] ).
cnf(11,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL024+2.p',unknown),
[] ).
cnf(12,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL024+2.p',unknown),
[] ).
cnf(13,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL024+2.p',unknown),
[] ).
cnf(14,axiom,
~ equal(join(composition(meet(skc5,converse(skc4)),meet(skc4,skc3)),composition(meet(skc5,converse(skc4)),skc3)),composition(meet(skc5,converse(skc4)),skc3)),
file('REL024+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('REL024+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(join(composition(meet(skc5,converse(skc4)),skc3),composition(meet(skc5,converse(skc4)),meet(skc4,skc3))),composition(meet(skc5,converse(skc4)),skc3)),
inference(rew,[status(thm),theory(equality)],[5,14]),
[iquote('0:Rew:5.0,14.0')] ).
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(32,plain,
equal(converse(composition(u,converse(v))),composition(v,converse(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(join(composition(meet(skc5,converse(skc4)),skc3),composition(meet(skc5,converse(skc4)),meet(skc3,skc4))),composition(meet(skc5,converse(skc4)),skc3)),
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(268,plain,
equal(join(converse(composition(u,v)),composition(w,converse(u))),composition(join(converse(v),w),converse(u))),
inference(spr,[status(thm),theory(equality)],[8,11]),
[iquote('0:SpR:8.0,11.0')] ).
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(910,plain,
equal(join(converse(u),composition(v,converse(w))),converse(join(u,composition(w,converse(v))))),
inference(spr,[status(thm),theory(equality)],[32,7]),
[iquote('0:SpR:32.0,7.0')] ).
cnf(933,plain,
equal(converse(join(composition(u,v),composition(u,converse(w)))),composition(join(converse(v),w),converse(u))),
inference(rew,[status(thm),theory(equality)],[910,268]),
[iquote('0:Rew:910.0,268.0')] ).
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(1035,plain,
equal(composition(join(converse(u),v),converse(w)),converse(composition(w,join(u,converse(v))))),
inference(spr,[status(thm),theory(equality)],[36,8]),
[iquote('0:SpR:36.0,8.0')] ).
cnf(1072,plain,
equal(converse(join(composition(u,v),composition(u,converse(w)))),converse(composition(u,join(v,converse(w))))),
inference(rew,[status(thm),theory(equality)],[1035,933]),
[iquote('0:Rew:1035.0,933.0')] ).
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(1181,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(1191,plain,
equal(meet(u,meet(u,top)),u),
inference(rew,[status(thm),theory(equality)],[1161,1015]),
[iquote('0:Rew:1161.0,1015.0')] ).
cnf(1194,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(1208,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[1168,1169]),
[iquote('0:Rew:1168.0,1169.0')] ).
cnf(1242,plain,
equal(join(top,complement(u)),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[1208,1194]),
[iquote('0:Rew:1208.0,1194.0')] ).
cnf(1269,plain,
equal(meet(u,top),u),
inference(rew,[status(thm),theory(equality)],[1161,1179,1168,1191,1181]),
[iquote('0:Rew:1161.0,1179.0,1168.0,1179.0,1191.0,1179.0,1181.0,1179.0')] ).
cnf(1379,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(1618,plain,
equal(join(u,complement(meet(zero,join(u,top)))),top),
inference(spr,[status(thm),theory(equality)],[1242,160]),
[iquote('0:SpR:1242.0,160.0')] ).
cnf(1640,plain,
equal(join(top,converse(top)),converse(top)),
inference(spr,[status(thm),theory(equality)],[1379,870]),
[iquote('0:SpR:1379.0,870.0')] ).
cnf(1673,plain,
equal(join(converse(top),top),converse(converse(top))),
inference(spr,[status(thm),theory(equality)],[1640,36]),
[iquote('0:SpR:1640.0,36.0')] ).
cnf(1676,plain,
equal(converse(top),top),
inference(rew,[status(thm),theory(equality)],[1640,1673,5,2]),
[iquote('0:Rew:1640.0,1673.0,5.0,1673.0,2.0,1673.0')] ).
cnf(1698,plain,
equal(composition(top,complement(composition(top,top))),zero),
inference(spr,[status(thm),theory(equality)],[1676,1176]),
[iquote('0:SpR:1676.0,1176.0')] ).
cnf(1701,plain,
equal(join(complement(u),composition(top,complement(composition(top,u)))),complement(u)),
inference(spr,[status(thm),theory(equality)],[1676,18]),
[iquote('0:SpR:1676.0,18.0')] ).
