TSTP Solution File: REL031+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL031+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 20:02:08 EDT 2022
% Result : Theorem 116.62s 116.83s
% Output : Refutation 120.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 16
% Syntax : Number of clauses : 159 ( 159 unt; 0 nHn; 159 RR)
% Number of literals : 159 ( 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 : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(composition(u,one),u),
file('REL031+1.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL031+1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,complement(u)),top),
file('REL031+1.p',unknown),
[] ).
cnf(4,axiom,
equal(meet(u,complement(u)),zero),
file('REL031+1.p',unknown),
[] ).
cnf(5,axiom,
equal(join(u,v),join(v,u)),
file('REL031+1.p',unknown),
[] ).
cnf(6,axiom,
equal(join(composition(converse(skc3),skc3),one),one),
file('REL031+1.p',unknown),
[] ).
cnf(7,axiom,
equal(join(composition(converse(skc2),skc2),one),one),
file('REL031+1.p',unknown),
[] ).
cnf(8,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL031+1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL031+1.p',unknown),
[] ).
cnf(10,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL031+1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL031+1.p',unknown),
[] ).
cnf(12,axiom,
equal(composition(composition(u,v),w),composition(u,composition(v,w))),
file('REL031+1.p',unknown),
[] ).
cnf(13,axiom,
~ equal(join(composition(converse(composition(skc3,skc2)),composition(skc3,skc2)),one),one),
file('REL031+1.p',unknown),
[] ).
cnf(14,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL031+1.p',unknown),
[] ).
cnf(15,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL031+1.p',unknown),
[] ).
cnf(16,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL031+1.p',unknown),
[] ).
cnf(17,plain,
equal(join(one,composition(converse(skc2),skc2)),one),
inference(rew,[status(thm),theory(equality)],[5,7]),
[iquote('0:Rew:5.0,7.0')] ).
cnf(18,plain,
equal(join(one,composition(converse(skc3),skc3)),one),
inference(rew,[status(thm),theory(equality)],[5,6]),
[iquote('0:Rew:5.0,6.0')] ).
cnf(19,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[5,15]),
[iquote('0:Rew:5.0,15.0')] ).
cnf(20,plain,
~ equal(join(one,composition(converse(composition(skc3,skc2)),composition(skc3,skc2))),one),
inference(rew,[status(thm),theory(equality)],[5,13]),
[iquote('0:Rew:5.0,13.0')] ).
cnf(21,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[8,16]),
[iquote('0:Rew:8.0,16.0')] ).
cnf(34,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(converse(u),v)),join(u,converse(v))),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(44,plain,
equal(join(join(complement(u),complement(v)),meet(u,v)),top),
inference(spr,[status(thm),theory(equality)],[8,3]),
[iquote('0:SpR:8.0,3.0')] ).
cnf(45,plain,
equal(meet(join(complement(u),complement(v)),w),complement(join(meet(u,v),complement(w)))),
inference(spr,[status(thm),theory(equality)],[8]),
[iquote('0:SpR:8.0,8.0')] ).
cnf(48,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpR:3.0,8.0')] ).
cnf(49,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(51,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[4,48]),
[iquote('0:Rew:4.0,48.0')] ).
cnf(52,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[8,49]),
[iquote('0:Rew:8.0,49.0')] ).
cnf(55,plain,
equal(join(meet(u,v),join(complement(u),complement(v))),top),
inference(rew,[status(thm),theory(equality)],[5,44]),
[iquote('0:Rew:5.0,44.0')] ).
cnf(60,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[51,8]),
[iquote('0:SpR:51.0,8.0')] ).
cnf(72,plain,
equal(join(meet(join(complement(u),complement(v)),w),complement(join(meet(u,v),w))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[8,21]),
[iquote('0:SpR:8.0,21.0')] ).
cnf(73,plain,
equal(join(meet(top,u),complement(join(zero,u))),top),
inference(spr,[status(thm),theory(equality)],[51,21]),
[iquote('0:SpR:51.0,21.0')] ).
cnf(74,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(75,plain,
equal(join(meet(u,v),complement(join(v,complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[5,21]),
[iquote('0:SpR:5.0,21.0')] ).
