TSTP Solution File: REL028+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL028+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 20:02:02 EDT 2022
% Result : Theorem 15.98s 16.16s
% Output : Refutation 16.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 19
% Syntax : Number of clauses : 220 ( 220 unt; 0 nHn; 220 RR)
% Number of literals : 220 ( 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 : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(join(skc3,one),one),
file('REL028+2.p',unknown),
[] ).
cnf(2,axiom,
equal(join(skc2,one),one),
file('REL028+2.p',unknown),
[] ).
cnf(3,axiom,
equal(composition(u,one),u),
file('REL028+2.p',unknown),
[] ).
cnf(4,axiom,
equal(converse(converse(u)),u),
file('REL028+2.p',unknown),
[] ).
cnf(5,axiom,
equal(join(u,complement(u)),top),
file('REL028+2.p',unknown),
[] ).
cnf(6,axiom,
equal(meet(u,complement(u)),zero),
file('REL028+2.p',unknown),
[] ).
cnf(7,axiom,
equal(join(u,v),join(v,u)),
file('REL028+2.p',unknown),
[] ).
cnf(8,axiom,
~ equal(meet(skc3,skc2),composition(skc3,skc2)),
file('REL028+2.p',unknown),
[] ).
cnf(9,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL028+2.p',unknown),
[] ).
cnf(10,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL028+2.p',unknown),
[] ).
cnf(11,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL028+2.p',unknown),
[] ).
cnf(12,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL028+2.p',unknown),
[] ).
cnf(13,axiom,
equal(composition(composition(u,v),w),composition(u,composition(v,w))),
file('REL028+2.p',unknown),
[] ).
cnf(14,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL028+2.p',unknown),
[] ).
cnf(15,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL028+2.p',unknown),
[] ).
cnf(16,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL028+2.p',unknown),
[] ).
cnf(17,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('REL028+2.p',unknown),
[] ).
cnf(18,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('REL028+2.p',unknown),
[] ).
cnf(19,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('REL028+2.p',unknown),
[] ).
cnf(20,plain,
equal(join(one,skc3),one),
inference(rew,[status(thm),theory(equality)],[7,1]),
[iquote('0:Rew:7.0,1.0')] ).
cnf(21,plain,
equal(join(one,skc2),one),
inference(rew,[status(thm),theory(equality)],[7,2]),
[iquote('0:Rew:7.0,2.0')] ).
cnf(22,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[7,15]),
[iquote('0:Rew:7.0,15.0')] ).
cnf(23,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[9,16]),
[iquote('0:Rew:9.0,16.0')] ).
cnf(36,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[4,11]),
[iquote('0:SpR:4.0,11.0')] ).
cnf(42,plain,
equal(converse(join(converse(u),v)),join(u,converse(v))),
inference(spr,[status(thm),theory(equality)],[4,10]),
[iquote('0:SpR:4.0,10.0')] ).
cnf(80,plain,
equal(join(join(complement(u),complement(v)),meet(u,v)),top),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(84,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[5,9]),
[iquote('0:SpR:5.0,9.0')] ).
cnf(85,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[7,9]),
[iquote('0:SpR:7.0,9.0')] ).
cnf(87,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[6,84]),
[iquote('0:Rew:6.0,84.0')] ).
cnf(88,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[9,85]),
[iquote('0:Rew:9.0,85.0')] ).
cnf(89,plain,
~ equal(meet(skc2,skc3),composition(skc3,skc2)),
inference(rew,[status(thm),theory(equality)],[88,8]),
[iquote('0:Rew:88.0,8.0')] ).
cnf(90,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)],[88,18]),
[iquote('0:Rew:88.0,18.0')] ).
cnf(91,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)],[88,17]),
[iquote('0:Rew:88.0,17.0')] ).
cnf(94,plain,
equal(join(meet(u,v),join(complement(u),complement(v))),top),
inference(rew,[status(thm),theory(equality)],[7,80]),
[iquote('0:Rew:7.0,80.0')] ).
cnf(99,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[87,9]),
[iquote('0:SpR:87.0,9.0')] ).
cnf(112,plain,
equal(complement(join(meet(top,u),complement(v))),meet(join(zero,complement(u)),v)),
inference(spr,[status(thm),theory(equality)],[99,9]),
[iquote('0:SpR:99.0,9.0')] ).
cnf(114,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,join(zero,complement(v)))),
inference(spr,[status(thm),theory(equality)],[99,9]),
[iquote('0:SpR:99.0,9.0')] ).
cnf(141,plain,
equal(join(meet(top,u),complement(join(zero,u))),top),
inference(spr,[status(thm),theory(equality)],[87,23]),
[iquote('0:SpR:87.0,23.0')] ).
cnf(142,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[5,23]),
[iquote('0:SpR:5.0,23.0')] ).
cnf(143,plain,
equal(join(meet(u,v),complement(join(v,complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[7,23]),
[iquote('0:SpR:7.0,23.0')] ).
cnf(145,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[9,23]),
[iquote('0:SpR:9.0,23.0')] ).
cnf(146,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[6,23]),
[iquote('0:SpR:6.0,23.0')] ).
cnf(155,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[7,142,87]),
[iquote('0:Rew:7.0,142.0,87.0,142.0')] ).
cnf(156,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[7,145]),
[iquote('0:Rew:7.0,145.0')] ).
cnf(157,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[9,146]),
[iquote('0:Rew:9.0,146.0')] ).
cnf(210,plain,
equal(join(u,join(v,complement(join(u,v)))),top),
inference(spr,[status(thm),theory(equality)],[12,5]),
[iquote('0:SpR:12.0,5.0')] ).
