TSTP Solution File: REL018+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : REL018+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 20:01:47 EDT 2022

% Result   : Theorem 3.46s 3.68s
% Output   : Refutation 3.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :   15
% Syntax   : Number of clauses     :  125 ( 125 unt;   0 nHn; 125 RR)
%            Number of literals    :  125 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   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(skc1,top),skc1),
    file('REL018+1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(composition(u,one),u),
    file('REL018+1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(converse(converse(u)),u),
    file('REL018+1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(join(u,complement(u)),top),
    file('REL018+1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(meet(u,complement(u)),zero),
    file('REL018+1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(join(u,v),join(v,u)),
    file('REL018+1.p',unknown),
    [] ).

cnf(7,axiom,
    ~ equal(composition(complement(skc1),top),complement(skc1)),
    file('REL018+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(complement(join(complement(u),complement(v))),meet(u,v)),
    file('REL018+1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(join(converse(u),converse(v)),converse(join(u,v))),
    file('REL018+1.p',unknown),
    [] ).

cnf(10,axiom,
    equal(composition(converse(u),converse(v)),converse(composition(v,u))),
    file('REL018+1.p',unknown),
    [] ).

cnf(11,axiom,
    equal(join(join(u,v),w),join(u,join(v,w))),
    file('REL018+1.p',unknown),
    [] ).

cnf(12,axiom,
    equal(composition(composition(u,v),w),composition(u,composition(v,w))),
    file('REL018+1.p',unknown),
    [] ).

cnf(13,axiom,
    equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
    file('REL018+1.p',unknown),
    [] ).

cnf(14,axiom,
    equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
    file('REL018+1.p',unknown),
    [] ).

cnf(15,axiom,
    equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
    file('REL018+1.p',unknown),
    [] ).

cnf(16,plain,
    equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
    inference(rew,[status(thm),theory(equality)],[6,14]),
    [iquote('0:Rew:6.0,14.0')] ).

cnf(17,plain,
    equal(join(meet(u,v),complement(join(complement(u),v))),u),
    inference(rew,[status(thm),theory(equality)],[8,15]),
    [iquote('0:Rew:8.0,15.0')] ).

cnf(29,plain,
    equal(converse(composition(converse(u),v)),composition(converse(v),u)),
    inference(spr,[status(thm),theory(equality)],[3,10]),
    [iquote('0:SpR:3.0,10.0')] ).

cnf(34,plain,
    equal(converse(join(u,converse(v))),join(converse(u),v)),
    inference(spr,[status(thm),theory(equality)],[3,9]),
    [iquote('0:SpR:3.0,9.0')] ).

cnf(35,plain,
    equal(converse(join(converse(u),v)),join(u,converse(v))),
    inference(spr,[status(thm),theory(equality)],[3,9]),
    [iquote('0:SpR:3.0,9.0')] ).

cnf(39,plain,
    equal(join(join(complement(u),complement(v)),meet(u,v)),top),
    inference(spr,[status(thm),theory(equality)],[8,4]),
    [iquote('0:SpR:8.0,4.0')] ).

cnf(43,plain,
    equal(meet(u,complement(u)),complement(top)),
    inference(spr,[status(thm),theory(equality)],[4,8]),
    [iquote('0:SpR:4.0,8.0')] ).

cnf(46,plain,
    equal(complement(top),zero),
    inference(rew,[status(thm),theory(equality)],[5,43]),
    [iquote('0:Rew:5.0,43.0')] ).

cnf(50,plain,
    equal(join(meet(u,v),join(complement(u),complement(v))),top),
    inference(rew,[status(thm),theory(equality)],[6,39]),
    [iquote('0:Rew:6.0,39.0')] ).

cnf(55,plain,
    equal(complement(join(zero,complement(u))),meet(top,u)),
    inference(spr,[status(thm),theory(equality)],[46,8]),
    [iquote('0:SpR:46.0,8.0')] ).