cnf(77,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(78,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(79,plain,
equal(join(meet(u,v),complement(join(complement(v),u))),v),
inference(spr,[status(thm),theory(equality)],[52,21]),
[iquote('0:SpR:52.0,21.0')] ).
cnf(83,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[5,74,51]),
[iquote('0:Rew:5.0,74.0,51.0,74.0')] ).
cnf(84,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[5,77]),
[iquote('0:Rew:5.0,77.0')] ).
cnf(85,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[8,78]),
[iquote('0:Rew:8.0,78.0')] ).
cnf(86,plain,
equal(join(complement(join(meet(u,v),w)),meet(join(complement(u),complement(v)),w)),join(complement(u),complement(v))),
inference(rew,[status(thm),theory(equality)],[5,72]),
[iquote('0:Rew:5.0,72.0')] ).
cnf(87,plain,
equal(join(complement(join(meet(u,v),w)),complement(join(meet(u,v),complement(w)))),join(complement(u),complement(v))),
inference(rew,[status(thm),theory(equality)],[45,86]),
[iquote('0:Rew:45.0,86.0')] ).
cnf(94,plain,
equal(meet(join(zero,complement(u)),meet(top,u)),zero),
inference(spr,[status(thm),theory(equality)],[60,4]),
[iquote('0:SpR:60.0,4.0')] ).
cnf(96,plain,
equal(complement(join(meet(top,u),complement(v))),meet(join(zero,complement(u)),v)),
inference(spr,[status(thm),theory(equality)],[60,8]),
[iquote('0:SpR:60.0,8.0')] ).
cnf(99,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,join(zero,complement(v)))),
inference(spr,[status(thm),theory(equality)],[60,8]),
[iquote('0:SpR:60.0,8.0')] ).
cnf(108,plain,
equal(meet(meet(top,u),join(zero,complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[52,94]),
[iquote('0:Rew:52.0,94.0')] ).
cnf(122,plain,
equal(composition(converse(u),composition(converse(v),w)),composition(converse(composition(v,u)),w)),
inference(spr,[status(thm),theory(equality)],[10,12]),
[iquote('0:SpR:10.0,12.0')] ).
cnf(158,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(159,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(163,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(166,plain,
equal(join(one,join(composition(converse(skc2),skc2),u)),join(one,u)),
inference(spr,[status(thm),theory(equality)],[17,11]),
[iquote('0:SpR:17.0,11.0')] ).
cnf(170,plain,
equal(join(meet(u,v),join(complement(join(complement(u),v)),w)),join(u,w)),
inference(spr,[status(thm),theory(equality)],[21,11]),
[iquote('0:SpR:21.0,11.0')] ).
cnf(175,plain,
equal(join(complement(u),join(meet(v,u),complement(v))),top),
inference(rew,[status(thm),theory(equality)],[159,55]),
[iquote('0:Rew:159.0,55.0')] ).
cnf(181,plain,
equal(join(complement(u),join(complement(v),meet(v,u))),top),
inference(rew,[status(thm),theory(equality)],[5,175]),
[iquote('0:Rew:5.0,175.0')] ).
cnf(320,plain,
equal(meet(meet(u,top),join(zero,complement(u))),zero),
inference(spr,[status(thm),theory(equality)],[52,108]),
[iquote('0:SpR:52.0,108.0')] ).
cnf(341,plain,
equal(join(composition(u,v),join(composition(w,v),x)),join(composition(join(u,w),v),x)),
inference(spr,[status(thm),theory(equality)],[14,11]),
[iquote('0:SpR:14.0,11.0')] ).
cnf(431,plain,
equal(join(zero,complement(join(complement(meet(u,top)),join(zero,complement(u))))),meet(u,top)),
inference(spr,[status(thm),theory(equality)],[320,21]),
[iquote('0:SpR:320.0,21.0')] ).
cnf(451,plain,
equal(join(zero,complement(join(zero,join(complement(u),complement(meet(u,top)))))),meet(u,top)),
inference(rew,[status(thm),theory(equality)],[159,431]),
[iquote('0:Rew:159.0,431.0')] ).
cnf(453,plain,
equal(composition(composition(converse(u),v),converse(w)),converse(composition(w,composition(converse(v),u)))),
inference(spr,[status(thm),theory(equality)],[34,10]),
[iquote('0:SpR:34.0,10.0')] ).