cnf(211,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[12,7]),
[iquote('0:SpR:12.0,7.0')] ).
cnf(217,plain,
equal(join(one,join(skc3,u)),join(one,u)),
inference(spr,[status(thm),theory(equality)],[20,12]),
[iquote('0:SpR:20.0,12.0')] ).
cnf(218,plain,
equal(join(one,join(skc2,u)),join(one,u)),
inference(spr,[status(thm),theory(equality)],[21,12]),
[iquote('0:SpR:21.0,12.0')] ).
cnf(219,plain,
equal(join(u,join(complement(u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[5,12]),
[iquote('0:SpR:5.0,12.0')] ).
cnf(223,plain,
equal(join(meet(u,v),join(complement(join(complement(u),v)),w)),join(u,w)),
inference(spr,[status(thm),theory(equality)],[23,12]),
[iquote('0:SpR:23.0,12.0')] ).
cnf(230,plain,
equal(join(complement(u),join(meet(v,u),complement(v))),top),
inference(rew,[status(thm),theory(equality)],[211,94]),
[iquote('0:Rew:211.0,94.0')] ).
cnf(236,plain,
equal(join(complement(u),join(complement(v),meet(v,u))),top),
inference(rew,[status(thm),theory(equality)],[7,230]),
[iquote('0:Rew:7.0,230.0')] ).
cnf(269,plain,
equal(join(zero,composition(converse(u),complement(composition(u,top)))),zero),
inference(spr,[status(thm),theory(equality)],[87,22]),
[iquote('0:SpR:87.0,22.0')] ).
cnf(472,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)],[4,91]),
[iquote('0:SpR:4.0,91.0')] ).
cnf(479,plain,
equal(join(meet(composition(u,one),v),meet(v,meet(u,composition(v,converse(one))))),meet(v,meet(u,composition(v,converse(one))))),
inference(spr,[status(thm),theory(equality)],[3,91]),
[iquote('0:SpR:3.0,91.0')] ).
cnf(488,plain,
equal(join(meet(u,v),meet(v,meet(u,composition(v,converse(one))))),meet(v,meet(u,composition(v,converse(one))))),
inference(rew,[status(thm),theory(equality)],[3,479]),
[iquote('0:Rew:3.0,479.0')] ).
cnf(579,plain,
equal(join(meet(composition(u,v),one),composition(meet(u,composition(one,converse(v))),meet(v,converse(u)))),composition(meet(u,composition(one,converse(v))),meet(v,converse(u)))),
inference(spr,[status(thm),theory(equality)],[3,19]),
[iquote('0:SpR:3.0,19.0')] ).
cnf(591,plain,
equal(join(meet(u,v),composition(meet(u,composition(v,converse(one))),meet(one,composition(converse(u),v)))),composition(meet(u,composition(v,converse(one))),meet(one,composition(converse(u),v)))),
inference(spr,[status(thm),theory(equality)],[3,19]),
[iquote('0:SpR:3.0,19.0')] ).
cnf(598,plain,
equal(join(meet(one,composition(u,v)),composition(meet(u,composition(one,converse(v))),meet(v,converse(u)))),composition(meet(u,composition(one,converse(v))),meet(v,converse(u)))),
inference(rew,[status(thm),theory(equality)],[88,579]),
[iquote('0:Rew:88.0,579.0')] ).
cnf(639,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[3,36]),
[iquote('0:SpR:3.0,36.0')] ).
cnf(642,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[4,639]),
[iquote('0:Rew:4.0,639.0')] ).
cnf(653,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[642,3]),
[iquote('0:SpR:642.0,3.0')] ).
cnf(656,plain,
equal(join(u,composition(v,u)),composition(join(converse(one),v),u)),
inference(spr,[status(thm),theory(equality)],[642,14]),
[iquote('0:SpR:642.0,14.0')] ).
cnf(665,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[642,22]),
[iquote('0:SpR:642.0,22.0')] ).
cnf(671,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[653,642]),
[iquote('0:Rew:653.0,642.0')] ).
cnf(672,plain,
equal(join(meet(u,v),meet(v,meet(u,composition(v,one)))),meet(v,meet(u,composition(v,one)))),
inference(rew,[status(thm),theory(equality)],[653,488]),
[iquote('0:Rew:653.0,488.0')] ).
cnf(673,plain,
equal(join(meet(u,v),composition(meet(u,composition(v,one)),meet(one,composition(converse(u),v)))),composition(meet(u,composition(v,one)),meet(one,composition(converse(u),v)))),
inference(rew,[status(thm),theory(equality)],[653,591]),
[iquote('0:Rew:653.0,591.0')] ).
cnf(676,plain,
equal(join(meet(one,composition(u,v)),composition(meet(u,converse(v)),meet(v,converse(u)))),composition(meet(u,converse(v)),meet(v,converse(u)))),
inference(rew,[status(thm),theory(equality)],[671,598]),
[iquote('0:Rew:671.0,598.0')] ).
cnf(686,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[671,665]),
[iquote('0:Rew:671.0,665.0')] ).
cnf(687,plain,
equal(join(u,composition(v,u)),composition(join(one,v),u)),
inference(rew,[status(thm),theory(equality)],[653,656]),
[iquote('0:Rew:653.0,656.0')] ).
cnf(692,plain,
equal(join(meet(u,v),meet(v,meet(u,v))),meet(v,meet(u,v))),
inference(rew,[status(thm),theory(equality)],[3,672]),
[iquote('0:Rew:3.0,672.0')] ).
