TSTP Solution File: REL004+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL004+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 20:01:25 EDT 2022
% Result : Theorem 9.75s 10.00s
% Output : Refutation 10.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 61
% Number of leaves : 16
% Syntax : Number of clauses : 202 ( 202 unt; 0 nHn; 202 RR)
% Number of literals : 202 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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('REL004+2.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL004+2.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,complement(u)),top),
file('REL004+2.p',unknown),
[] ).
cnf(4,axiom,
equal(meet(u,complement(u)),zero),
file('REL004+2.p',unknown),
[] ).
cnf(5,axiom,
equal(join(u,v),join(v,u)),
file('REL004+2.p',unknown),
[] ).
cnf(6,axiom,
~ equal(converse(complement(skc1)),complement(converse(skc1))),
file('REL004+2.p',unknown),
[] ).
cnf(7,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL004+2.p',unknown),
[] ).
cnf(8,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL004+2.p',unknown),
[] ).
cnf(9,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL004+2.p',unknown),
[] ).
cnf(10,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL004+2.p',unknown),
[] ).
cnf(11,axiom,
equal(composition(composition(u,v),w),composition(u,composition(v,w))),
file('REL004+2.p',unknown),
[] ).
cnf(12,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL004+2.p',unknown),
[] ).
cnf(13,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL004+2.p',unknown),
[] ).
cnf(14,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL004+2.p',unknown),
[] ).
cnf(15,axiom,
equal(join(meet(composition(u,v),w),meet(composition(meet(u,composition(w,converse(v))),v),w)),meet(composition(meet(u,composition(w,converse(v))),v),w)),
file('REL004+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('REL004+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)],[5,13]),
[iquote('0:Rew:5.0,13.0')] ).
cnf(19,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[7,14]),
[iquote('0:Rew:7.0,14.0')] ).
cnf(30,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(35,plain,
equal(converse(join(u,converse(v))),join(converse(u),v)),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(36,plain,
equal(converse(join(converse(u),v)),join(u,converse(v))),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(78,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(79,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[5,7]),
[iquote('0:SpR:5.0,7.0')] ).
cnf(81,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[4,78]),
[iquote('0:Rew:4.0,78.0')] ).
cnf(82,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[7,79]),
[iquote('0:Rew:7.0,79.0')] ).
cnf(83,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)],[82,16]),
[iquote('0:Rew:82.0,16.0')] ).
cnf(84,plain,
equal(join(meet(composition(u,v),w),meet(w,composition(meet(u,composition(w,converse(v))),v))),meet(w,composition(meet(u,composition(w,converse(v))),v))),
inference(rew,[status(thm),theory(equality)],[82,15]),
[iquote('0:Rew:82.0,15.0')] ).
cnf(91,plain,
equal(join(top,zero),top),
inference(spr,[status(thm),theory(equality)],[81,3]),
[iquote('0:SpR:81.0,3.0')] ).
cnf(92,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[81,7]),
[iquote('0:SpR:81.0,7.0')] ).
cnf(105,plain,
equal(join(meet(top,u),complement(join(zero,u))),top),
inference(spr,[status(thm),theory(equality)],[81,19]),
[iquote('0:SpR:81.0,19.0')] ).
cnf(106,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(107,plain,
equal(join(meet(u,v),complement(join(v,complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[5,19]),
[iquote('0:SpR:5.0,19.0')] ).
cnf(109,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[7,19]),
[iquote('0:SpR:7.0,19.0')] ).
cnf(110,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(115,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[5,106,81]),
[iquote('0:Rew:5.0,106.0,81.0,106.0')] ).
cnf(116,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[5,109]),
[iquote('0:Rew:5.0,109.0')] ).
cnf(117,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[7,110]),
[iquote('0:Rew:7.0,110.0')] ).
cnf(126,plain,
equal(meet(join(zero,complement(u)),meet(top,u)),zero),
inference(spr,[status(thm),theory(equality)],[92,4]),
[iquote('0:SpR:92.0,4.0')] ).
cnf(128,plain,
equal(complement(join(meet(top,u),complement(v))),meet(join(zero,complement(u)),v)),
inference(spr,[status(thm),theory(equality)],[92,7]),
[iquote('0:SpR:92.0,7.0')] ).
cnf(131,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,join(zero,complement(v)))),
inference(spr,[status(thm),theory(equality)],[92,7]),
[iquote('0:SpR:92.0,7.0')] ).
cnf(134,plain,
equal(complement(join(zero,zero)),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[81,92]),
[iquote('0:SpR:81.0,92.0')] ).
cnf(140,plain,
equal(meet(meet(top,u),join(zero,complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[82,126]),
[iquote('0:Rew:82.0,126.0')] ).