cnf(463,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[1,34]),
[iquote('0:SpR:1.0,34.0')] ).
cnf(466,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[2,463]),
[iquote('0:Rew:2.0,463.0')] ).
cnf(471,plain,
equal(composition(converse(u),composition(v,converse(w))),converse(composition(w,composition(converse(v),u)))),
inference(rew,[status(thm),theory(equality)],[12,453]),
[iquote('0:Rew:12.0,453.0')] ).
cnf(475,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[466,1]),
[iquote('0:SpR:466.0,1.0')] ).
cnf(480,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[466,19]),
[iquote('0:SpR:466.0,19.0')] ).
cnf(485,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[475,466]),
[iquote('0:Rew:475.0,466.0')] ).
cnf(492,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[485,480]),
[iquote('0:Rew:485.0,480.0')] ).
cnf(528,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[492,8]),
[iquote('0:SpR:492.0,8.0')] ).
cnf(534,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[51,492]),
[iquote('0:SpR:51.0,492.0')] ).
cnf(552,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[528,85]),
[iquote('0:Rew:528.0,85.0')] ).
cnf(579,plain,
equal(meet(top,complement(u)),complement(u)),
inference(spr,[status(thm),theory(equality)],[552,60]),
[iquote('0:SpR:552.0,60.0')] ).
cnf(586,plain,
equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[8,552]),
[iquote('0:SpR:8.0,552.0')] ).
cnf(614,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[534,11]),
[iquote('0:SpR:534.0,11.0')] ).
cnf(632,plain,
equal(join(complement(u),complement(join(zero,complement(u)))),top),
inference(spr,[status(thm),theory(equality)],[579,73]),
[iquote('0:SpR:579.0,73.0')] ).
cnf(640,plain,
equal(join(complement(u),meet(top,u)),top),
inference(rew,[status(thm),theory(equality)],[60,632]),
[iquote('0:Rew:60.0,632.0')] ).
cnf(665,plain,
equal(join(complement(u),join(meet(top,u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[640,11]),
[iquote('0:SpR:640.0,11.0')] ).
cnf(669,plain,
equal(join(complement(u),meet(u,top)),top),
inference(spr,[status(thm),theory(equality)],[52,640]),
[iquote('0:SpR:52.0,640.0')] ).
cnf(722,plain,
equal(join(meet(u,meet(u,top)),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[669,21]),
[iquote('0:SpR:669.0,21.0')] ).
cnf(732,plain,
equal(join(zero,meet(u,meet(u,top))),u),
inference(rew,[status(thm),theory(equality)],[5,722,51]),
[iquote('0:Rew:5.0,722.0,51.0,722.0')] ).
cnf(823,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[83,614]),
[iquote('0:SpR:83.0,614.0')] ).
cnf(830,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[823,552]),
[iquote('0:Rew:823.0,552.0')] ).
cnf(831,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[823,60]),
[iquote('0:Rew:823.0,60.0')] ).
cnf(837,plain,
equal(join(zero,complement(join(complement(u),complement(meet(u,top))))),meet(u,top)),
inference(rew,[status(thm),theory(equality)],[823,451]),
[iquote('0:Rew:823.0,451.0')] ).
cnf(843,plain,
equal(join(complement(u),complement(v)),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[823,586]),
[iquote('0:Rew:823.0,586.0')] ).
cnf(845,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[823,99]),
[iquote('0:Rew:823.0,99.0')] ).
cnf(847,plain,
equal(complement(join(meet(top,u),complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[823,96]),
[iquote('0:Rew:823.0,96.0')] ).
cnf(852,plain,
equal(meet(u,meet(u,top)),u),
inference(rew,[status(thm),theory(equality)],[823,732]),
[iquote('0:Rew:823.0,732.0')] ).
cnf(854,plain,
equal(meet(u,u),u),
inference(rew,[status(thm),theory(equality)],[830,528]),
[iquote('0:Rew:830.0,528.0')] ).
cnf(860,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[830,831]),
[iquote('0:Rew:830.0,831.0')] ).
cnf(864,plain,
equal(join(complement(u),join(u,v)),join(top,v)),
inference(rew,[status(thm),theory(equality)],[860,665]),
[iquote('0:Rew:860.0,665.0')] ).