cnf(1735,plain,
equal(join(u,meet(u,complement(top))),u),
inference(spr,[status(thm),theory(equality)],[1269,101]),
[iquote('0:SpR:1269.0,101.0')] ).
cnf(1742,plain,
equal(join(u,meet(u,zero)),u),
inference(rew,[status(thm),theory(equality)],[82,1735]),
[iquote('0:Rew:82.0,1735.0')] ).
cnf(1758,plain,
equal(join(u,complement(u)),join(top,meet(complement(u),zero))),
inference(spr,[status(thm),theory(equality)],[1742,167]),
[iquote('0:SpR:1742.0,167.0')] ).
cnf(1768,plain,
equal(complement(meet(zero,join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[3,1758,1242,1133,83]),
[iquote('0:Rew:3.0,1758.0,1242.0,1758.0,1133.0,1758.0,83.0,1758.0')] ).
cnf(1877,plain,
equal(join(composition(u,complement(composition(top,top))),zero),composition(join(u,top),complement(composition(top,top)))),
inference(spr,[status(thm),theory(equality)],[1698,11]),
[iquote('0:SpR:1698.0,11.0')] ).
cnf(1881,plain,
equal(composition(join(u,top),complement(composition(top,top))),composition(u,complement(composition(top,top)))),
inference(rew,[status(thm),theory(equality)],[1161,1877,5]),
[iquote('0:Rew:1161.0,1877.0,5.0,1877.0')] ).
cnf(1896,plain,
equal(complement(meet(zero,join(u,top))),top),
inference(spr,[status(thm),theory(equality)],[5,1768]),
[iquote('0:SpR:5.0,1768.0')] ).
cnf(1918,plain,
equal(join(u,top),top),
inference(rew,[status(thm),theory(equality)],[1896,1618]),
[iquote('0:Rew:1896.0,1618.0')] ).
cnf(1932,plain,
equal(composition(top,complement(composition(top,top))),composition(u,complement(composition(top,top)))),
inference(rew,[status(thm),theory(equality)],[1918,1881]),
[iquote('0:Rew:1918.0,1881.0')] ).
cnf(1951,plain,
equal(composition(u,complement(composition(top,top))),zero),
inference(rew,[status(thm),theory(equality)],[1698,1932]),
[iquote('0:Rew:1698.0,1932.0')] ).
cnf(2130,plain,
equal(complement(composition(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[1951,629]),
[iquote('0:SpR:1951.0,629.0')] ).
cnf(2273,plain,
equal(composition(top,top),complement(zero)),
inference(spr,[status(thm),theory(equality)],[2130,1168]),
[iquote('0:SpR:2130.0,1168.0')] ).
cnf(2281,plain,
equal(composition(top,top),top),
inference(rew,[status(thm),theory(equality)],[774,2273]),
[iquote('0:Rew:774.0,2273.0')] ).
cnf(2294,plain,
equal(composition(top,composition(top,u)),composition(top,u)),
inference(spr,[status(thm),theory(equality)],[2281,10]),
[iquote('0:SpR:2281.0,10.0')] ).
cnf(2296,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)],[2281,85]),
[iquote('0:SpR:2281.0,85.0')] ).
cnf(2308,plain,
equal(join(u,meet(u,composition(top,composition(top,u)))),meet(u,composition(top,composition(top,u)))),
inference(rew,[status(thm),theory(equality)],[1208,2296,1676]),
[iquote('0:Rew:1208.0,2296.0,1208.0,2296.0,1676.0,2296.0')] ).
cnf(2309,plain,
equal(join(u,meet(u,composition(top,u))),meet(u,composition(top,u))),
inference(rew,[status(thm),theory(equality)],[2294,2308]),
[iquote('0:Rew:2294.0,2308.0')] ).
cnf(2757,plain,
equal(join(complement(composition(top,u)),composition(converse(top),complement(composition(top,u)))),complement(composition(top,u))),
inference(spr,[status(thm),theory(equality)],[2294,18]),
[iquote('0:SpR:2294.0,18.0')] ).
cnf(2774,plain,
equal(join(complement(composition(top,u)),composition(top,complement(composition(top,u)))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[1676,2757]),
[iquote('0:Rew:1676.0,2757.0')] ).
cnf(2775,plain,
equal(composition(join(one,top),complement(composition(top,u))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[645,2774]),
[iquote('0:Rew:645.0,2774.0')] ).