cnf(157,plain,
equal(meet(join(zero,zero),meet(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[134,4]),
[iquote('0:SpR:134.0,4.0')] ).
cnf(166,plain,
equal(meet(meet(top,top),join(zero,zero)),zero),
inference(rew,[status(thm),theory(equality)],[82,157]),
[iquote('0:Rew:82.0,157.0')] ).
cnf(173,plain,
equal(join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[166,19]),
[iquote('0:SpR:166.0,19.0')] ).
cnf(179,plain,
equal(join(zero,complement(join(join(zero,zero),complement(meet(top,top))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[5,173]),
[iquote('0:Rew:5.0,173.0')] ).
cnf(180,plain,
equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[10,179]),
[iquote('0:Rew:10.0,179.0')] ).
cnf(196,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[10,5]),
[iquote('0:SpR:10.0,5.0')] ).
cnf(202,plain,
equal(join(u,join(complement(u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[3,10]),
[iquote('0:SpR:3.0,10.0')] ).
cnf(206,plain,
equal(join(top,join(zero,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[91,10]),
[iquote('0:SpR:91.0,10.0')] ).
cnf(207,plain,
equal(join(meet(u,v),join(complement(join(complement(u),v)),w)),join(u,w)),
inference(spr,[status(thm),theory(equality)],[19,10]),
[iquote('0:SpR:19.0,10.0')] ).
cnf(232,plain,
equal(join(top,meet(u,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[117,206]),
[iquote('0:SpR:117.0,206.0')] ).
cnf(250,plain,
equal(join(complement(one),composition(converse(u),complement(u))),complement(one)),
inference(spr,[status(thm),theory(equality)],[1,18]),
[iquote('0:SpR:1.0,18.0')] ).
cnf(259,plain,
equal(join(zero,composition(converse(u),complement(composition(u,top)))),zero),
inference(spr,[status(thm),theory(equality)],[81,18]),
[iquote('0:SpR:81.0,18.0')] ).
cnf(352,plain,
equal(meet(meet(u,top),join(zero,complement(u))),zero),
inference(spr,[status(thm),theory(equality)],[82,140]),
[iquote('0:SpR:82.0,140.0')] ).
cnf(462,plain,
equal(join(zero,complement(join(complement(meet(u,top)),join(zero,complement(u))))),meet(u,top)),
inference(spr,[status(thm),theory(equality)],[352,19]),
[iquote('0:SpR:352.0,19.0')] ).
cnf(481,plain,
equal(join(zero,complement(join(zero,join(complement(u),complement(meet(u,top)))))),meet(u,top)),
inference(rew,[status(thm),theory(equality)],[196,462]),
[iquote('0:Rew:196.0,462.0')] ).
cnf(484,plain,
equal(join(meet(composition(u,converse(v)),w),meet(w,composition(meet(u,composition(w,v)),converse(v)))),meet(w,composition(meet(u,composition(w,v)),converse(v)))),
inference(spr,[status(thm),theory(equality)],[2,84]),
[iquote('0:SpR:2.0,84.0')] ).
cnf(606,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[1,30]),
[iquote('0:SpR:1.0,30.0')] ).
cnf(609,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[2,606]),
[iquote('0:Rew:2.0,606.0')] ).
cnf(620,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[609,1]),
[iquote('0:SpR:609.0,1.0')] ).
cnf(623,plain,
equal(join(u,composition(v,u)),composition(join(converse(one),v),u)),
inference(spr,[status(thm),theory(equality)],[609,12]),
[iquote('0:SpR:609.0,12.0')] ).
cnf(632,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[609,18]),
[iquote('0:SpR:609.0,18.0')] ).
cnf(638,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[620,609]),
[iquote('0:Rew:620.0,609.0')] ).
cnf(653,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[638,632]),
[iquote('0:Rew:638.0,632.0')] ).
cnf(654,plain,
equal(join(u,composition(v,u)),composition(join(one,v),u)),
inference(rew,[status(thm),theory(equality)],[620,623]),
[iquote('0:Rew:620.0,623.0')] ).
cnf(763,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[653,7]),
[iquote('0:SpR:653.0,7.0')] ).
cnf(769,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[81,653]),
[iquote('0:SpR:81.0,653.0')] ).
cnf(775,plain,
equal(meet(top,top),complement(zero)),
inference(rew,[status(thm),theory(equality)],[769,134]),
[iquote('0:Rew:769.0,134.0')] ).
cnf(788,plain,
equal(join(zero,complement(join(zero,join(zero,complement(complement(zero)))))),complement(zero)),
inference(rew,[status(thm),theory(equality)],[775,180]),
[iquote('0:Rew:775.0,180.0')] ).