cnf(884,plain,
equal(complement(meet(join(meet(u,v),w),join(meet(u,v),complement(w)))),join(complement(u),complement(v))),
inference(rew,[status(thm),theory(equality)],[843,87]),
[iquote('0:Rew:843.0,87.0')] ).
cnf(890,plain,
equal(join(u,join(v,complement(u))),join(top,v)),
inference(rew,[status(thm),theory(equality)],[159,864]),
[iquote('0:Rew:159.0,864.0')] ).
cnf(901,plain,
equal(complement(join(complement(u),v)),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[860,845]),
[iquote('0:Rew:860.0,845.0')] ).
cnf(903,plain,
equal(join(meet(u,v),meet(v,complement(u))),v),
inference(rew,[status(thm),theory(equality)],[901,79]),
[iquote('0:Rew:901.0,79.0')] ).
cnf(904,plain,
equal(join(meet(u,v),join(meet(u,complement(v)),w)),join(u,w)),
inference(rew,[status(thm),theory(equality)],[901,170]),
[iquote('0:Rew:901.0,170.0')] ).
cnf(905,plain,
equal(complement(join(u,complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[860,847]),
[iquote('0:Rew:860.0,847.0')] ).
cnf(906,plain,
equal(join(meet(u,v),meet(complement(v),u)),u),
inference(rew,[status(thm),theory(equality)],[905,75]),
[iquote('0:Rew:905.0,75.0')] ).
cnf(910,plain,
equal(meet(u,top),u),
inference(rew,[status(thm),theory(equality)],[823,837,830,852,843]),
[iquote('0:Rew:823.0,837.0,830.0,837.0,852.0,837.0,843.0,837.0')] ).
cnf(927,plain,
equal(complement(meet(join(meet(u,v),w),join(meet(u,v),complement(w)))),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[843,884]),
[iquote('0:Rew:843.0,884.0')] ).
cnf(929,plain,
equal(join(u,zero),u),
inference(spr,[status(thm),theory(equality)],[823,5]),
[iquote('0:SpR:823.0,5.0')] ).
cnf(983,plain,
equal(join(u,converse(complement(converse(u)))),converse(top)),
inference(spr,[status(thm),theory(equality)],[3,40]),
[iquote('0:SpR:3.0,40.0')] ).
cnf(1204,plain,
equal(join(top,converse(complement(converse(complement(u))))),join(u,converse(top))),
inference(spr,[status(thm),theory(equality)],[983,163]),
[iquote('0:SpR:983.0,163.0')] ).
cnf(1329,plain,
equal(join(meet(u,v),meet(complement(u),v)),v),
inference(spr,[status(thm),theory(equality)],[52,906]),
[iquote('0:SpR:52.0,906.0')] ).
cnf(1561,plain,
equal(join(complement(u),join(complement(u),u)),top),
inference(spr,[status(thm),theory(equality)],[854,181]),
[iquote('0:SpR:854.0,181.0')] ).
cnf(1573,plain,
equal(join(top,complement(u)),top),
inference(rew,[status(thm),theory(equality)],[5,1561,3]),
[iquote('0:Rew:5.0,1561.0,3.0,1561.0,5.0,1561.0')] ).
cnf(1584,plain,
equal(join(u,top),top),
inference(spr,[status(thm),theory(equality)],[1573,158]),
[iquote('0:SpR:1573.0,158.0')] ).
cnf(1588,plain,
equal(join(top,u),top),
inference(spr,[status(thm),theory(equality)],[830,1573]),
[iquote('0:SpR:830.0,1573.0')] ).
cnf(1596,plain,
equal(join(u,converse(top)),top),
inference(rew,[status(thm),theory(equality)],[1588,1204]),
[iquote('0:Rew:1588.0,1204.0')] ).
cnf(1599,plain,
equal(join(u,join(v,complement(u))),top),
inference(rew,[status(thm),theory(equality)],[1588,890]),
[iquote('0:Rew:1588.0,890.0')] ).
cnf(1609,plain,
equal(join(u,converse(top)),converse(top)),
inference(spr,[status(thm),theory(equality)],[1584,40]),
[iquote('0:SpR:1584.0,40.0')] ).