cnf(69,plain,
    equal(join(meet(u,complement(complement(u))),complement(top)),u),
    inference(spr,[status(thm),theory(equality)],[4,17]),
    [iquote('0:SpR:4.0,17.0')] ).

cnf(70,plain,
    equal(join(meet(u,v),complement(join(v,complement(u)))),u),
    inference(spr,[status(thm),theory(equality)],[6,17]),
    [iquote('0:SpR:6.0,17.0')] ).

cnf(72,plain,
    equal(join(meet(u,complement(v)),meet(u,v)),u),
    inference(spr,[status(thm),theory(equality)],[8,17]),
    [iquote('0:SpR:8.0,17.0')] ).

cnf(73,plain,
    equal(join(zero,complement(join(complement(u),complement(u)))),u),
    inference(spr,[status(thm),theory(equality)],[5,17]),
    [iquote('0:SpR:5.0,17.0')] ).

cnf(78,plain,
    equal(join(zero,meet(u,complement(complement(u)))),u),
    inference(rew,[status(thm),theory(equality)],[6,69,46]),
    [iquote('0:Rew:6.0,69.0,46.0,69.0')] ).

cnf(79,plain,
    equal(join(meet(u,v),meet(u,complement(v))),u),
    inference(rew,[status(thm),theory(equality)],[6,72]),
    [iquote('0:Rew:6.0,72.0')] ).

cnf(80,plain,
    equal(join(zero,meet(u,u)),u),
    inference(rew,[status(thm),theory(equality)],[8,73]),
    [iquote('0:Rew:8.0,73.0')] ).

cnf(91,plain,
    equal(complement(join(meet(top,u),complement(v))),meet(join(zero,complement(u)),v)),
    inference(spr,[status(thm),theory(equality)],[55,8]),
    [iquote('0:SpR:55.0,8.0')] ).

cnf(94,plain,
    equal(complement(join(complement(u),meet(top,v))),meet(u,join(zero,complement(v)))),
    inference(spr,[status(thm),theory(equality)],[55,8]),
    [iquote('0:SpR:55.0,8.0')] ).

cnf(159,plain,
    equal(join(u,join(v,w)),join(w,join(u,v))),
    inference(spr,[status(thm),theory(equality)],[11,6]),
    [iquote('0:SpR:11.0,6.0')] ).

cnf(163,plain,
    equal(join(u,join(complement(u),v)),join(top,v)),
    inference(spr,[status(thm),theory(equality)],[4,11]),
    [iquote('0:SpR:4.0,11.0')] ).

cnf(168,plain,
    equal(join(meet(u,v),join(complement(join(complement(u),v)),w)),join(u,w)),
    inference(spr,[status(thm),theory(equality)],[17,11]),
    [iquote('0:SpR:17.0,11.0')] ).

cnf(172,plain,
    equal(join(complement(u),join(meet(v,u),complement(v))),top),
    inference(rew,[status(thm),theory(equality)],[159,50]),
    [iquote('0:Rew:159.0,50.0')] ).

cnf(178,plain,
    equal(join(complement(u),join(complement(v),meet(v,u))),top),
    inference(rew,[status(thm),theory(equality)],[6,172]),
    [iquote('0:Rew:6.0,172.0')] ).

cnf(205,plain,
    equal(join(complement(top),composition(converse(skc1),complement(skc1))),complement(top)),
    inference(spr,[status(thm),theory(equality)],[1,16]),
    [iquote('0:SpR:1.0,16.0')] ).

cnf(210,plain,
    equal(join(complement(u),composition(v,complement(composition(converse(v),u)))),complement(u)),
    inference(spr,[status(thm),theory(equality)],[3,16]),
    [iquote('0:SpR:3.0,16.0')] ).

cnf(214,plain,
    equal(join(zero,composition(converse(u),complement(composition(u,top)))),zero),
    inference(spr,[status(thm),theory(equality)],[46,16]),
    [iquote('0:SpR:46.0,16.0')] ).