cnf(792,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[763,117]),
[iquote('0:Rew:763.0,117.0')] ).
cnf(793,plain,
equal(join(top,complement(complement(u))),join(top,u)),
inference(rew,[status(thm),theory(equality)],[763,232]),
[iquote('0:Rew:763.0,232.0')] ).
cnf(821,plain,
equal(join(zero,complement(zero)),complement(zero)),
inference(rew,[status(thm),theory(equality)],[769,788,792]),
[iquote('0:Rew:769.0,788.0,792.0,788.0')] ).
cnf(822,plain,
equal(complement(zero),top),
inference(rew,[status(thm),theory(equality)],[3,821]),
[iquote('0:Rew:3.0,821.0')] ).
cnf(849,plain,
equal(complement(join(top,complement(u))),meet(zero,u)),
inference(spr,[status(thm),theory(equality)],[822,7]),
[iquote('0:SpR:822.0,7.0')] ).
cnf(850,plain,
equal(join(meet(zero,u),complement(join(top,u))),zero),
inference(spr,[status(thm),theory(equality)],[822,19]),
[iquote('0:SpR:822.0,19.0')] ).
cnf(858,plain,
equal(join(top,top),top),
inference(spr,[status(thm),theory(equality)],[822,653]),
[iquote('0:SpR:822.0,653.0')] ).
cnf(876,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[769,10]),
[iquote('0:SpR:769.0,10.0')] ).
cnf(894,plain,
equal(join(top,join(top,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[858,10]),
[iquote('0:SpR:858.0,10.0')] ).
cnf(901,plain,
equal(meet(top,complement(u)),complement(u)),
inference(spr,[status(thm),theory(equality)],[792,92]),
[iquote('0:SpR:792.0,92.0')] ).
cnf(908,plain,
equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[7,792]),
[iquote('0:SpR:7.0,792.0')] ).
cnf(931,plain,
equal(join(complement(u),complement(join(zero,complement(u)))),top),
inference(spr,[status(thm),theory(equality)],[901,105]),
[iquote('0:SpR:901.0,105.0')] ).
cnf(942,plain,
equal(join(complement(u),meet(top,u)),top),
inference(rew,[status(thm),theory(equality)],[92,931]),
[iquote('0:Rew:92.0,931.0')] ).
cnf(984,plain,
equal(join(complement(u),join(meet(top,u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[942,10]),
[iquote('0:SpR:942.0,10.0')] ).
cnf(989,plain,
equal(join(complement(u),meet(u,top)),top),
inference(spr,[status(thm),theory(equality)],[82,942]),
[iquote('0:SpR:82.0,942.0')] ).
cnf(1016,plain,
equal(join(meet(u,meet(u,top)),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[989,19]),
[iquote('0:SpR:989.0,19.0')] ).
cnf(1028,plain,
equal(join(zero,meet(u,meet(u,top))),u),
inference(rew,[status(thm),theory(equality)],[5,1016,81]),
[iquote('0:Rew:5.0,1016.0,81.0,1016.0')] ).
cnf(1128,plain,
equal(meet(top,join(top,complement(u))),complement(join(zero,meet(zero,u)))),
inference(spr,[status(thm),theory(equality)],[849,92]),
[iquote('0:SpR:849.0,92.0')] ).
cnf(1147,plain,
equal(meet(zero,complement(u)),complement(join(top,u))),
inference(spr,[status(thm),theory(equality)],[793,849]),
[iquote('0:SpR:793.0,849.0')] ).
cnf(1193,plain,
equal(join(u,converse(complement(converse(u)))),converse(top)),
inference(spr,[status(thm),theory(equality)],[3,36]),
[iquote('0:SpR:3.0,36.0')] ).
cnf(1219,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[115,876]),
[iquote('0:SpR:115.0,876.0')] ).
cnf(1226,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[1219,792]),
[iquote('0:Rew:1219.0,792.0')] ).
cnf(1227,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[1219,92]),
[iquote('0:Rew:1219.0,92.0')] ).
cnf(1233,plain,
equal(composition(converse(u),complement(composition(u,top))),zero),
inference(rew,[status(thm),theory(equality)],[1219,259]),
[iquote('0:Rew:1219.0,259.0')] ).
cnf(1236,plain,
equal(join(zero,complement(join(complement(u),complement(meet(u,top))))),meet(u,top)),
inference(rew,[status(thm),theory(equality)],[1219,481]),
[iquote('0:Rew:1219.0,481.0')] ).
cnf(1239,plain,
equal(join(complement(u),complement(v)),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[1219,908]),
[iquote('0:Rew:1219.0,908.0')] ).
cnf(1241,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[1219,131]),
[iquote('0:Rew:1219.0,131.0')] ).
