TSTP Solution File: REL043+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL043+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 20:02:25 EDT 2022
% Result : Theorem 23.62s 23.79s
% Output : Refutation 24.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 16
% Syntax : Number of clauses : 132 ( 132 unt; 0 nHn; 132 RR)
% Number of literals : 132 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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('REL043+2.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL043+2.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,complement(u)),top),
file('REL043+2.p',unknown),
[] ).
cnf(4,axiom,
equal(meet(u,complement(u)),zero),
file('REL043+2.p',unknown),
[] ).
cnf(5,axiom,
equal(join(u,v),join(v,u)),
file('REL043+2.p',unknown),
[] ).
cnf(6,axiom,
equal(join(composition(skc3,converse(skc4)),skc5),skc5),
file('REL043+2.p',unknown),
[] ).
cnf(7,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL043+2.p',unknown),
[] ).
cnf(8,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL043+2.p',unknown),
[] ).
cnf(9,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL043+2.p',unknown),
[] ).
cnf(10,axiom,
~ equal(join(composition(complement(skc5),skc4),complement(skc3)),complement(skc3)),
file('REL043+2.p',unknown),
[] ).
cnf(11,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL043+2.p',unknown),
[] ).
cnf(13,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL043+2.p',unknown),
[] ).
cnf(14,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL043+2.p',unknown),
[] ).
cnf(15,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL043+2.p',unknown),
[] ).
cnf(16,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('REL043+2.p',unknown),
[] ).
cnf(18,axiom,
equal(join(meet(composition(u,v),w),composition(meet(u,composition(w,converse(v))),meet(v,composition(converse(u),w)))),composition(meet(u,composition(w,converse(v))),meet(v,composition(converse(u),w)))),
file('REL043+2.p',unknown),
[] ).
cnf(19,plain,
equal(join(skc5,composition(skc3,converse(skc4))),skc5),
inference(rew,[status(thm),theory(equality)],[5,6]),
[iquote('0:Rew:5.0,6.0')] ).
cnf(20,plain,
~ equal(join(complement(skc3),composition(complement(skc5),skc4)),complement(skc3)),
inference(rew,[status(thm),theory(equality)],[5,10]),
[iquote('0:Rew:5.0,10.0')] ).
cnf(21,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[5,14]),
[iquote('0:Rew:5.0,14.0')] ).
cnf(22,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[7,15]),
[iquote('0:Rew:7.0,15.0')] ).
cnf(34,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(39,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(40,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(82,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(83,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(85,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[4,82]),
[iquote('0:Rew:4.0,82.0')] ).
cnf(86,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[7,83]),
[iquote('0:Rew:7.0,83.0')] ).
cnf(88,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)],[86,16]),
[iquote('0:Rew:86.0,16.0')] ).
cnf(96,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[85,7]),
[iquote('0:SpR:85.0,7.0')] ).
cnf(107,plain,
equal(meet(join(zero,complement(u)),meet(top,u)),zero),
inference(spr,[status(thm),theory(equality)],[96,4]),
[iquote('0:SpR:96.0,4.0')] ).
cnf(111,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,join(zero,complement(v)))),
inference(spr,[status(thm),theory(equality)],[96,7]),
[iquote('0:SpR:96.0,7.0')] ).
cnf(117,plain,
equal(meet(meet(top,u),join(zero,complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[86,107]),
[iquote('0:Rew:86.0,107.0')] ).
cnf(146,plain,
equal(join(meet(top,u),complement(join(zero,u))),top),
inference(spr,[status(thm),theory(equality)],[85,22]),
[iquote('0:SpR:85.0,22.0')] ).
cnf(150,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[7,22]),
[iquote('0:SpR:7.0,22.0')] ).
cnf(151,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[4,22]),
[iquote('0:SpR:4.0,22.0')] ).
cnf(162,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[5,150]),
[iquote('0:Rew:5.0,150.0')] ).
cnf(163,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[7,151]),
[iquote('0:Rew:7.0,151.0')] ).