cnf(702,plain,
equal(join(meet(u,v),composition(meet(u,v),meet(one,composition(converse(u),v)))),composition(meet(u,v),meet(one,composition(converse(u),v)))),
inference(rew,[status(thm),theory(equality)],[3,673]),
[iquote('0:Rew:3.0,673.0')] ).
cnf(744,plain,
equal(join(one,converse(u)),converse(join(one,u))),
inference(spr,[status(thm),theory(equality)],[653,10]),
[iquote('0:SpR:653.0,10.0')] ).
cnf(796,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[686,9]),
[iquote('0:SpR:686.0,9.0')] ).
cnf(802,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[87,686]),
[iquote('0:SpR:87.0,686.0')] ).
cnf(824,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[796,157]),
[iquote('0:Rew:796.0,157.0')] ).
cnf(859,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[802,12]),
[iquote('0:SpR:802.0,12.0')] ).
cnf(876,plain,
equal(meet(top,complement(u)),complement(u)),
inference(spr,[status(thm),theory(equality)],[824,99]),
[iquote('0:SpR:824.0,99.0')] ).
cnf(883,plain,
equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[9,824]),
[iquote('0:SpR:9.0,824.0')] ).
cnf(917,plain,
equal(join(complement(u),complement(join(zero,complement(u)))),top),
inference(spr,[status(thm),theory(equality)],[876,141]),
[iquote('0:SpR:876.0,141.0')] ).
cnf(925,plain,
equal(join(complement(u),meet(top,u)),top),
inference(rew,[status(thm),theory(equality)],[99,917]),
[iquote('0:Rew:99.0,917.0')] ).
cnf(966,plain,
equal(join(complement(u),join(meet(top,u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[925,12]),
[iquote('0:SpR:925.0,12.0')] ).
cnf(1108,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[155,859]),
[iquote('0:SpR:155.0,859.0')] ).
cnf(1115,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[1108,824]),
[iquote('0:Rew:1108.0,824.0')] ).
cnf(1117,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[1108,99]),
[iquote('0:Rew:1108.0,99.0')] ).
cnf(1127,plain,
equal(composition(converse(u),complement(composition(u,top))),zero),
inference(rew,[status(thm),theory(equality)],[1108,269]),
[iquote('0:Rew:1108.0,269.0')] ).
cnf(1133,plain,
equal(join(complement(u),complement(v)),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[1108,883]),
[iquote('0:Rew:1108.0,883.0')] ).
cnf(1135,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[1108,114]),
[iquote('0:Rew:1108.0,114.0')] ).
cnf(1136,plain,
equal(complement(join(meet(top,u),complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[1108,112]),
[iquote('0:Rew:1108.0,112.0')] ).
cnf(1139,plain,
equal(meet(u,u),u),
inference(rew,[status(thm),theory(equality)],[1115,796]),
[iquote('0:Rew:1115.0,796.0')] ).
cnf(1153,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[1115,1117]),
[iquote('0:Rew:1115.0,1117.0')] ).
cnf(1157,plain,
equal(join(complement(u),join(u,v)),join(top,v)),
inference(rew,[status(thm),theory(equality)],[1153,966]),
[iquote('0:Rew:1153.0,966.0')] ).
cnf(1182,plain,
equal(join(u,join(v,complement(u))),join(top,v)),
inference(rew,[status(thm),theory(equality)],[211,1157]),
[iquote('0:Rew:211.0,1157.0')] ).
cnf(1193,plain,
equal(complement(join(complement(u),v)),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[1153,1135]),
[iquote('0:Rew:1153.0,1135.0')] ).
cnf(1196,plain,
equal(join(meet(u,v),join(meet(u,complement(v)),w)),join(u,w)),
inference(rew,[status(thm),theory(equality)],[1193,223]),
[iquote('0:Rew:1193.0,223.0')] ).
cnf(1197,plain,
equal(complement(join(u,complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[1153,1136]),
[iquote('0:Rew:1153.0,1136.0')] ).
cnf(1198,plain,
equal(join(meet(u,v),meet(complement(v),u)),u),
inference(rew,[status(thm),theory(equality)],[1197,143]),
[iquote('0:Rew:1197.0,143.0')] ).
cnf(1227,plain,
equal(complement(zero),top),
inference(spr,[status(thm),theory(equality)],[87,1115]),
[iquote('0:SpR:87.0,1115.0')] ).
cnf(1308,plain,
equal(join(u,converse(complement(converse(u)))),converse(top)),
inference(spr,[status(thm),theory(equality)],[5,42]),
[iquote('0:SpR:5.0,42.0')] ).
cnf(1595,plain,
equal(join(top,converse(complement(converse(complement(u))))),join(u,converse(top))),
inference(spr,[status(thm),theory(equality)],[1308,219]),
[iquote('0:SpR:1308.0,219.0')] ).
cnf(1972,plain,
equal(join(complement(u),join(complement(u),u)),top),
inference(spr,[status(thm),theory(equality)],[1139,236]),
[iquote('0:SpR:1139.0,236.0')] ).
cnf(1984,plain,
equal(join(top,complement(u)),top),
inference(rew,[status(thm),theory(equality)],[7,1972,5]),
[iquote('0:Rew:7.0,1972.0,5.0,1972.0,7.0,1972.0')] ).
cnf(1995,plain,
equal(join(u,top),top),
inference(spr,[status(thm),theory(equality)],[1984,210]),
[iquote('0:SpR:1984.0,210.0')] ).
cnf(1998,plain,
equal(join(top,u),top),
inference(spr,[status(thm),theory(equality)],[1115,1984]),
[iquote('0:SpR:1115.0,1984.0')] ).