cnf(1614,plain,
equal(converse(top),top),
inference(rew,[status(thm),theory(equality)],[1596,1609]),
[iquote('0:Rew:1596.0,1609.0')] ).
cnf(1615,plain,
equal(join(u,converse(complement(converse(u)))),top),
inference(rew,[status(thm),theory(equality)],[1614,983]),
[iquote('0:Rew:1614.0,983.0')] ).
cnf(2638,plain,
equal(join(one,composition(join(converse(skc2),u),skc2)),join(one,composition(u,skc2))),
inference(spr,[status(thm),theory(equality)],[14,166]),
[iquote('0:SpR:14.0,166.0')] ).
cnf(4148,plain,
equal(join(u,complement(meet(u,v))),top),
inference(spr,[status(thm),theory(equality)],[904,1599]),
[iquote('0:SpR:904.0,1599.0')] ).
cnf(6038,plain,
equal(join(composition(join(u,v),w),complement(composition(v,w))),join(composition(u,w),top)),
inference(spr,[status(thm),theory(equality)],[3,341]),
[iquote('0:SpR:3.0,341.0')] ).
cnf(6098,plain,
equal(join(complement(composition(u,v)),composition(join(w,u),v)),top),
inference(rew,[status(thm),theory(equality)],[5,6038,1588]),
[iquote('0:Rew:5.0,6038.0,1588.0,6038.0,5.0,6038.0')] ).
cnf(7525,plain,
equal(meet(join(meet(u,v),w),join(meet(u,v),complement(w))),complement(complement(meet(u,v)))),
inference(spr,[status(thm),theory(equality)],[927,830]),
[iquote('0:SpR:927.0,830.0')] ).
cnf(7616,plain,
equal(meet(join(meet(u,v),w),join(meet(u,v),complement(w))),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[830,7525]),
[iquote('0:Rew:830.0,7525.0')] ).
cnf(7938,plain,
equal(complement(meet(u,meet(complement(u),v))),top),
inference(spr,[status(thm),theory(equality)],[843,4148]),
[iquote('0:SpR:843.0,4148.0')] ).
cnf(7966,plain,
equal(complement(meet(complement(u),v)),join(u,complement(v))),
inference(spr,[status(thm),theory(equality)],[830,843]),
[iquote('0:SpR:830.0,843.0')] ).
cnf(8009,plain,
equal(meet(u,meet(complement(u),v)),complement(top)),
inference(spr,[status(thm),theory(equality)],[7938,830]),
[iquote('0:SpR:7938.0,830.0')] ).
cnf(8055,plain,
equal(meet(u,meet(complement(u),v)),zero),
inference(rew,[status(thm),theory(equality)],[51,8009]),
[iquote('0:Rew:51.0,8009.0')] ).
cnf(8087,plain,
equal(join(zero,meet(u,complement(meet(complement(u),v)))),u),
inference(spr,[status(thm),theory(equality)],[8055,84]),
[iquote('0:SpR:8055.0,84.0')] ).
cnf(8104,plain,
equal(meet(complement(u),meet(u,v)),zero),
inference(spr,[status(thm),theory(equality)],[830,8055]),
[iquote('0:SpR:830.0,8055.0')] ).
cnf(8121,plain,
equal(meet(u,complement(meet(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[823,8087]),
[iquote('0:Rew:823.0,8087.0')] ).
cnf(8122,plain,
equal(meet(u,join(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[7966,8121]),
[iquote('0:Rew:7966.0,8121.0')] ).
cnf(8142,plain,
equal(meet(complement(u),meet(v,u)),zero),
inference(spr,[status(thm),theory(equality)],[52,8104]),
[iquote('0:SpR:52.0,8104.0')] ).
cnf(8412,plain,
equal(meet(u,join(u,v)),u),
inference(spr,[status(thm),theory(equality)],[830,8122]),
[iquote('0:SpR:830.0,8122.0')] ).
cnf(8460,plain,
equal(meet(complement(join(u,v)),u),zero),
inference(spr,[status(thm),theory(equality)],[8412,8142]),
[iquote('0:SpR:8412.0,8142.0')] ).
cnf(8539,plain,
equal(meet(u,complement(join(u,v))),zero),
inference(rew,[status(thm),theory(equality)],[52,8460]),
[iquote('0:Rew:52.0,8460.0')] ).