cnf(215,plain,
    equal(join(zero,composition(converse(skc1),complement(skc1))),zero),
    inference(rew,[status(thm),theory(equality)],[46,205]),
    [iquote('0:Rew:46.0,205.0')] ).

cnf(333,plain,
    equal(composition(converse(one),u),converse(converse(u))),
    inference(spr,[status(thm),theory(equality)],[2,29]),
    [iquote('0:SpR:2.0,29.0')] ).

cnf(336,plain,
    equal(composition(converse(one),u),u),
    inference(rew,[status(thm),theory(equality)],[3,333]),
    [iquote('0:Rew:3.0,333.0')] ).

cnf(345,plain,
    equal(converse(one),one),
    inference(spr,[status(thm),theory(equality)],[336,2]),
    [iquote('0:SpR:336.0,2.0')] ).

cnf(348,plain,
    equal(join(u,composition(v,u)),composition(join(converse(one),v),u)),
    inference(spr,[status(thm),theory(equality)],[336,13]),
    [iquote('0:SpR:336.0,13.0')] ).

cnf(351,plain,
    equal(join(complement(u),complement(composition(one,u))),complement(u)),
    inference(spr,[status(thm),theory(equality)],[336,16]),
    [iquote('0:SpR:336.0,16.0')] ).

cnf(355,plain,
    equal(composition(one,u),u),
    inference(rew,[status(thm),theory(equality)],[345,336]),
    [iquote('0:Rew:345.0,336.0')] ).

cnf(362,plain,
    equal(join(complement(u),complement(u)),complement(u)),
    inference(rew,[status(thm),theory(equality)],[355,351]),
    [iquote('0:Rew:355.0,351.0')] ).

cnf(363,plain,
    equal(join(u,composition(v,u)),composition(join(one,v),u)),
    inference(rew,[status(thm),theory(equality)],[345,348]),
    [iquote('0:Rew:345.0,348.0')] ).

cnf(398,plain,
    equal(meet(u,u),complement(complement(u))),
    inference(spr,[status(thm),theory(equality)],[362,8]),
    [iquote('0:SpR:362.0,8.0')] ).

cnf(404,plain,
    equal(join(zero,zero),zero),
    inference(spr,[status(thm),theory(equality)],[46,362]),
    [iquote('0:SpR:46.0,362.0')] ).

cnf(421,plain,
    equal(join(zero,complement(complement(u))),u),
    inference(rew,[status(thm),theory(equality)],[398,80]),
    [iquote('0:Rew:398.0,80.0')] ).

cnf(449,plain,
    equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
    inference(spr,[status(thm),theory(equality)],[8,421]),
    [iquote('0:SpR:8.0,421.0')] ).

cnf(460,plain,
    equal(join(zero,join(zero,u)),join(zero,u)),
    inference(spr,[status(thm),theory(equality)],[404,11]),
    [iquote('0:SpR:404.0,11.0')] ).

cnf(635,plain,
    equal(join(zero,u),u),
    inference(spr,[status(thm),theory(equality)],[78,460]),
    [iquote('0:SpR:78.0,460.0')] ).

cnf(640,plain,
    equal(composition(converse(skc1),complement(skc1)),zero),
    inference(rew,[status(thm),theory(equality)],[635,215]),
    [iquote('0:Rew:635.0,215.0')] ).

cnf(642,plain,
    equal(complement(complement(u)),u),
    inference(rew,[status(thm),theory(equality)],[635,421]),
    [iquote('0:Rew:635.0,421.0')] ).

cnf(643,plain,
    equal(meet(top,u),complement(complement(u))),
    inference(rew,[status(thm),theory(equality)],[635,55]),
    [iquote('0:Rew:635.0,55.0')] ).

cnf(645,plain,
    equal(composition(converse(u),complement(composition(u,top))),zero),
    inference(rew,[status(thm),theory(equality)],[635,214]),
    [iquote('0:Rew:635.0,214.0')] ).

cnf(650,plain,
    equal(join(complement(u),complement(v)),complement(meet(u,v))),
    inference(rew,[status(thm),theory(equality)],[635,449]),
    [iquote('0:Rew:635.0,449.0')] ).