cnf(2015,plain,
equal(join(u,converse(top)),top),
inference(rew,[status(thm),theory(equality)],[1998,1595]),
[iquote('0:Rew:1998.0,1595.0')] ).
cnf(2020,plain,
equal(join(u,join(v,complement(u))),top),
inference(rew,[status(thm),theory(equality)],[1998,1182]),
[iquote('0:Rew:1998.0,1182.0')] ).
cnf(2034,plain,
equal(join(u,converse(top)),converse(top)),
inference(spr,[status(thm),theory(equality)],[1995,42]),
[iquote('0:SpR:1995.0,42.0')] ).
cnf(2041,plain,
equal(converse(top),top),
inference(rew,[status(thm),theory(equality)],[2015,2034]),
[iquote('0:Rew:2015.0,2034.0')] ).
cnf(2067,plain,
equal(composition(top,complement(composition(top,top))),zero),
inference(spr,[status(thm),theory(equality)],[2041,1127]),
[iquote('0:SpR:2041.0,1127.0')] ).
cnf(2074,plain,
equal(join(complement(u),composition(top,complement(composition(top,u)))),complement(u)),
inference(spr,[status(thm),theory(equality)],[2041,22]),
[iquote('0:SpR:2041.0,22.0')] ).
cnf(2505,plain,
equal(join(zero,composition(u,complement(composition(top,top)))),composition(join(top,u),complement(composition(top,top)))),
inference(spr,[status(thm),theory(equality)],[2067,14]),
[iquote('0:SpR:2067.0,14.0')] ).
cnf(2512,plain,
equal(composition(u,complement(composition(top,top))),zero),
inference(rew,[status(thm),theory(equality)],[1108,2505,2067,1998]),
[iquote('0:Rew:1108.0,2505.0,2067.0,2505.0,1998.0,2505.0')] ).
cnf(2868,plain,
equal(complement(composition(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[2512,671]),
[iquote('0:SpR:2512.0,671.0')] ).
cnf(3370,plain,
equal(composition(top,top),complement(zero)),
inference(spr,[status(thm),theory(equality)],[2868,1115]),
[iquote('0:SpR:2868.0,1115.0')] ).
cnf(3381,plain,
equal(composition(top,top),top),
inference(rew,[status(thm),theory(equality)],[1227,3370]),
[iquote('0:Rew:1227.0,3370.0')] ).
cnf(3402,plain,
equal(composition(top,composition(top,u)),composition(top,u)),
inference(spr,[status(thm),theory(equality)],[3381,13]),
[iquote('0:SpR:3381.0,13.0')] ).
cnf(3404,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)],[3381,90]),
[iquote('0:SpR:3381.0,90.0')] ).
cnf(3416,plain,
equal(join(u,meet(u,composition(top,composition(top,u)))),meet(u,composition(top,composition(top,u)))),
inference(rew,[status(thm),theory(equality)],[1153,3404,2041]),
[iquote('0:Rew:1153.0,3404.0,1153.0,3404.0,2041.0,3404.0')] ).
cnf(3417,plain,
equal(join(u,meet(u,composition(top,u))),meet(u,composition(top,u))),
inference(rew,[status(thm),theory(equality)],[3402,3416]),
[iquote('0:Rew:3402.0,3416.0')] ).
cnf(4203,plain,
equal(join(complement(composition(top,u)),composition(converse(top),complement(composition(top,u)))),complement(composition(top,u))),
inference(spr,[status(thm),theory(equality)],[3402,22]),
[iquote('0:SpR:3402.0,22.0')] ).
cnf(4221,plain,
equal(join(complement(composition(top,u)),composition(top,complement(composition(top,u)))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[2041,4203]),
[iquote('0:Rew:2041.0,4203.0')] ).
cnf(4222,plain,
equal(composition(join(one,top),complement(composition(top,u))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[687,4221]),
[iquote('0:Rew:687.0,4221.0')] ).
cnf(4223,plain,
equal(composition(top,complement(composition(top,u))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[1995,4222]),
[iquote('0:Rew:1995.0,4222.0')] ).
cnf(4224,plain,
equal(join(complement(u),complement(composition(top,u))),complement(u)),
inference(rew,[status(thm),theory(equality)],[4223,2074]),
[iquote('0:Rew:4223.0,2074.0')] ).
cnf(4226,plain,
equal(complement(meet(u,composition(top,u))),complement(u)),
inference(rew,[status(thm),theory(equality)],[1133,4224]),
[iquote('0:Rew:1133.0,4224.0')] ).
cnf(4244,plain,
equal(join(u,complement(meet(u,v))),top),
inference(spr,[status(thm),theory(equality)],[1196,2020]),
[iquote('0:SpR:1196.0,2020.0')] ).
cnf(4276,plain,
equal(join(u,meet(complement(complement(v)),u)),join(meet(u,v),u)),
inference(spr,[status(thm),theory(equality)],[1198,1196]),
[iquote('0:SpR:1198.0,1196.0')] ).
cnf(4301,plain,
equal(join(u,meet(v,u)),join(u,meet(u,v))),
inference(rew,[status(thm),theory(equality)],[1115,4276,7]),
[iquote('0:Rew:1115.0,4276.0,7.0,4276.0')] ).
cnf(4625,plain,
equal(meet(u,composition(top,u)),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[4226,1115]),
[iquote('0:SpR:4226.0,1115.0')] ).
cnf(4654,plain,
equal(meet(u,composition(top,u)),u),
inference(rew,[status(thm),theory(equality)],[1115,4625]),
[iquote('0:Rew:1115.0,4625.0')] ).