cnf(1243,plain,
equal(complement(join(meet(top,u),complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[1219,128]),
[iquote('0:Rew:1219.0,128.0')] ).
cnf(1249,plain,
equal(meet(u,meet(u,top)),u),
inference(rew,[status(thm),theory(equality)],[1219,1028]),
[iquote('0:Rew:1219.0,1028.0')] ).
cnf(1252,plain,
equal(meet(top,join(top,complement(u))),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[1219,1128]),
[iquote('0:Rew:1219.0,1128.0')] ).
cnf(1266,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[1226,1227]),
[iquote('0:Rew:1226.0,1227.0')] ).
cnf(1270,plain,
equal(join(complement(u),join(u,v)),join(top,v)),
inference(rew,[status(thm),theory(equality)],[1266,984]),
[iquote('0:Rew:1266.0,984.0')] ).
cnf(1296,plain,
equal(join(u,join(v,complement(u))),join(top,v)),
inference(rew,[status(thm),theory(equality)],[196,1270]),
[iquote('0:Rew:196.0,1270.0')] ).
cnf(1300,plain,
equal(join(top,complement(u)),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[1266,1252]),
[iquote('0:Rew:1266.0,1252.0')] ).
cnf(1318,plain,
equal(complement(join(complement(u),v)),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[1266,1241]),
[iquote('0:Rew:1266.0,1241.0')] ).
cnf(1321,plain,
equal(join(meet(u,v),join(meet(u,complement(v)),w)),join(u,w)),
inference(rew,[status(thm),theory(equality)],[1318,207]),
[iquote('0:Rew:1318.0,207.0')] ).
cnf(1322,plain,
equal(complement(join(u,complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[1266,1243]),
[iquote('0:Rew:1266.0,1243.0')] ).
cnf(1323,plain,
equal(join(meet(u,v),meet(complement(v),u)),u),
inference(rew,[status(thm),theory(equality)],[1322,107]),
[iquote('0:Rew:1322.0,107.0')] ).
cnf(1327,plain,
equal(meet(u,top),u),
inference(rew,[status(thm),theory(equality)],[1219,1236,1226,1249,1239]),
[iquote('0:Rew:1219.0,1236.0,1226.0,1236.0,1249.0,1236.0,1239.0,1236.0')] ).
cnf(1350,plain,
equal(join(u,zero),u),
inference(spr,[status(thm),theory(equality)],[1219,5]),
[iquote('0:SpR:1219.0,5.0')] ).
cnf(1354,plain,
equal(join(converse(zero),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[1219,35]),
[iquote('0:SpR:1219.0,35.0')] ).
cnf(1365,plain,
equal(join(converse(zero),u),u),
inference(rew,[status(thm),theory(equality)],[2,1354]),
[iquote('0:Rew:2.0,1354.0')] ).
cnf(1477,plain,
equal(converse(zero),zero),
inference(spr,[status(thm),theory(equality)],[1365,1350]),
[iquote('0:SpR:1365.0,1350.0')] ).
cnf(1579,plain,
equal(join(top,converse(complement(converse(complement(u))))),join(u,converse(top))),
inference(spr,[status(thm),theory(equality)],[1193,202]),
[iquote('0:SpR:1193.0,202.0')] ).
cnf(1580,plain,
equal(join(top,converse(top)),converse(top)),
inference(spr,[status(thm),theory(equality)],[1193,894]),
[iquote('0:SpR:1193.0,894.0')] ).
cnf(1628,plain,
equal(join(u,meet(u,complement(top))),u),
inference(spr,[status(thm),theory(equality)],[1327,116]),
[iquote('0:SpR:1327.0,116.0')] ).
cnf(1635,plain,
equal(join(u,meet(u,zero)),u),
inference(rew,[status(thm),theory(equality)],[81,1628]),
[iquote('0:Rew:81.0,1628.0')] ).
cnf(1649,plain,
equal(join(converse(top),top),converse(converse(top))),
inference(spr,[status(thm),theory(equality)],[1580,35]),
[iquote('0:SpR:1580.0,35.0')] ).
cnf(1652,plain,
equal(converse(top),top),
inference(rew,[status(thm),theory(equality)],[1580,1649,5,2]),
[iquote('0:Rew:1580.0,1649.0,5.0,1649.0,2.0,1649.0')] ).
cnf(1659,plain,
equal(join(top,converse(complement(converse(complement(u))))),join(u,top)),
inference(rew,[status(thm),theory(equality)],[1652,1579]),
[iquote('0:Rew:1652.0,1579.0')] ).
cnf(1668,plain,
equal(join(top,converse(u)),converse(join(top,u))),
inference(spr,[status(thm),theory(equality)],[1652,8]),
[iquote('0:SpR:1652.0,8.0')] ).