cnf(652,plain,
    equal(complement(join(complement(u),meet(top,v))),meet(u,complement(v))),
    inference(rew,[status(thm),theory(equality)],[635,94]),
    [iquote('0:Rew:635.0,94.0')] ).

cnf(655,plain,
    equal(complement(join(meet(top,u),complement(v))),meet(complement(u),v)),
    inference(rew,[status(thm),theory(equality)],[635,91]),
    [iquote('0:Rew:635.0,91.0')] ).

cnf(663,plain,
    equal(meet(u,u),u),
    inference(rew,[status(thm),theory(equality)],[642,398]),
    [iquote('0:Rew:642.0,398.0')] ).

cnf(670,plain,
    equal(meet(top,u),u),
    inference(rew,[status(thm),theory(equality)],[642,643]),
    [iquote('0:Rew:642.0,643.0')] ).

cnf(698,plain,
    equal(complement(join(complement(u),v)),meet(u,complement(v))),
    inference(rew,[status(thm),theory(equality)],[670,652]),
    [iquote('0:Rew:670.0,652.0')] ).

cnf(701,plain,
    equal(join(meet(u,v),join(meet(u,complement(v)),w)),join(u,w)),
    inference(rew,[status(thm),theory(equality)],[698,168]),
    [iquote('0:Rew:698.0,168.0')] ).

cnf(702,plain,
    equal(complement(join(u,complement(v))),meet(complement(u),v)),
    inference(rew,[status(thm),theory(equality)],[670,655]),
    [iquote('0:Rew:670.0,655.0')] ).

cnf(703,plain,
    equal(join(meet(u,v),meet(complement(v),u)),u),
    inference(rew,[status(thm),theory(equality)],[702,70]),
    [iquote('0:Rew:702.0,70.0')] ).

cnf(712,plain,
    equal(complement(zero),top),
    inference(spr,[status(thm),theory(equality)],[635,4]),
    [iquote('0:SpR:635.0,4.0')] ).

cnf(713,plain,
    equal(join(u,zero),u),
    inference(spr,[status(thm),theory(equality)],[635,6]),
    [iquote('0:SpR:635.0,6.0')] ).

cnf(717,plain,
    equal(join(converse(zero),u),converse(converse(u))),
    inference(spr,[status(thm),theory(equality)],[635,34]),
    [iquote('0:SpR:635.0,34.0')] ).

cnf(727,plain,
    equal(join(converse(zero),u),u),
    inference(rew,[status(thm),theory(equality)],[3,717]),
    [iquote('0:Rew:3.0,717.0')] ).

cnf(750,plain,
    equal(join(complement(complement(skc1)),composition(converse(converse(skc1)),complement(zero))),complement(complement(skc1))),
    inference(spr,[status(thm),theory(equality)],[640,16]),
    [iquote('0:SpR:640.0,16.0')] ).

cnf(753,plain,
    equal(composition(converse(complement(skc1)),skc1),converse(zero)),
    inference(spr,[status(thm),theory(equality)],[640,29]),
    [iquote('0:SpR:640.0,29.0')] ).

cnf(755,plain,
    equal(join(skc1,skc1),skc1),
    inference(rew,[status(thm),theory(equality)],[1,750,3,712,642]),
    [iquote('0:Rew:1.0,750.0,3.0,750.0,712.0,750.0,642.0,750.0')] ).

cnf(759,plain,
    equal(join(skc1,join(skc1,u)),join(skc1,u)),
    inference(spr,[status(thm),theory(equality)],[755,11]),
    [iquote('0:SpR:755.0,11.0')] ).

cnf(815,plain,
    equal(join(u,converse(complement(converse(u)))),converse(top)),
    inference(spr,[status(thm),theory(equality)],[4,35]),
    [iquote('0:SpR:4.0,35.0')] ).