cnf(2776,plain,
equal(composition(top,complement(composition(top,u))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[1918,2775]),
[iquote('0:Rew:1918.0,2775.0')] ).
cnf(2777,plain,
equal(join(complement(u),complement(composition(top,u))),complement(u)),
inference(rew,[status(thm),theory(equality)],[2776,1701]),
[iquote('0:Rew:2776.0,1701.0')] ).
cnf(2778,plain,
equal(complement(meet(u,composition(top,u))),complement(u)),
inference(rew,[status(thm),theory(equality)],[1181,2777]),
[iquote('0:Rew:1181.0,2777.0')] ).
cnf(2974,plain,
equal(meet(u,composition(top,u)),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[2778,1168]),
[iquote('0:SpR:2778.0,1168.0')] ).
cnf(2996,plain,
equal(meet(u,composition(top,u)),u),
inference(rew,[status(thm),theory(equality)],[1168,2974]),
[iquote('0:Rew:1168.0,2974.0')] ).
cnf(2998,plain,
equal(join(u,u),u),
inference(rew,[status(thm),theory(equality)],[2996,2309]),
[iquote('0:Rew:2996.0,2309.0')] ).
cnf(3063,plain,
equal(join(u,join(u,v)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[2998,9]),
[iquote('0:SpR:2998.0,9.0')] ).
cnf(3264,plain,
equal(join(meet(u,v),u),u),
inference(spr,[status(thm),theory(equality)],[101,3063]),
[iquote('0:SpR:101.0,3063.0')] ).
cnf(3274,plain,
equal(join(u,meet(u,v)),u),
inference(rew,[status(thm),theory(equality)],[5,3264]),
[iquote('0:Rew:5.0,3264.0')] ).
cnf(5857,plain,
equal(converse(join(composition(u,v),composition(u,w))),converse(composition(u,join(v,w)))),
inference(spr,[status(thm),theory(equality)],[2,1072]),
[iquote('0:SpR:2.0,1072.0')] ).
cnf(114337,plain,
equal(join(composition(u,v),composition(u,w)),converse(converse(composition(u,join(v,w))))),
inference(spr,[status(thm),theory(equality)],[5857,2]),
[iquote('0:SpR:5857.0,2.0')] ).
cnf(114606,plain,
equal(join(composition(u,v),composition(u,w)),composition(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[2,114337]),
[iquote('0:Rew:2.0,114337.0')] ).
cnf(114609,plain,
~ equal(composition(meet(skc5,converse(skc4)),join(skc3,meet(skc3,skc4))),composition(meet(skc5,converse(skc4)),skc3)),
inference(rew,[status(thm),theory(equality)],[114606,84]),
[iquote('0:Rew:114606.0,84.0')] ).
cnf(114711,plain,
~ equal(composition(meet(skc5,converse(skc4)),skc3),composition(meet(skc5,converse(skc4)),skc3)),
inference(rew,[status(thm),theory(equality)],[3274,114609]),
[iquote('0:Rew:3274.0,114609.0')] ).
cnf(114712,plain,
$false,
inference(obv,[status(thm),theory(equality)],[114711]),
[iquote('0:Obv:114711.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL024+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 8 14:39:29 EDT 2022
% 0.13/0.33 % CPUTime :
% 86.93/87.08
% 86.93/87.08 SPASS V 3.9
% 86.93/87.08 SPASS beiseite: Proof found.
% 86.93/87.08 % SZS status Theorem
% 86.93/87.08 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 86.93/87.08 SPASS derived 69251 clauses, backtracked 0 clauses, performed 0 splits and kept 9097 clauses.
% 86.93/87.08 SPASS allocated 204830 KBytes.
% 86.93/87.08 SPASS spent 0:1:26.54 on the problem.
% 86.93/87.08 0:00:00.04 for the input.
% 86.93/87.08 0:00:00.02 for the FLOTTER CNF translation.
% 86.93/87.08 0:00:00.54 for inferences.
% 86.93/87.08 0:00:00.00 for the backtracking.
% 86.93/87.08 0:1:25.79 for the reduction.
% 86.93/87.08
% 86.93/87.08
% 86.93/87.08 Here is a proof with depth 16, length 141 :
% 86.93/87.08 % SZS output start Refutation
% See solution above
% 89.93/90.11 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
% 89.93/90.11
%------------------------------------------------------------------------------