cnf(1676,plain,
equal(join(complement(u),composition(top,complement(composition(top,u)))),complement(u)),
inference(spr,[status(thm),theory(equality)],[1652,18]),
[iquote('0:SpR:1652.0,18.0')] ).
cnf(1684,plain,
equal(converse(join(top,complement(converse(complement(u))))),join(u,top)),
inference(rew,[status(thm),theory(equality)],[1668,1659]),
[iquote('0:Rew:1668.0,1659.0')] ).
cnf(1690,plain,
equal(converse(complement(meet(zero,converse(complement(u))))),join(u,top)),
inference(rew,[status(thm),theory(equality)],[1300,1684]),
[iquote('0:Rew:1300.0,1684.0')] ).
cnf(1698,plain,
equal(join(u,complement(u)),join(top,meet(complement(u),zero))),
inference(spr,[status(thm),theory(equality)],[1635,202]),
[iquote('0:SpR:1635.0,202.0')] ).
cnf(1708,plain,
equal(join(top,complement(join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[3,1698,1147,82]),
[iquote('0:Rew:3.0,1698.0,1147.0,1698.0,82.0,1698.0')] ).
cnf(1709,plain,
equal(complement(meet(zero,join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[1300,1708]),
[iquote('0:Rew:1300.0,1708.0')] ).
cnf(1815,plain,
equal(meet(zero,join(top,u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[1709,1226]),
[iquote('0:SpR:1709.0,1226.0')] ).
cnf(1841,plain,
equal(meet(zero,join(top,u)),zero),
inference(rew,[status(thm),theory(equality)],[81,1815]),
[iquote('0:Rew:81.0,1815.0')] ).
cnf(1885,plain,
equal(join(zero,meet(zero,complement(join(top,u)))),zero),
inference(spr,[status(thm),theory(equality)],[1841,116]),
[iquote('0:SpR:1841.0,116.0')] ).
cnf(1903,plain,
equal(complement(join(top,u)),zero),
inference(rew,[status(thm),theory(equality)],[1219,1885,894,1147]),
[iquote('0:Rew:1219.0,1885.0,894.0,1885.0,1147.0,1885.0')] ).
cnf(1905,plain,
equal(join(meet(zero,u),zero),zero),
inference(rew,[status(thm),theory(equality)],[1903,850]),
[iquote('0:Rew:1903.0,850.0')] ).
cnf(1907,plain,
equal(meet(zero,u),zero),
inference(rew,[status(thm),theory(equality)],[1219,1905,5]),
[iquote('0:Rew:1219.0,1905.0,5.0,1905.0')] ).
cnf(1912,plain,
equal(join(u,top),converse(complement(zero))),
inference(rew,[status(thm),theory(equality)],[1907,1690]),
[iquote('0:Rew:1907.0,1690.0')] ).
cnf(1926,plain,
equal(join(u,top),top),
inference(rew,[status(thm),theory(equality)],[1652,1912,822]),
[iquote('0:Rew:1652.0,1912.0,822.0,1912.0')] ).
cnf(1990,plain,
equal(join(top,u),top),
inference(spr,[status(thm),theory(equality)],[1926,5]),
[iquote('0:SpR:1926.0,5.0')] ).
cnf(2006,plain,
equal(join(u,join(v,complement(u))),top),
inference(rew,[status(thm),theory(equality)],[1990,1296]),
[iquote('0:Rew:1990.0,1296.0')] ).
cnf(2194,plain,
equal(composition(top,complement(composition(top,top))),zero),
inference(spr,[status(thm),theory(equality)],[1652,1233]),
[iquote('0:SpR:1652.0,1233.0')] ).
cnf(2404,plain,
equal(join(zero,composition(u,complement(composition(top,top)))),composition(join(top,u),complement(composition(top,top)))),
inference(spr,[status(thm),theory(equality)],[2194,12]),
[iquote('0:SpR:2194.0,12.0')] ).
cnf(2411,plain,
equal(composition(u,complement(composition(top,top))),zero),
inference(rew,[status(thm),theory(equality)],[1219,2404,2194,1990]),
[iquote('0:Rew:1219.0,2404.0,2194.0,2404.0,1990.0,2404.0')] ).
cnf(2433,plain,
equal(composition(converse(complement(composition(top,top))),u),converse(zero)),
inference(spr,[status(thm),theory(equality)],[2411,30]),
[iquote('0:SpR:2411.0,30.0')] ).
cnf(2434,plain,
equal(complement(composition(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[2411,638]),
[iquote('0:SpR:2411.0,638.0')] ).