cnf(219,plain,
equal(meet(meet(u,top),join(zero,complement(u))),zero),
inference(spr,[status(thm),theory(equality)],[86,117]),
[iquote('0:SpR:86.0,117.0')] ).
cnf(237,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(238,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(254,plain,
equal(join(meet(u,v),join(complement(join(complement(u),v)),w)),join(u,w)),
inference(spr,[status(thm),theory(equality)],[22,11]),
[iquote('0:SpR:22.0,11.0')] ).
cnf(307,plain,
equal(join(zero,composition(converse(u),complement(composition(u,top)))),zero),
inference(spr,[status(thm),theory(equality)],[85,21]),
[iquote('0:SpR:85.0,21.0')] ).
cnf(344,plain,
equal(join(zero,complement(join(complement(meet(u,top)),join(zero,complement(u))))),meet(u,top)),
inference(spr,[status(thm),theory(equality)],[219,22]),
[iquote('0:SpR:219.0,22.0')] ).
cnf(364,plain,
equal(join(zero,complement(join(zero,join(complement(u),complement(meet(u,top)))))),meet(u,top)),
inference(rew,[status(thm),theory(equality)],[238,344]),
[iquote('0:Rew:238.0,344.0')] ).
cnf(548,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(551,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[2,548]),
[iquote('0:Rew:2.0,548.0')] ).
cnf(585,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[551,1]),
[iquote('0:SpR:551.0,1.0')] ).
cnf(596,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[551,21]),
[iquote('0:SpR:551.0,21.0')] ).
cnf(600,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[585,551]),
[iquote('0:Rew:585.0,551.0')] ).
cnf(611,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[600,596]),
[iquote('0:Rew:600.0,596.0')] ).
cnf(667,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[611,7]),
[iquote('0:SpR:611.0,7.0')] ).
cnf(673,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[85,611]),
[iquote('0:SpR:85.0,611.0')] ).
cnf(695,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[667,163]),
[iquote('0:Rew:667.0,163.0')] ).
cnf(770,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[673,11]),
[iquote('0:SpR:673.0,11.0')] ).
cnf(787,plain,
equal(meet(top,complement(u)),complement(u)),
inference(spr,[status(thm),theory(equality)],[695,96]),
[iquote('0:SpR:695.0,96.0')] ).
cnf(794,plain,
equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[7,695]),
[iquote('0:SpR:7.0,695.0')] ).
cnf(828,plain,
equal(join(complement(u),complement(join(zero,complement(u)))),top),
inference(spr,[status(thm),theory(equality)],[787,146]),
[iquote('0:SpR:787.0,146.0')] ).
cnf(836,plain,
equal(join(complement(u),meet(top,u)),top),
inference(rew,[status(thm),theory(equality)],[96,828]),
[iquote('0:Rew:96.0,828.0')] ).
cnf(917,plain,
equal(join(complement(u),join(meet(top,u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[836,11]),
[iquote('0:SpR:836.0,11.0')] ).
cnf(922,plain,
equal(join(complement(u),meet(u,top)),top),
inference(spr,[status(thm),theory(equality)],[86,836]),
[iquote('0:SpR:86.0,836.0')] ).
cnf(947,plain,
equal(join(meet(u,meet(u,top)),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[922,22]),
[iquote('0:SpR:922.0,22.0')] ).
cnf(957,plain,
equal(join(zero,meet(u,meet(u,top))),u),
inference(rew,[status(thm),theory(equality)],[5,947,85]),
[iquote('0:Rew:5.0,947.0,85.0,947.0')] ).
cnf(1058,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[695,770]),
[iquote('0:SpR:695.0,770.0')] ).
cnf(1066,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[1058,695]),
[iquote('0:Rew:1058.0,695.0')] ).
cnf(1067,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[1058,96]),
[iquote('0:Rew:1058.0,96.0')] ).
cnf(1072,plain,
equal(join(zero,complement(join(complement(u),complement(meet(u,top))))),meet(u,top)),
inference(rew,[status(thm),theory(equality)],[1058,364]),
[iquote('0:Rew:1058.0,364.0')] ).