cnf(844,plain,
    equal(converse(zero),zero),
    inference(spr,[status(thm),theory(equality)],[727,713]),
    [iquote('0:SpR:727.0,713.0')] ).

cnf(851,plain,
    equal(composition(converse(complement(skc1)),skc1),zero),
    inference(rew,[status(thm),theory(equality)],[844,753]),
    [iquote('0:Rew:844.0,753.0')] ).

cnf(880,plain,
    equal(join(complement(skc1),composition(converse(converse(complement(skc1))),complement(zero))),complement(skc1)),
    inference(spr,[status(thm),theory(equality)],[851,16]),
    [iquote('0:SpR:851.0,16.0')] ).

cnf(886,plain,
    equal(join(complement(skc1),composition(complement(skc1),top)),complement(skc1)),
    inference(rew,[status(thm),theory(equality)],[3,880,712]),
    [iquote('0:Rew:3.0,880.0,712.0,880.0')] ).

cnf(1029,plain,
    equal(join(skc1,converse(top)),converse(top)),
    inference(spr,[status(thm),theory(equality)],[815,759]),
    [iquote('0:SpR:815.0,759.0')] ).

cnf(1030,plain,
    equal(join(top,converse(complement(converse(complement(u))))),join(u,converse(top))),
    inference(spr,[status(thm),theory(equality)],[815,163]),
    [iquote('0:SpR:815.0,163.0')] ).

cnf(1512,plain,
    equal(join(complement(u),join(complement(u),u)),top),
    inference(spr,[status(thm),theory(equality)],[663,178]),
    [iquote('0:SpR:663.0,178.0')] ).

cnf(1524,plain,
    equal(join(top,complement(u)),top),
    inference(rew,[status(thm),theory(equality)],[6,1512,4]),
    [iquote('0:Rew:6.0,1512.0,4.0,1512.0,6.0,1512.0')] ).

cnf(1552,plain,
    equal(join(top,u),top),
    inference(spr,[status(thm),theory(equality)],[642,1524]),
    [iquote('0:SpR:642.0,1524.0')] ).

cnf(1558,plain,
    equal(join(u,converse(top)),top),
    inference(rew,[status(thm),theory(equality)],[1552,1030]),
    [iquote('0:Rew:1552.0,1030.0')] ).

cnf(1569,plain,
    equal(converse(top),top),
    inference(rew,[status(thm),theory(equality)],[1558,1029]),
    [iquote('0:Rew:1558.0,1029.0')] ).

cnf(1585,plain,
    equal(composition(top,converse(u)),converse(composition(u,top))),
    inference(spr,[status(thm),theory(equality)],[1569,10]),
    [iquote('0:SpR:1569.0,10.0')] ).

cnf(1590,plain,
    equal(composition(top,complement(composition(top,top))),zero),
    inference(spr,[status(thm),theory(equality)],[1569,645]),
    [iquote('0:SpR:1569.0,645.0')] ).

cnf(1597,plain,
    equal(join(complement(u),composition(top,complement(composition(top,u)))),complement(u)),
    inference(spr,[status(thm),theory(equality)],[1569,16]),
    [iquote('0:SpR:1569.0,16.0')] ).

cnf(1706,plain,
    equal(join(zero,composition(u,complement(composition(top,top)))),composition(join(top,u),complement(composition(top,top)))),
    inference(spr,[status(thm),theory(equality)],[1590,13]),
    [iquote('0:SpR:1590.0,13.0')] ).

cnf(1711,plain,
    equal(composition(u,complement(composition(top,top))),zero),
    inference(rew,[status(thm),theory(equality)],[635,1706,1590,1552]),
    [iquote('0:Rew:635.0,1706.0,1590.0,1706.0,1552.0,1706.0')] ).

cnf(1950,plain,
    equal(complement(composition(top,top)),zero),
    inference(spr,[status(thm),theory(equality)],[1711,355]),
    [iquote('0:SpR:1711.0,355.0')] ).

cnf(2262,plain,
    equal(composition(top,top),complement(zero)),
    inference(spr,[status(thm),theory(equality)],[1950,642]),
    [iquote('0:SpR:1950.0,642.0')] ).