cnf(9088,plain,
equal(meet(converse(u),complement(converse(join(u,v)))),zero),
inference(spr,[status(thm),theory(equality)],[9,8539]),
[iquote('0:SpR:9.0,8539.0')] ).
cnf(16008,plain,
equal(meet(converse(meet(u,v)),complement(converse(v))),zero),
inference(spr,[status(thm),theory(equality)],[1329,9088]),
[iquote('0:SpR:1329.0,9088.0')] ).
cnf(16124,plain,
equal(meet(complement(converse(u)),converse(meet(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[52,16008]),
[iquote('0:Rew:52.0,16008.0')] ).
cnf(18318,plain,
equal(meet(complement(u),converse(meet(v,converse(u)))),zero),
inference(spr,[status(thm),theory(equality)],[2,16124]),
[iquote('0:SpR:2.0,16124.0')] ).
cnf(21087,plain,
equal(meet(u,converse(meet(v,converse(complement(u))))),zero),
inference(spr,[status(thm),theory(equality)],[830,18318]),
[iquote('0:SpR:830.0,18318.0')] ).
cnf(22228,plain,
equal(meet(u,complement(converse(complement(converse(complement(u)))))),complement(top)),
inference(spr,[status(thm),theory(equality)],[1615,901]),
[iquote('0:SpR:1615.0,901.0')] ).
cnf(22356,plain,
equal(meet(u,complement(converse(complement(converse(complement(u)))))),zero),
inference(rew,[status(thm),theory(equality)],[51,22228]),
[iquote('0:Rew:51.0,22228.0')] ).
cnf(23486,plain,
equal(join(complement(composition(composition(converse(skc3),skc3),u)),composition(one,u)),top),
inference(spr,[status(thm),theory(equality)],[18,6098]),
[iquote('0:SpR:18.0,6098.0')] ).
cnf(23653,plain,
equal(join(u,complement(composition(converse(skc3),composition(skc3,u)))),top),
inference(rew,[status(thm),theory(equality)],[5,23486,12,485]),
[iquote('0:Rew:5.0,23486.0,12.0,23486.0,485.0,23486.0')] ).
cnf(27341,plain,
equal(join(meet(u,converse(complement(converse(complement(u))))),zero),u),
inference(spr,[status(thm),theory(equality)],[22356,84]),
[iquote('0:SpR:22356.0,84.0')] ).
cnf(27422,plain,
equal(meet(u,converse(complement(converse(complement(u))))),u),
inference(rew,[status(thm),theory(equality)],[823,27341,5]),
[iquote('0:Rew:823.0,27341.0,5.0,27341.0')] ).
cnf(27465,plain,
equal(join(u,meet(converse(complement(converse(complement(u)))),complement(u))),converse(complement(converse(complement(u))))),
inference(spr,[status(thm),theory(equality)],[27422,903]),
[iquote('0:SpR:27422.0,903.0')] ).
cnf(27502,plain,
equal(meet(converse(complement(u)),converse(u)),zero),
inference(spr,[status(thm),theory(equality)],[27422,21087]),
[iquote('0:SpR:27422.0,21087.0')] ).
cnf(27525,plain,
equal(meet(converse(u),converse(complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[52,27502]),
[iquote('0:Rew:52.0,27502.0')] ).
cnf(27553,plain,
equal(join(u,meet(complement(u),converse(complement(converse(complement(u)))))),converse(complement(converse(complement(u))))),
inference(rew,[status(thm),theory(equality)],[52,27465]),
[iquote('0:Rew:52.0,27465.0')] ).
cnf(28583,plain,
equal(meet(u,converse(complement(converse(u)))),zero),
inference(spr,[status(thm),theory(equality)],[2,27525]),
[iquote('0:SpR:2.0,27525.0')] ).
cnf(28616,plain,
equal(converse(complement(converse(complement(u)))),join(u,zero)),
inference(rew,[status(thm),theory(equality)],[28583,27553]),
[iquote('0:Rew:28583.0,27553.0')] ).
cnf(28624,plain,
equal(converse(complement(converse(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[929,28616]),
[iquote('0:Rew:929.0,28616.0')] ).