cnf(2452,plain,
equal(composition(converse(complement(composition(top,top))),u),zero),
inference(rew,[status(thm),theory(equality)],[1477,2433]),
[iquote('0:Rew:1477.0,2433.0')] ).
cnf(2453,plain,
equal(composition(converse(zero),u),zero),
inference(rew,[status(thm),theory(equality)],[2434,2452]),
[iquote('0:Rew:2434.0,2452.0')] ).
cnf(2454,plain,
equal(composition(zero,u),zero),
inference(rew,[status(thm),theory(equality)],[1477,2453]),
[iquote('0:Rew:1477.0,2453.0')] ).
cnf(2695,plain,
equal(composition(top,top),complement(zero)),
inference(spr,[status(thm),theory(equality)],[2434,1226]),
[iquote('0:SpR:2434.0,1226.0')] ).
cnf(2706,plain,
equal(composition(top,top),top),
inference(rew,[status(thm),theory(equality)],[822,2695]),
[iquote('0:Rew:822.0,2695.0')] ).
cnf(2727,plain,
equal(composition(top,composition(top,u)),composition(top,u)),
inference(spr,[status(thm),theory(equality)],[2706,11]),
[iquote('0:SpR:2706.0,11.0')] ).
cnf(2729,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)],[2706,83]),
[iquote('0:SpR:2706.0,83.0')] ).
cnf(2741,plain,
equal(join(u,meet(u,composition(top,composition(top,u)))),meet(u,composition(top,composition(top,u)))),
inference(rew,[status(thm),theory(equality)],[1266,2729,1652]),
[iquote('0:Rew:1266.0,2729.0,1266.0,2729.0,1652.0,2729.0')] ).
cnf(2742,plain,
equal(join(u,meet(u,composition(top,u))),meet(u,composition(top,u))),
inference(rew,[status(thm),theory(equality)],[2727,2741]),
[iquote('0:Rew:2727.0,2741.0')] ).
cnf(3031,plain,
equal(join(complement(composition(top,u)),composition(converse(top),complement(composition(top,u)))),complement(composition(top,u))),
inference(spr,[status(thm),theory(equality)],[2727,18]),
[iquote('0:SpR:2727.0,18.0')] ).
cnf(3048,plain,
equal(join(complement(composition(top,u)),composition(top,complement(composition(top,u)))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[1652,3031]),
[iquote('0:Rew:1652.0,3031.0')] ).
cnf(3049,plain,
equal(composition(join(one,top),complement(composition(top,u))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[654,3048]),
[iquote('0:Rew:654.0,3048.0')] ).
cnf(3050,plain,
equal(composition(top,complement(composition(top,u))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[1926,3049]),
[iquote('0:Rew:1926.0,3049.0')] ).
cnf(3051,plain,
equal(join(complement(u),complement(composition(top,u))),complement(u)),
inference(rew,[status(thm),theory(equality)],[3050,1676]),
[iquote('0:Rew:3050.0,1676.0')] ).
cnf(3052,plain,
equal(complement(meet(u,composition(top,u))),complement(u)),
inference(rew,[status(thm),theory(equality)],[1239,3051]),
[iquote('0:Rew:1239.0,3051.0')] ).
cnf(3159,plain,
equal(meet(u,composition(top,u)),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[3052,1226]),
[iquote('0:SpR:3052.0,1226.0')] ).
cnf(3182,plain,
equal(meet(u,composition(top,u)),u),
inference(rew,[status(thm),theory(equality)],[1226,3159]),
[iquote('0:Rew:1226.0,3159.0')] ).
cnf(3184,plain,
equal(join(u,u),u),
inference(rew,[status(thm),theory(equality)],[3182,2742]),
[iquote('0:Rew:3182.0,2742.0')] ).
cnf(3250,plain,
equal(join(u,join(u,v)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[3184,10]),
[iquote('0:SpR:3184.0,10.0')] ).
cnf(3421,plain,
equal(join(meet(u,v),u),u),
inference(spr,[status(thm),theory(equality)],[116,3250]),
[iquote('0:SpR:116.0,3250.0')] ).
cnf(3432,plain,
equal(join(u,meet(u,v)),u),
inference(rew,[status(thm),theory(equality)],[5,3421]),
[iquote('0:Rew:5.0,3421.0')] ).
cnf(3503,plain,
equal(join(u,meet(v,u)),u),
inference(spr,[status(thm),theory(equality)],[82,3432]),
[iquote('0:SpR:82.0,3432.0')] ).
cnf(3526,plain,
equal(join(u,converse(meet(v,converse(u)))),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[3503,36]),
[iquote('0:SpR:3503.0,36.0')] ).