cnf(1076,plain,
equal(composition(converse(u),complement(composition(u,top))),zero),
inference(rew,[status(thm),theory(equality)],[1058,307]),
[iquote('0:Rew:1058.0,307.0')] ).
cnf(1079,plain,
equal(meet(u,meet(u,top)),u),
inference(rew,[status(thm),theory(equality)],[1058,957]),
[iquote('0:Rew:1058.0,957.0')] ).
cnf(1083,plain,
equal(join(complement(u),complement(v)),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[1058,794]),
[iquote('0:Rew:1058.0,794.0')] ).
cnf(1085,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[1058,111]),
[iquote('0:Rew:1058.0,111.0')] ).
cnf(1103,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[1066,1067]),
[iquote('0:Rew:1066.0,1067.0')] ).
cnf(1107,plain,
equal(join(complement(u),join(u,v)),join(top,v)),
inference(rew,[status(thm),theory(equality)],[1103,917]),
[iquote('0:Rew:1103.0,917.0')] ).
cnf(1132,plain,
equal(join(u,join(v,complement(u))),join(top,v)),
inference(rew,[status(thm),theory(equality)],[238,1107]),
[iquote('0:Rew:238.0,1107.0')] ).
cnf(1143,plain,
equal(complement(join(complement(u),v)),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[1103,1085]),
[iquote('0:Rew:1103.0,1085.0')] ).
cnf(1146,plain,
equal(join(meet(u,v),join(meet(u,complement(v)),w)),join(u,w)),
inference(rew,[status(thm),theory(equality)],[1143,254]),
[iquote('0:Rew:1143.0,254.0')] ).
cnf(1150,plain,
equal(meet(u,top),u),
inference(rew,[status(thm),theory(equality)],[1058,1072,1066,1079,1083]),
[iquote('0:Rew:1058.0,1072.0,1066.0,1072.0,1079.0,1072.0,1083.0,1072.0')] ).
cnf(1172,plain,
equal(complement(zero),top),
inference(spr,[status(thm),theory(equality)],[1058,3]),
[iquote('0:SpR:1058.0,3.0')] ).
cnf(1173,plain,
equal(join(u,zero),u),
inference(spr,[status(thm),theory(equality)],[1058,5]),
[iquote('0:SpR:1058.0,5.0')] ).
cnf(1177,plain,
equal(join(converse(zero),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[1058,39]),
[iquote('0:SpR:1058.0,39.0')] ).
cnf(1190,plain,
equal(join(converse(zero),u),u),
inference(rew,[status(thm),theory(equality)],[2,1177]),
[iquote('0:Rew:2.0,1177.0')] ).
cnf(1284,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(1308,plain,
equal(converse(zero),zero),
inference(spr,[status(thm),theory(equality)],[1190,1173]),
[iquote('0:SpR:1190.0,1173.0')] ).
cnf(1355,plain,
equal(composition(converse(complement(composition(u,top))),u),converse(zero)),
inference(spr,[status(thm),theory(equality)],[1076,34]),
[iquote('0:SpR:1076.0,34.0')] ).
cnf(1359,plain,
equal(composition(u,complement(composition(converse(u),top))),zero),
inference(spr,[status(thm),theory(equality)],[2,1076]),
[iquote('0:SpR:2.0,1076.0')] ).
cnf(1371,plain,
equal(composition(converse(complement(composition(u,top))),u),zero),
inference(rew,[status(thm),theory(equality)],[1308,1355]),
[iquote('0:Rew:1308.0,1355.0')] ).
cnf(1413,plain,
equal(join(meet(composition(u,v),w),join(meet(w,composition(meet(u,composition(w,converse(v))),v)),complement(meet(w,composition(meet(u,composition(w,converse(v))),v))))),top),
inference(spr,[status(thm),theory(equality)],[88,237]),
[iquote('0:SpR:88.0,237.0')] ).
cnf(1435,plain,
equal(join(top,meet(composition(u,v),w)),top),
inference(rew,[status(thm),theory(equality)],[5,1413,3]),
[iquote('0:Rew:5.0,1413.0,3.0,1413.0')] ).