cnf(4656,plain,
equal(join(u,u),u),
inference(rew,[status(thm),theory(equality)],[4654,3417]),
[iquote('0:Rew:4654.0,3417.0')] ).
cnf(4809,plain,
equal(join(meet(u,v),meet(u,complement(v))),join(u,meet(u,complement(v)))),
inference(spr,[status(thm),theory(equality)],[4656,1196]),
[iquote('0:SpR:4656.0,1196.0')] ).
cnf(4830,plain,
equal(join(u,meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[156,4809]),
[iquote('0:Rew:156.0,4809.0')] ).
cnf(5093,plain,
equal(join(u,meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[1115,4830]),
[iquote('0:SpR:1115.0,4830.0')] ).
cnf(5106,plain,
equal(join(u,meet(v,u)),u),
inference(rew,[status(thm),theory(equality)],[5093,4301]),
[iquote('0:Rew:5093.0,4301.0')] ).
cnf(5109,plain,
equal(meet(u,meet(v,u)),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[5106,692]),
[iquote('0:Rew:5106.0,692.0')] ).
cnf(5201,plain,
equal(join(u,converse(meet(converse(u),v))),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[5093,42]),
[iquote('0:SpR:5093.0,42.0')] ).
cnf(5206,plain,
equal(join(one,meet(skc3,u)),join(one,skc3)),
inference(spr,[status(thm),theory(equality)],[5093,217]),
[iquote('0:SpR:5093.0,217.0')] ).
cnf(5226,plain,
equal(join(one,meet(skc3,u)),one),
inference(rew,[status(thm),theory(equality)],[20,5206]),
[iquote('0:Rew:20.0,5206.0')] ).
cnf(5231,plain,
equal(join(u,converse(meet(converse(u),v))),u),
inference(rew,[status(thm),theory(equality)],[4,5201]),
[iquote('0:Rew:4.0,5201.0')] ).
cnf(5243,plain,
equal(join(one,meet(u,skc3)),one),
inference(spr,[status(thm),theory(equality)],[88,5226]),
[iquote('0:SpR:88.0,5226.0')] ).
cnf(5961,plain,
equal(join(one,converse(meet(converse(skc3),u))),join(one,skc3)),
inference(spr,[status(thm),theory(equality)],[5231,217]),
[iquote('0:SpR:5231.0,217.0')] ).
cnf(5962,plain,
equal(join(one,converse(meet(converse(skc2),u))),join(one,skc2)),
inference(spr,[status(thm),theory(equality)],[5231,218]),
[iquote('0:SpR:5231.0,218.0')] ).
cnf(6002,plain,
equal(converse(join(one,meet(converse(skc3),u))),one),
inference(rew,[status(thm),theory(equality)],[744,5961,20]),
[iquote('0:Rew:744.0,5961.0,20.0,5961.0')] ).
cnf(6003,plain,
equal(converse(join(one,meet(converse(skc2),u))),one),
inference(rew,[status(thm),theory(equality)],[744,5962,21]),
[iquote('0:Rew:744.0,5962.0,21.0,5962.0')] ).
cnf(6021,plain,
equal(join(one,meet(converse(skc3),u)),converse(one)),
inference(spr,[status(thm),theory(equality)],[6002,4]),
[iquote('0:SpR:6002.0,4.0')] ).
cnf(6068,plain,
equal(join(one,meet(converse(skc3),u)),one),
inference(rew,[status(thm),theory(equality)],[653,6021]),
[iquote('0:Rew:653.0,6021.0')] ).
cnf(6302,plain,
equal(join(one,meet(converse(skc2),u)),converse(one)),
inference(spr,[status(thm),theory(equality)],[6003,4]),
[iquote('0:SpR:6003.0,4.0')] ).
cnf(6350,plain,
equal(join(one,meet(converse(skc2),u)),one),
inference(rew,[status(thm),theory(equality)],[653,6302]),
[iquote('0:Rew:653.0,6302.0')] ).
cnf(17629,plain,
equal(complement(meet(u,meet(complement(u),v))),top),
inference(spr,[status(thm),theory(equality)],[1133,4244]),
[iquote('0:SpR:1133.0,4244.0')] ).
cnf(17683,plain,
equal(complement(meet(complement(u),v)),join(u,complement(v))),
inference(spr,[status(thm),theory(equality)],[1115,1133]),
[iquote('0:SpR:1115.0,1133.0')] ).
cnf(17731,plain,
equal(meet(u,meet(complement(u),v)),complement(top)),
inference(spr,[status(thm),theory(equality)],[17629,1115]),
[iquote('0:SpR:17629.0,1115.0')] ).
cnf(17805,plain,
equal(meet(u,meet(complement(u),v)),zero),
inference(rew,[status(thm),theory(equality)],[87,17731]),
[iquote('0:Rew:87.0,17731.0')] ).
cnf(17834,plain,
equal(join(zero,meet(u,complement(meet(complement(u),v)))),u),
inference(spr,[status(thm),theory(equality)],[17805,156]),
[iquote('0:SpR:17805.0,156.0')] ).
cnf(17888,plain,
equal(meet(complement(u),meet(u,v)),zero),
inference(spr,[status(thm),theory(equality)],[1115,17805]),
[iquote('0:SpR:1115.0,17805.0')] ).
cnf(17924,plain,
equal(meet(u,complement(meet(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[1108,17834]),
[iquote('0:Rew:1108.0,17834.0')] ).
cnf(17925,plain,
equal(meet(u,join(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[17683,17924]),
[iquote('0:Rew:17683.0,17924.0')] ).