cnf(3550,plain,
equal(join(u,converse(meet(v,converse(u)))),u),
inference(rew,[status(thm),theory(equality)],[2,3526]),
[iquote('0:Rew:2.0,3526.0')] ).
cnf(4399,plain,
equal(join(u,complement(meet(u,v))),top),
inference(spr,[status(thm),theory(equality)],[1321,2006]),
[iquote('0:SpR:1321.0,2006.0')] ).
cnf(10620,plain,
equal(complement(meet(u,meet(complement(u),v))),top),
inference(spr,[status(thm),theory(equality)],[1239,4399]),
[iquote('0:SpR:1239.0,4399.0')] ).
cnf(10656,plain,
equal(complement(meet(complement(u),v)),join(u,complement(v))),
inference(spr,[status(thm),theory(equality)],[1226,1239]),
[iquote('0:SpR:1226.0,1239.0')] ).
cnf(10703,plain,
equal(meet(u,meet(complement(u),v)),complement(top)),
inference(spr,[status(thm),theory(equality)],[10620,1226]),
[iquote('0:SpR:10620.0,1226.0')] ).
cnf(10782,plain,
equal(meet(u,meet(complement(u),v)),zero),
inference(rew,[status(thm),theory(equality)],[81,10703]),
[iquote('0:Rew:81.0,10703.0')] ).
cnf(10820,plain,
equal(join(zero,meet(u,complement(meet(complement(u),v)))),u),
inference(spr,[status(thm),theory(equality)],[10782,116]),
[iquote('0:SpR:10782.0,116.0')] ).
cnf(10858,plain,
equal(meet(complement(u),meet(u,v)),zero),
inference(spr,[status(thm),theory(equality)],[1226,10782]),
[iquote('0:SpR:1226.0,10782.0')] ).
cnf(10887,plain,
equal(meet(u,complement(meet(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[1219,10820]),
[iquote('0:Rew:1219.0,10820.0')] ).
cnf(10888,plain,
equal(meet(u,join(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[10656,10887]),
[iquote('0:Rew:10656.0,10887.0')] ).
cnf(10927,plain,
equal(meet(complement(u),meet(v,u)),zero),
inference(spr,[status(thm),theory(equality)],[82,10858]),
[iquote('0:SpR:82.0,10858.0')] ).
cnf(11354,plain,
equal(meet(u,join(u,v)),u),
inference(spr,[status(thm),theory(equality)],[1226,10888]),
[iquote('0:SpR:1226.0,10888.0')] ).
cnf(11575,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[5,11354]),
[iquote('0:SpR:5.0,11354.0')] ).
cnf(11720,plain,
equal(meet(complement(join(u,v)),v),zero),
inference(spr,[status(thm),theory(equality)],[11575,10927]),
[iquote('0:SpR:11575.0,10927.0')] ).
cnf(11846,plain,
equal(meet(u,complement(join(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[82,11720]),
[iquote('0:Rew:82.0,11720.0')] ).
cnf(12566,plain,
equal(meet(converse(meet(u,converse(v))),complement(v)),zero),
inference(spr,[status(thm),theory(equality)],[3550,11846]),
[iquote('0:SpR:3550.0,11846.0')] ).
cnf(12607,plain,
equal(meet(composition(converse(u),complement(u)),complement(complement(one))),zero),
inference(spr,[status(thm),theory(equality)],[250,11846]),
[iquote('0:SpR:250.0,11846.0')] ).
cnf(12690,plain,
equal(meet(complement(u),converse(meet(v,converse(u)))),zero),
inference(rew,[status(thm),theory(equality)],[82,12566]),
[iquote('0:Rew:82.0,12566.0')] ).
cnf(12731,plain,
equal(meet(one,composition(converse(u),complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[82,12607,1226]),
[iquote('0:Rew:82.0,12607.0,1226.0,12607.0')] ).
cnf(13129,plain,
equal(join(meet(composition(one,converse(complement(u))),converse(u)),meet(converse(u),composition(zero,converse(complement(u))))),meet(converse(u),composition(zero,converse(complement(u))))),
inference(spr,[status(thm),theory(equality)],[12731,484]),
[iquote('0:SpR:12731.0,484.0')] ).
cnf(13177,plain,
equal(meet(converse(u),converse(complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[1219,13129,5,82,638,1907,2454]),
[iquote('0:Rew:1219.0,13129.0,5.0,13129.0,82.0,13129.0,638.0,13129.0,1907.0,13129.0,82.0,13129.0,2454.0,13129.0')] ).
cnf(13179,plain,
equal(join(zero,meet(converse(u),complement(converse(complement(u))))),converse(u)),
inference(spr,[status(thm),theory(equality)],[13177,116]),
[iquote('0:SpR:13177.0,116.0')] ).