cnf(28654,plain,
equal(complement(converse(complement(u))),converse(u)),
inference(spr,[status(thm),theory(equality)],[28624,2]),
[iquote('0:SpR:28624.0,2.0')] ).
cnf(28978,plain,
equal(complement(converse(u)),converse(complement(u))),
inference(spr,[status(thm),theory(equality)],[28654,830]),
[iquote('0:SpR:28654.0,830.0')] ).
cnf(118951,plain,
equal(join(u,converse(complement(composition(converse(skc3),composition(skc3,converse(u)))))),converse(top)),
inference(spr,[status(thm),theory(equality)],[23653,40]),
[iquote('0:SpR:23653.0,40.0')] ).
cnf(119096,plain,
equal(join(u,complement(composition(u,composition(converse(skc3),skc3)))),top),
inference(rew,[status(thm),theory(equality)],[2,118951,28978,471,1614]),
[iquote('0:Rew:2.0,118951.0,28978.0,118951.0,471.0,118951.0,1614.0,118951.0')] ).
cnf(138357,plain,
equal(meet(join(u,v),join(u,complement(v))),u),
inference(spr,[status(thm),theory(equality)],[910,7616]),
[iquote('0:SpR:910.0,7616.0')] ).
cnf(139175,plain,
equal(meet(join(u,v),join(v,complement(u))),v),
inference(spr,[status(thm),theory(equality)],[5,138357]),
[iquote('0:SpR:5.0,138357.0')] ).
cnf(148447,plain,
equal(meet(join(composition(u,composition(converse(skc3),skc3)),u),top),u),
inference(spr,[status(thm),theory(equality)],[119096,139175]),
[iquote('0:SpR:119096.0,139175.0')] ).
cnf(148618,plain,
equal(join(u,composition(u,composition(converse(skc3),skc3))),u),
inference(rew,[status(thm),theory(equality)],[860,148447,52,5]),
[iquote('0:Rew:860.0,148447.0,52.0,148447.0,5.0,148447.0')] ).
cnf(148891,plain,
equal(join(one,composition(composition(converse(skc2),composition(converse(skc3),skc3)),skc2)),join(one,composition(converse(skc2),skc2))),
inference(spr,[status(thm),theory(equality)],[148618,2638]),
[iquote('0:SpR:148618.0,2638.0')] ).
cnf(149032,plain,
equal(join(one,composition(converse(composition(skc3,skc2)),composition(skc3,skc2))),one),
inference(rew,[status(thm),theory(equality)],[12,148891,122,17]),
[iquote('0:Rew:12.0,148891.0,122.0,148891.0,17.0,148891.0')] ).
cnf(149033,plain,
$false,
inference(mrr,[status(thm)],[149032,20]),
[iquote('0:MRR:149032.0,20.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : REL031+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.07 % Command : run_spass %d %s
% 0.06/0.26 % Computer : n005.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 600
% 0.06/0.26 % DateTime : Fri Jul 8 11:44:07 EDT 2022
% 0.06/0.26 % CPUTime :
% 116.62/116.83
% 116.62/116.83 SPASS V 3.9
% 116.62/116.83 SPASS beiseite: Proof found.
% 116.62/116.83 % SZS status Theorem
% 116.62/116.83 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 116.62/116.83 SPASS derived 88558 clauses, backtracked 0 clauses, performed 0 splits and kept 9468 clauses.
% 116.62/116.83 SPASS allocated 201729 KBytes.
% 116.62/116.83 SPASS spent 0:1:56.38 on the problem.
% 116.62/116.83 0:00:00.02 for the input.
% 116.62/116.83 0:00:00.01 for the FLOTTER CNF translation.
% 116.62/116.83 0:00:00.67 for inferences.
% 116.62/116.83 0:00:00.00 for the backtracking.
% 116.62/116.83 0:1:55.51 for the reduction.
% 116.62/116.83
% 116.62/116.83
% 116.62/116.83 Here is a proof with depth 17, length 159 :
% 116.62/116.83 % SZS output start Refutation
% See solution above
% 120.75/120.93 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_associativity composition_distributivity converse_cancellativity maddux3_a_kind_of_de_Morgan
% 120.75/120.93
%------------------------------------------------------------------------------