cnf(2273,plain,
    equal(composition(top,top),top),
    inference(rew,[status(thm),theory(equality)],[712,2262]),
    [iquote('0:Rew:712.0,2262.0')] ).

cnf(2298,plain,
    equal(composition(top,composition(top,u)),composition(top,u)),
    inference(spr,[status(thm),theory(equality)],[2273,12]),
    [iquote('0:SpR:2273.0,12.0')] ).

cnf(2568,plain,
    equal(join(u,composition(v,complement(composition(converse(v),complement(u))))),u),
    inference(spr,[status(thm),theory(equality)],[642,210]),
    [iquote('0:SpR:642.0,210.0')] ).

cnf(3201,plain,
    equal(join(complement(composition(top,u)),composition(converse(top),complement(composition(top,u)))),complement(composition(top,u))),
    inference(spr,[status(thm),theory(equality)],[2298,16]),
    [iquote('0:SpR:2298.0,16.0')] ).

cnf(3222,plain,
    equal(join(complement(composition(top,u)),composition(top,complement(composition(top,u)))),complement(composition(top,u))),
    inference(rew,[status(thm),theory(equality)],[1569,3201]),
    [iquote('0:Rew:1569.0,3201.0')] ).

cnf(3223,plain,
    equal(composition(join(one,top),complement(composition(top,u))),complement(composition(top,u))),
    inference(rew,[status(thm),theory(equality)],[363,3222]),
    [iquote('0:Rew:363.0,3222.0')] ).

cnf(3224,plain,
    equal(composition(top,complement(composition(top,u))),complement(composition(top,u))),
    inference(rew,[status(thm),theory(equality)],[1552,3223,6]),
    [iquote('0:Rew:1552.0,3223.0,6.0,3223.0')] ).

cnf(3225,plain,
    equal(join(complement(u),complement(composition(top,u))),complement(u)),
    inference(rew,[status(thm),theory(equality)],[3224,1597]),
    [iquote('0:Rew:3224.0,1597.0')] ).

cnf(3227,plain,
    equal(complement(meet(u,composition(top,u))),complement(u)),
    inference(rew,[status(thm),theory(equality)],[650,3225]),
    [iquote('0:Rew:650.0,3225.0')] ).

cnf(3304,plain,
    equal(join(u,meet(complement(complement(v)),u)),join(meet(u,v),u)),
    inference(spr,[status(thm),theory(equality)],[703,701]),
    [iquote('0:SpR:703.0,701.0')] ).

cnf(3335,plain,
    equal(join(u,meet(v,u)),join(u,meet(u,v))),
    inference(rew,[status(thm),theory(equality)],[642,3304,6]),
    [iquote('0:Rew:642.0,3304.0,6.0,3304.0')] ).

cnf(3880,plain,
    equal(meet(u,composition(top,u)),complement(complement(u))),
    inference(spr,[status(thm),theory(equality)],[3227,642]),
    [iquote('0:SpR:3227.0,642.0')] ).

cnf(3909,plain,
    equal(meet(u,composition(top,u)),u),
    inference(rew,[status(thm),theory(equality)],[642,3880]),
    [iquote('0:Rew:642.0,3880.0')] ).

cnf(3954,plain,
    equal(meet(converse(u),converse(composition(u,top))),converse(u)),
    inference(spr,[status(thm),theory(equality)],[1585,3909]),
    [iquote('0:SpR:1585.0,3909.0')] ).

cnf(12885,plain,
    equal(converse(join(converse(u),meet(converse(u),v))),join(u,converse(meet(v,converse(u))))),
    inference(spr,[status(thm),theory(equality)],[3335,35]),
    [iquote('0:SpR:3335.0,35.0')] ).

cnf(13009,plain,
    equal(join(u,converse(meet(converse(u),v))),join(u,converse(meet(v,converse(u))))),
    inference(rew,[status(thm),theory(equality)],[35,12885]),
    [iquote('0:Rew:35.0,12885.0')] ).