cnf(17951,plain,
equal(meet(complement(u),meet(v,u)),zero),
inference(spr,[status(thm),theory(equality)],[88,17888]),
[iquote('0:SpR:88.0,17888.0')] ).
cnf(18390,plain,
equal(meet(u,join(u,v)),u),
inference(spr,[status(thm),theory(equality)],[1115,17925]),
[iquote('0:SpR:1115.0,17925.0')] ).
cnf(18575,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[7,18390]),
[iquote('0:SpR:7.0,18390.0')] ).
cnf(19209,plain,
equal(meet(complement(join(u,v)),v),zero),
inference(spr,[status(thm),theory(equality)],[18575,17951]),
[iquote('0:SpR:18575.0,17951.0')] ).
cnf(19250,plain,
equal(meet(skc3,one),skc3),
inference(spr,[status(thm),theory(equality)],[20,18575]),
[iquote('0:SpR:20.0,18575.0')] ).
cnf(19251,plain,
equal(meet(skc2,one),skc2),
inference(spr,[status(thm),theory(equality)],[21,18575]),
[iquote('0:SpR:21.0,18575.0')] ).
cnf(19322,plain,
equal(meet(meet(u,skc3),one),meet(u,skc3)),
inference(spr,[status(thm),theory(equality)],[5243,18575]),
[iquote('0:SpR:5243.0,18575.0')] ).
cnf(19442,plain,
equal(meet(one,skc3),skc3),
inference(rew,[status(thm),theory(equality)],[88,19250]),
[iquote('0:Rew:88.0,19250.0')] ).
cnf(19443,plain,
equal(meet(one,skc2),skc2),
inference(rew,[status(thm),theory(equality)],[88,19251]),
[iquote('0:Rew:88.0,19251.0')] ).
cnf(19450,plain,
equal(meet(u,complement(join(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[88,19209]),
[iquote('0:Rew:88.0,19209.0')] ).
cnf(19456,plain,
equal(meet(one,meet(u,skc3)),meet(u,skc3)),
inference(rew,[status(thm),theory(equality)],[88,19322]),
[iquote('0:Rew:88.0,19322.0')] ).
cnf(19519,plain,
equal(join(skc2,composition(skc2,meet(one,composition(converse(one),skc2)))),composition(skc2,meet(one,composition(converse(one),skc2)))),
inference(spr,[status(thm),theory(equality)],[19443,702]),
[iquote('0:SpR:19443.0,702.0')] ).
cnf(19538,plain,
equal(join(skc2,composition(skc2,skc2)),composition(skc2,skc2)),
inference(rew,[status(thm),theory(equality)],[19443,19519,671,653]),
[iquote('0:Rew:19443.0,19519.0,671.0,19519.0,653.0,19519.0')] ).
cnf(19539,plain,
equal(composition(join(one,skc2),skc2),composition(skc2,skc2)),
inference(rew,[status(thm),theory(equality)],[687,19538]),
[iquote('0:Rew:687.0,19538.0')] ).
cnf(19540,plain,
equal(composition(skc2,skc2),skc2),
inference(rew,[status(thm),theory(equality)],[671,19539,21]),
[iquote('0:Rew:671.0,19539.0,21.0,19539.0')] ).
cnf(21479,plain,
equal(meet(meet(converse(skc3),u),complement(one)),zero),
inference(spr,[status(thm),theory(equality)],[6068,19450]),
[iquote('0:SpR:6068.0,19450.0')] ).
cnf(21480,plain,
equal(meet(meet(converse(skc2),u),complement(one)),zero),
inference(spr,[status(thm),theory(equality)],[6350,19450]),
[iquote('0:SpR:6350.0,19450.0')] ).
cnf(21650,plain,
equal(meet(complement(one),meet(converse(skc3),u)),zero),
inference(rew,[status(thm),theory(equality)],[88,21479]),
[iquote('0:Rew:88.0,21479.0')] ).
cnf(21651,plain,
equal(meet(complement(one),meet(converse(skc2),u)),zero),
inference(rew,[status(thm),theory(equality)],[88,21480]),
[iquote('0:Rew:88.0,21480.0')] ).
cnf(22717,plain,
equal(meet(converse(skc3),complement(one)),zero),
inference(spr,[status(thm),theory(equality)],[21650,5109]),
[iquote('0:SpR:21650.0,5109.0')] ).
cnf(22753,plain,
equal(meet(complement(one),converse(skc3)),zero),
inference(rew,[status(thm),theory(equality)],[88,22717]),
[iquote('0:Rew:88.0,22717.0')] ).
cnf(22840,plain,
equal(join(meet(converse(skc3),one),zero),converse(skc3)),
inference(spr,[status(thm),theory(equality)],[22753,1198]),
[iquote('0:SpR:22753.0,1198.0')] ).
cnf(22854,plain,
equal(meet(one,converse(skc3)),converse(skc3)),
inference(rew,[status(thm),theory(equality)],[1108,22840,7,88]),
[iquote('0:Rew:1108.0,22840.0,7.0,22840.0,88.0,22840.0')] ).
cnf(22882,plain,
equal(join(meet(one,composition(one,skc3)),composition(converse(skc3),meet(skc3,converse(one)))),composition(converse(skc3),meet(skc3,converse(one)))),
inference(spr,[status(thm),theory(equality)],[22854,676]),
[iquote('0:SpR:22854.0,676.0')] ).
cnf(22902,plain,
equal(join(skc3,composition(converse(skc3),skc3)),composition(converse(skc3),skc3)),
inference(rew,[status(thm),theory(equality)],[19442,22882,671,88,653]),
[iquote('0:Rew:19442.0,22882.0,671.0,22882.0,19442.0,22882.0,88.0,22882.0,653.0,22882.0')] ).