cnf(1817,plain,
equal(composition(complement(composition(top,top)),complement(zero)),zero),
inference(spr,[status(thm),theory(equality)],[1371,1359]),
[iquote('0:SpR:1371.0,1359.0')] ).
cnf(1824,plain,
equal(composition(complement(composition(top,top)),top),zero),
inference(rew,[status(thm),theory(equality)],[1172,1817]),
[iquote('0:Rew:1172.0,1817.0')] ).
cnf(1843,plain,
equal(join(meet(zero,u),composition(meet(complement(composition(top,top)),composition(u,converse(top))),meet(top,composition(converse(complement(composition(top,top))),u)))),composition(meet(complement(composition(top,top)),composition(u,converse(top))),meet(top,composition(converse(complement(composition(top,top))),u)))),
inference(spr,[status(thm),theory(equality)],[1824,18]),
[iquote('0:SpR:1824.0,18.0')] ).
cnf(1855,plain,
equal(join(meet(zero,u),composition(meet(complement(composition(top,top)),composition(u,converse(top))),composition(converse(complement(composition(top,top))),u))),composition(meet(complement(composition(top,top)),composition(u,converse(top))),composition(converse(complement(composition(top,top))),u))),
inference(rew,[status(thm),theory(equality)],[1103,1843]),
[iquote('0:Rew:1103.0,1843.0')] ).
cnf(1884,plain,
equal(join(top,meet(u,v)),top),
inference(spr,[status(thm),theory(equality)],[1,1435]),
[iquote('0:SpR:1.0,1435.0')] ).
cnf(1941,plain,
equal(join(top,u),top),
inference(spr,[status(thm),theory(equality)],[1150,1884]),
[iquote('0:SpR:1150.0,1884.0')] ).
cnf(1953,plain,
equal(join(u,join(v,complement(u))),top),
inference(rew,[status(thm),theory(equality)],[1941,1132]),
[iquote('0:Rew:1941.0,1132.0')] ).
cnf(1963,plain,
equal(converse(top),top),
inference(spr,[status(thm),theory(equality)],[1941,1284]),
[iquote('0:SpR:1941.0,1284.0')] ).
cnf(1983,plain,
equal(join(meet(zero,u),composition(meet(complement(composition(top,top)),composition(u,top)),composition(converse(complement(composition(top,top))),u))),composition(meet(complement(composition(top,top)),composition(u,top)),composition(converse(complement(composition(top,top))),u))),
inference(rew,[status(thm),theory(equality)],[1963,1855]),
[iquote('0:Rew:1963.0,1855.0')] ).
cnf(2000,plain,
equal(composition(top,complement(composition(top,top))),zero),
inference(spr,[status(thm),theory(equality)],[1963,1076]),
[iquote('0:SpR:1963.0,1076.0')] ).
cnf(2089,plain,
equal(join(zero,composition(u,complement(composition(top,top)))),composition(join(top,u),complement(composition(top,top)))),
inference(spr,[status(thm),theory(equality)],[2000,13]),
[iquote('0:SpR:2000.0,13.0')] ).
cnf(2096,plain,
equal(composition(u,complement(composition(top,top))),zero),
inference(rew,[status(thm),theory(equality)],[1058,2089,2000,1941]),
[iquote('0:Rew:1058.0,2089.0,2000.0,2089.0,1941.0,2089.0')] ).
cnf(2187,plain,
equal(composition(converse(complement(composition(top,top))),u),converse(zero)),
inference(spr,[status(thm),theory(equality)],[2096,34]),
[iquote('0:SpR:2096.0,34.0')] ).
cnf(2191,plain,
equal(complement(composition(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[2096,600]),
[iquote('0:SpR:2096.0,600.0')] ).
cnf(2193,plain,
equal(composition(u,zero),zero),
inference(rew,[status(thm),theory(equality)],[2191,2096]),
[iquote('0:Rew:2191.0,2096.0')] ).
cnf(2199,plain,
equal(join(meet(zero,u),composition(meet(zero,composition(u,top)),composition(converse(zero),u))),composition(meet(zero,composition(u,top)),composition(converse(zero),u))),
inference(rew,[status(thm),theory(equality)],[2191,1983]),
[iquote('0:Rew:2191.0,1983.0')] ).