cnf(18818,plain,
    equal(join(u,complement(composition(converse(one),complement(u)))),u),
    inference(spr,[status(thm),theory(equality)],[355,2568]),
    [iquote('0:SpR:355.0,2568.0')] ).

cnf(18834,plain,
    equal(join(u,u),u),
    inference(rew,[status(thm),theory(equality)],[642,18818,355,345]),
    [iquote('0:Rew:642.0,18818.0,355.0,18818.0,345.0,18818.0')] ).

cnf(19020,plain,
    equal(join(meet(u,v),meet(u,complement(v))),join(u,meet(u,complement(v)))),
    inference(spr,[status(thm),theory(equality)],[18834,701]),
    [iquote('0:SpR:18834.0,701.0')] ).

cnf(19150,plain,
    equal(join(u,meet(u,complement(v))),u),
    inference(rew,[status(thm),theory(equality)],[79,19020]),
    [iquote('0:Rew:79.0,19020.0')] ).

cnf(19221,plain,
    equal(join(u,meet(u,v)),u),
    inference(spr,[status(thm),theory(equality)],[642,19150]),
    [iquote('0:SpR:642.0,19150.0')] ).

cnf(19330,plain,
    equal(join(u,converse(meet(converse(u),v))),converse(converse(u))),
    inference(spr,[status(thm),theory(equality)],[19221,35]),
    [iquote('0:SpR:19221.0,35.0')] ).

cnf(19446,plain,
    equal(join(u,converse(meet(converse(u),v))),u),
    inference(rew,[status(thm),theory(equality)],[3,19330]),
    [iquote('0:Rew:3.0,19330.0')] ).

cnf(19447,plain,
    equal(join(u,converse(meet(v,converse(u)))),u),
    inference(rew,[status(thm),theory(equality)],[19446,13009]),
    [iquote('0:Rew:19446.0,13009.0')] ).

cnf(21515,plain,
    equal(join(composition(u,top),converse(converse(u))),composition(u,top)),
    inference(spr,[status(thm),theory(equality)],[3954,19447]),
    [iquote('0:SpR:3954.0,19447.0')] ).

cnf(21544,plain,
    equal(join(u,composition(u,top)),composition(u,top)),
    inference(rew,[status(thm),theory(equality)],[6,21515,3]),
    [iquote('0:Rew:6.0,21515.0,3.0,21515.0')] ).

cnf(21545,plain,
    equal(composition(complement(skc1),top),complement(skc1)),
    inference(rew,[status(thm),theory(equality)],[21544,886]),
    [iquote('0:Rew:21544.0,886.0')] ).

cnf(21548,plain,
    $false,
    inference(mrr,[status(thm)],[21545,7]),
    [iquote('0:MRR:21545.0,7.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : REL018+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n008.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 09:38:53 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 3.46/3.68  
% 3.46/3.68  SPASS V 3.9 
% 3.46/3.68  SPASS beiseite: Proof found.
% 3.46/3.68  % SZS status Theorem
% 3.46/3.68  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 3.46/3.68  SPASS derived 13324 clauses, backtracked 0 clauses, performed 0 splits and kept 2113 clauses.
% 3.46/3.68  SPASS allocated 104345 KBytes.
% 3.46/3.68  SPASS spent	0:00:03.32 on the problem.
% 3.46/3.68  		0:00:00.04 for the input.
% 3.46/3.68  		0:00:00.03 for the FLOTTER CNF translation.
% 3.46/3.68  		0:00:00.09 for inferences.
% 3.46/3.68  		0:00:00.00 for the backtracking.
% 3.46/3.68  		0:00:03.12 for the reduction.
% 3.46/3.68  
% 3.46/3.68  
% 3.46/3.68  Here is a proof with depth 10, length 125 :
% 3.46/3.68  % SZS output start Refutation
% See solution above
% 3.60/3.83  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
% 3.60/3.83  
%------------------------------------------------------------------------------