cnf(22903,plain,
equal(composition(join(one,converse(skc3)),skc3),composition(converse(skc3),skc3)),
inference(rew,[status(thm),theory(equality)],[687,22902]),
[iquote('0:Rew:687.0,22902.0')] ).
cnf(22904,plain,
equal(composition(converse(skc3),skc3),skc3),
inference(rew,[status(thm),theory(equality)],[671,22903,653,20,744]),
[iquote('0:Rew:671.0,22903.0,653.0,22903.0,20.0,22903.0,744.0,22903.0')] ).
cnf(22958,plain,
equal(composition(converse(skc3),skc3),converse(skc3)),
inference(spr,[status(thm),theory(equality)],[22904,36]),
[iquote('0:SpR:22904.0,36.0')] ).
cnf(22971,plain,
equal(converse(skc3),skc3),
inference(rew,[status(thm),theory(equality)],[22904,22958]),
[iquote('0:Rew:22904.0,22958.0')] ).
cnf(23151,plain,
equal(composition(skc3,converse(u)),converse(composition(u,skc3))),
inference(spr,[status(thm),theory(equality)],[22971,11]),
[iquote('0:SpR:22971.0,11.0')] ).
cnf(23152,plain,
equal(join(skc3,converse(u)),converse(join(skc3,u))),
inference(spr,[status(thm),theory(equality)],[22971,10]),
[iquote('0:SpR:22971.0,10.0')] ).
cnf(24198,plain,
equal(meet(converse(skc2),complement(one)),zero),
inference(spr,[status(thm),theory(equality)],[21651,5109]),
[iquote('0:SpR:21651.0,5109.0')] ).
cnf(24235,plain,
equal(meet(complement(one),converse(skc2)),zero),
inference(rew,[status(thm),theory(equality)],[88,24198]),
[iquote('0:Rew:88.0,24198.0')] ).
cnf(25355,plain,
equal(join(meet(converse(skc2),one),zero),converse(skc2)),
inference(spr,[status(thm),theory(equality)],[24235,1198]),
[iquote('0:SpR:24235.0,1198.0')] ).
cnf(25370,plain,
equal(meet(one,converse(skc2)),converse(skc2)),
inference(rew,[status(thm),theory(equality)],[1108,25355,7,88]),
[iquote('0:Rew:1108.0,25355.0,7.0,25355.0,88.0,25355.0')] ).
cnf(25399,plain,
equal(join(meet(one,composition(one,skc2)),composition(converse(skc2),meet(skc2,converse(one)))),composition(converse(skc2),meet(skc2,converse(one)))),
inference(spr,[status(thm),theory(equality)],[25370,676]),
[iquote('0:SpR:25370.0,676.0')] ).
cnf(25419,plain,
equal(join(skc2,composition(converse(skc2),skc2)),composition(converse(skc2),skc2)),
inference(rew,[status(thm),theory(equality)],[19443,25399,671,88,653]),
[iquote('0:Rew:19443.0,25399.0,671.0,25399.0,19443.0,25399.0,88.0,25399.0,653.0,25399.0')] ).
cnf(25420,plain,
equal(composition(join(one,converse(skc2)),skc2),composition(converse(skc2),skc2)),
inference(rew,[status(thm),theory(equality)],[687,25419]),
[iquote('0:Rew:687.0,25419.0')] ).
cnf(25421,plain,
equal(composition(converse(skc2),skc2),skc2),
inference(rew,[status(thm),theory(equality)],[671,25420,653,21,744]),
[iquote('0:Rew:671.0,25420.0,653.0,25420.0,21.0,25420.0,744.0,25420.0')] ).
cnf(25475,plain,
equal(composition(converse(skc2),skc2),converse(skc2)),
inference(spr,[status(thm),theory(equality)],[25421,36]),
[iquote('0:SpR:25421.0,36.0')] ).
cnf(25488,plain,
equal(converse(skc2),skc2),
inference(rew,[status(thm),theory(equality)],[25421,25475]),
[iquote('0:Rew:25421.0,25475.0')] ).
cnf(30804,plain,
equal(join(meet(u,skc3),composition(meet(u,skc3),meet(one,composition(converse(one),meet(u,skc3))))),composition(meet(u,skc3),meet(one,composition(converse(one),meet(u,skc3))))),
inference(spr,[status(thm),theory(equality)],[19456,702]),
[iquote('0:SpR:19456.0,702.0')] ).
cnf(30829,plain,
equal(join(meet(u,skc3),composition(meet(u,skc3),meet(u,skc3))),composition(meet(u,skc3),meet(u,skc3))),
inference(rew,[status(thm),theory(equality)],[19456,30804,671,653]),
[iquote('0:Rew:19456.0,30804.0,671.0,30804.0,653.0,30804.0')] ).
cnf(30830,plain,
equal(composition(join(one,meet(u,skc3)),meet(u,skc3)),composition(meet(u,skc3),meet(u,skc3))),
inference(rew,[status(thm),theory(equality)],[687,30829]),
[iquote('0:Rew:687.0,30829.0')] ).
cnf(30831,plain,
equal(composition(meet(u,skc3),meet(u,skc3)),meet(u,skc3)),
inference(rew,[status(thm),theory(equality)],[671,30830,5243]),
[iquote('0:Rew:671.0,30830.0,5243.0,30830.0')] ).
cnf(34527,plain,
equal(converse(composition(skc2,skc3)),composition(skc3,skc2)),
inference(spr,[status(thm),theory(equality)],[25488,23151]),
[iquote('0:SpR:25488.0,23151.0')] ).