cnf(2289,plain,
equal(composition(converse(complement(composition(top,top))),u),zero),
inference(rew,[status(thm),theory(equality)],[1308,2187]),
[iquote('0:Rew:1308.0,2187.0')] ).
cnf(2290,plain,
equal(composition(converse(zero),u),zero),
inference(rew,[status(thm),theory(equality)],[2191,2289]),
[iquote('0:Rew:2191.0,2289.0')] ).
cnf(2291,plain,
equal(composition(zero,u),zero),
inference(rew,[status(thm),theory(equality)],[1308,2290]),
[iquote('0:Rew:1308.0,2290.0')] ).
cnf(2365,plain,
equal(join(meet(zero,u),composition(meet(zero,composition(u,top)),composition(zero,u))),composition(meet(zero,composition(u,top)),composition(zero,u))),
inference(rew,[status(thm),theory(equality)],[1308,2199]),
[iquote('0:Rew:1308.0,2199.0')] ).
cnf(2366,plain,
equal(join(meet(zero,u),zero),zero),
inference(rew,[status(thm),theory(equality)],[2193,2365,2291]),
[iquote('0:Rew:2193.0,2365.0,2291.0,2365.0')] ).
cnf(2367,plain,
equal(meet(zero,u),zero),
inference(rew,[status(thm),theory(equality)],[1058,2366,5]),
[iquote('0:Rew:1058.0,2366.0,5.0,2366.0')] ).
cnf(4611,plain,
equal(join(u,complement(meet(u,v))),top),
inference(spr,[status(thm),theory(equality)],[1146,1953]),
[iquote('0:SpR:1146.0,1953.0')] ).
cnf(11048,plain,
equal(complement(meet(u,meet(complement(u),v))),top),
inference(spr,[status(thm),theory(equality)],[1083,4611]),
[iquote('0:SpR:1083.0,4611.0')] ).
cnf(11081,plain,
equal(complement(meet(u,complement(v))),join(complement(u),v)),
inference(spr,[status(thm),theory(equality)],[1066,1083]),
[iquote('0:SpR:1066.0,1083.0')] ).
cnf(11084,plain,
equal(complement(meet(complement(u),v)),join(u,complement(v))),
inference(spr,[status(thm),theory(equality)],[1066,1083]),
[iquote('0:SpR:1066.0,1083.0')] ).
cnf(11131,plain,
equal(meet(u,meet(complement(u),v)),complement(top)),
inference(spr,[status(thm),theory(equality)],[11048,1066]),
[iquote('0:SpR:11048.0,1066.0')] ).
cnf(11210,plain,
equal(meet(u,meet(complement(u),v)),zero),
inference(rew,[status(thm),theory(equality)],[85,11131]),
[iquote('0:Rew:85.0,11131.0')] ).
cnf(11248,plain,
equal(join(zero,meet(u,complement(meet(complement(u),v)))),u),
inference(spr,[status(thm),theory(equality)],[11210,162]),
[iquote('0:SpR:11210.0,162.0')] ).
cnf(11287,plain,
equal(meet(complement(u),meet(u,v)),zero),
inference(spr,[status(thm),theory(equality)],[1066,11210]),
[iquote('0:SpR:1066.0,11210.0')] ).
cnf(11316,plain,
equal(meet(u,complement(meet(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[1058,11248]),
[iquote('0:Rew:1058.0,11248.0')] ).
cnf(11317,plain,
equal(meet(u,join(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[11084,11316]),
[iquote('0:Rew:11084.0,11316.0')] ).
cnf(11452,plain,
equal(meet(complement(u),meet(v,u)),zero),
inference(spr,[status(thm),theory(equality)],[86,11287]),
[iquote('0:SpR:86.0,11287.0')] ).
cnf(11947,plain,
equal(meet(u,join(u,v)),u),
inference(spr,[status(thm),theory(equality)],[1066,11317]),
[iquote('0:SpR:1066.0,11317.0')] ).
cnf(12037,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[5,11947]),
[iquote('0:SpR:5.0,11947.0')] ).