cnf(13218,plain,
equal(meet(u,converse(complement(converse(u)))),zero),
inference(spr,[status(thm),theory(equality)],[2,13177]),
[iquote('0:SpR:2.0,13177.0')] ).
cnf(13252,plain,
equal(meet(converse(u),complement(converse(complement(u)))),converse(u)),
inference(rew,[status(thm),theory(equality)],[1219,13179]),
[iquote('0:Rew:1219.0,13179.0')] ).
cnf(13531,plain,
equal(join(zero,meet(u,complement(converse(complement(converse(u)))))),u),
inference(spr,[status(thm),theory(equality)],[13218,116]),
[iquote('0:SpR:13218.0,116.0')] ).
cnf(13606,plain,
equal(meet(u,complement(converse(complement(converse(u))))),u),
inference(rew,[status(thm),theory(equality)],[1219,13531]),
[iquote('0:Rew:1219.0,13531.0')] ).
cnf(14273,plain,
equal(join(meet(complement(converse(complement(converse(complement(u))))),u),complement(u)),complement(converse(complement(converse(complement(u)))))),
inference(spr,[status(thm),theory(equality)],[13606,1323]),
[iquote('0:SpR:13606.0,1323.0')] ).
cnf(14319,plain,
equal(join(complement(u),meet(u,complement(converse(complement(converse(complement(u))))))),complement(converse(complement(converse(complement(u)))))),
inference(rew,[status(thm),theory(equality)],[5,14273,82]),
[iquote('0:Rew:5.0,14273.0,82.0,14273.0')] ).
cnf(20756,plain,
equal(meet(complement(converse(u)),converse(meet(v,u))),zero),
inference(spr,[status(thm),theory(equality)],[2,12690]),
[iquote('0:SpR:2.0,12690.0')] ).
cnf(26364,plain,
equal(meet(complement(converse(complement(converse(complement(u))))),converse(converse(u))),zero),
inference(spr,[status(thm),theory(equality)],[13252,20756]),
[iquote('0:SpR:13252.0,20756.0')] ).
cnf(26485,plain,
equal(meet(u,complement(converse(complement(converse(complement(u)))))),zero),
inference(rew,[status(thm),theory(equality)],[82,26364,2]),
[iquote('0:Rew:82.0,26364.0,2.0,26364.0')] ).
cnf(26486,plain,
equal(complement(converse(complement(converse(complement(u))))),join(complement(u),zero)),
inference(rew,[status(thm),theory(equality)],[26485,14319]),
[iquote('0:Rew:26485.0,14319.0')] ).
cnf(26487,plain,
equal(complement(converse(complement(converse(complement(u))))),complement(u)),
inference(rew,[status(thm),theory(equality)],[1219,26486,5]),
[iquote('0:Rew:1219.0,26486.0,5.0,26486.0')] ).
cnf(26711,plain,
equal(complement(converse(complement(converse(u)))),u),
inference(spr,[status(thm),theory(equality)],[1226,26487]),
[iquote('0:SpR:1226.0,26487.0')] ).
cnf(26823,plain,
equal(converse(complement(converse(u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[26711,1226]),
[iquote('0:SpR:26711.0,1226.0')] ).
cnf(27129,plain,
equal(converse(complement(u)),complement(converse(u))),
inference(spr,[status(thm),theory(equality)],[26823,2]),
[iquote('0:SpR:26823.0,2.0')] ).
cnf(27247,plain,
$false,
inference(unc,[status(thm)],[27129,6]),
[iquote('0:UnC:27129.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL004+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 07:51:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 9.75/10.00
% 9.75/10.00 SPASS V 3.9
% 9.75/10.00 SPASS beiseite: Proof found.
% 9.75/10.00 % SZS status Theorem
% 9.75/10.00 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.75/10.00 SPASS derived 17021 clauses, backtracked 0 clauses, performed 0 splits and kept 3452 clauses.
% 9.75/10.00 SPASS allocated 120628 KBytes.
% 9.75/10.00 SPASS spent 0:00:09.62 on the problem.
% 9.75/10.00 0:00:00.04 for the input.
% 9.75/10.00 0:00:00.02 for the FLOTTER CNF translation.
% 9.75/10.00 0:00:00.15 for inferences.
% 9.75/10.00 0:00:00.00 for the backtracking.
% 9.75/10.00 0:00:09.36 for the reduction.
% 9.75/10.00
% 9.75/10.00
% 9.75/10.00 Here is a proof with depth 21, length 202 :
% 9.75/10.00 % SZS output start Refutation
% See solution above
% 10.05/10.29 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_associativity composition_distributivity converse_cancellativity maddux3_a_kind_of_de_Morgan modular_law_2 modular_law_1
% 10.05/10.29
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