cnf(35427,plain,
equal(converse(join(skc3,composition(skc2,skc3))),join(skc3,composition(skc3,skc2))),
inference(spr,[status(thm),theory(equality)],[34527,23152]),
[iquote('0:SpR:34527.0,23152.0')] ).
cnf(35475,plain,
equal(converse(composition(join(one,skc2),skc3)),join(skc3,composition(skc3,skc2))),
inference(rew,[status(thm),theory(equality)],[687,35427]),
[iquote('0:Rew:687.0,35427.0')] ).
cnf(35476,plain,
equal(join(skc3,composition(skc3,skc2)),skc3),
inference(rew,[status(thm),theory(equality)],[22971,35475,671,21]),
[iquote('0:Rew:22971.0,35475.0,671.0,35475.0,21.0,35475.0')] ).
cnf(35508,plain,
equal(meet(composition(skc3,skc2),skc3),composition(skc3,skc2)),
inference(spr,[status(thm),theory(equality)],[35476,18575]),
[iquote('0:SpR:35476.0,18575.0')] ).
cnf(35513,plain,
equal(join(one,composition(skc3,skc2)),join(one,skc3)),
inference(spr,[status(thm),theory(equality)],[35476,217]),
[iquote('0:SpR:35476.0,217.0')] ).
cnf(35522,plain,
equal(meet(skc3,composition(skc3,skc2)),composition(skc3,skc2)),
inference(rew,[status(thm),theory(equality)],[88,35508]),
[iquote('0:Rew:88.0,35508.0')] ).
cnf(35523,plain,
equal(join(one,composition(skc3,skc2)),one),
inference(rew,[status(thm),theory(equality)],[20,35513]),
[iquote('0:Rew:20.0,35513.0')] ).
cnf(35553,plain,
equal(meet(composition(skc3,skc2),one),composition(skc3,skc2)),
inference(spr,[status(thm),theory(equality)],[35523,18575]),
[iquote('0:SpR:35523.0,18575.0')] ).
cnf(35566,plain,
equal(meet(one,composition(skc3,skc2)),composition(skc3,skc2)),
inference(rew,[status(thm),theory(equality)],[88,35553]),
[iquote('0:Rew:88.0,35553.0')] ).
cnf(41207,plain,
equal(join(meet(composition(one,converse(skc2)),skc3),meet(skc3,composition(composition(skc3,skc2),converse(skc2)))),meet(skc3,composition(composition(skc3,skc2),converse(skc2)))),
inference(spr,[status(thm),theory(equality)],[35566,472]),
[iquote('0:SpR:35566.0,472.0')] ).
cnf(41210,plain,
equal(join(composition(skc3,skc2),composition(meet(skc3,converse(skc2)),meet(skc2,converse(skc3)))),composition(meet(skc3,converse(skc2)),meet(skc2,converse(skc3)))),
inference(spr,[status(thm),theory(equality)],[35566,676]),
[iquote('0:SpR:35566.0,676.0')] ).
cnf(41218,plain,
equal(join(composition(skc3,skc2),composition(meet(skc2,skc3),meet(skc2,skc3))),composition(meet(skc2,skc3),meet(skc2,skc3))),
inference(rew,[status(thm),theory(equality)],[88,41210,25488,22971]),
[iquote('0:Rew:88.0,41210.0,25488.0,41210.0,22971.0,41210.0')] ).
cnf(41219,plain,
equal(join(composition(skc3,skc2),meet(skc2,skc3)),meet(skc2,skc3)),
inference(rew,[status(thm),theory(equality)],[30831,41218]),
[iquote('0:Rew:30831.0,41218.0')] ).
cnf(41220,plain,
equal(join(composition(skc3,skc2),meet(skc2,skc3)),composition(skc3,skc2)),
inference(rew,[status(thm),theory(equality)],[7,41207,671,35522,19540,13,25488]),
[iquote('0:Rew:7.0,41207.0,671.0,41207.0,35522.0,41207.0,19540.0,41207.0,13.0,41207.0,25488.0,41207.0')] ).
cnf(41221,plain,
equal(meet(skc2,skc3),composition(skc3,skc2)),
inference(rew,[status(thm),theory(equality)],[41219,41220]),
[iquote('0:Rew:41219.0,41220.0')] ).
cnf(41222,plain,
$false,
inference(mrr,[status(thm)],[41221,89]),
[iquote('0:MRR:41221.0,89.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL028+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 12:00:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 15.98/16.16
% 15.98/16.16 SPASS V 3.9
% 15.98/16.16 SPASS beiseite: Proof found.
% 15.98/16.16 % SZS status Theorem
% 15.98/16.16 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.98/16.16 SPASS derived 25357 clauses, backtracked 0 clauses, performed 0 splits and kept 4364 clauses.
% 15.98/16.16 SPASS allocated 132193 KBytes.
% 15.98/16.16 SPASS spent 0:0:15.78 on the problem.
% 15.98/16.16 0:00:00.03 for the input.
% 15.98/16.16 0:00:00.03 for the FLOTTER CNF translation.
% 15.98/16.16 0:00:00.22 for inferences.
% 15.98/16.16 0:00:00.00 for the backtracking.
% 15.98/16.16 0:0:15.45 for the reduction.
% 15.98/16.16
% 15.98/16.16
% 15.98/16.16 Here is a proof with depth 28, length 220 :
% 15.98/16.16 % SZS output start Refutation
% See solution above
% 16.52/16.68 Formulae used in the proof : goals 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 modular_law_2 modular_law_1 dedekind_law
% 16.52/16.68
%------------------------------------------------------------------------------