cnf(12189,plain,
equal(meet(complement(join(u,v)),v),zero),
inference(spr,[status(thm),theory(equality)],[12037,11452]),
[iquote('0:SpR:12037.0,11452.0')] ).
cnf(12324,plain,
equal(meet(u,complement(join(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[86,12189]),
[iquote('0:Rew:86.0,12189.0')] ).
cnf(13021,plain,
equal(meet(composition(skc3,converse(skc4)),complement(skc5)),zero),
inference(spr,[status(thm),theory(equality)],[19,12324]),
[iquote('0:SpR:19.0,12324.0')] ).
cnf(13131,plain,
equal(meet(complement(skc5),composition(skc3,converse(skc4))),zero),
inference(rew,[status(thm),theory(equality)],[86,13021]),
[iquote('0:Rew:86.0,13021.0')] ).
cnf(13243,plain,
equal(join(meet(composition(complement(skc5),skc4),skc3),meet(skc3,composition(zero,skc4))),meet(skc3,composition(zero,skc4))),
inference(spr,[status(thm),theory(equality)],[13131,88]),
[iquote('0:SpR:13131.0,88.0')] ).
cnf(13269,plain,
equal(meet(skc3,composition(complement(skc5),skc4)),zero),
inference(rew,[status(thm),theory(equality)],[1058,13243,5,86,2367,2291]),
[iquote('0:Rew:1058.0,13243.0,5.0,13243.0,86.0,13243.0,2367.0,13243.0,86.0,13243.0,2291.0,13243.0')] ).
cnf(13440,plain,
equal(join(zero,meet(skc3,complement(composition(complement(skc5),skc4)))),skc3),
inference(spr,[status(thm),theory(equality)],[13269,162]),
[iquote('0:SpR:13269.0,162.0')] ).
cnf(13475,plain,
equal(meet(skc3,complement(composition(complement(skc5),skc4))),skc3),
inference(rew,[status(thm),theory(equality)],[1058,13440]),
[iquote('0:Rew:1058.0,13440.0')] ).
cnf(49044,plain,
equal(join(complement(skc3),composition(complement(skc5),skc4)),complement(skc3)),
inference(spr,[status(thm),theory(equality)],[13475,11081]),
[iquote('0:SpR:13475.0,11081.0')] ).
cnf(49080,plain,
$false,
inference(mrr,[status(thm)],[49044,20]),
[iquote('0:MRR:49044.0,20.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : REL043+2 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.15 % Command : run_spass %d %s
% 0.15/0.37 % Computer : n018.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Fri Jul 8 12:42:40 EDT 2022
% 0.15/0.37 % CPUTime :
% 23.62/23.79
% 23.62/23.79 SPASS V 3.9
% 23.62/23.79 SPASS beiseite: Proof found.
% 23.62/23.79 % SZS status Theorem
% 23.62/23.79 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.62/23.79 SPASS derived 30105 clauses, backtracked 0 clauses, performed 0 splits and kept 5074 clauses.
% 23.62/23.79 SPASS allocated 142998 KBytes.
% 23.62/23.79 SPASS spent 0:0:23.36 on the problem.
% 23.62/23.79 0:00:00.03 for the input.
% 23.62/23.79 0:00:00.03 for the FLOTTER CNF translation.
% 23.62/23.79 0:00:00.26 for inferences.
% 23.62/23.79 0:00:00.00 for the backtracking.
% 23.62/23.79 0:0:22.97 for the reduction.
% 23.62/23.79
% 23.62/23.79
% 23.62/23.79 Here is a proof with depth 16, length 132 :
% 23.62/23.79 % SZS output start Refutation
% See solution above
% 24.35/24.56 Formulae used in the proof : composition_identity converse_idempotence def_top def_zero maddux1_join_commutativity goals maddux4_definiton_of_meet converse_additivity converse_multiplicativity maddux2_join_associativity composition_distributivity converse_cancellativity maddux3_a_kind_of_de_Morgan modular_law_2 dedekind_law
% 24.35/24.56
%------------------------------------------------------------------------------