TSTP Solution File: REL007-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL007-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 20:01:29 EDT 2022
% Result : Unsatisfiable 4.37s 4.55s
% Output : Refutation 4.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 13
% Syntax : Number of clauses : 158 ( 158 unt; 0 nHn; 158 RR)
% Number of literals : 158 ( 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(meet(sk1,converse(sk2)),zero),
file('REL007-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(meet(converse(sk1),sk2),zero),
file('REL007-1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,v),join(v,u)),
file('REL007-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL007-1.p',unknown),
[] ).
cnf(5,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL007-1.p',unknown),
[] ).
cnf(6,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL007-1.p',unknown),
[] ).
cnf(8,axiom,
equal(composition(u,one),u),
file('REL007-1.p',unknown),
[] ).
cnf(10,axiom,
equal(converse(converse(u)),u),
file('REL007-1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL007-1.p',unknown),
[] ).
cnf(12,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL007-1.p',unknown),
[] ).
cnf(13,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL007-1.p',unknown),
[] ).
cnf(14,axiom,
equal(join(u,complement(u)),top),
file('REL007-1.p',unknown),
[] ).
cnf(15,axiom,
equal(meet(u,complement(u)),zero),
file('REL007-1.p',unknown),
[] ).
cnf(16,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[3,13]),
[iquote('0:Rew:3.0,13.0')] ).
cnf(17,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[6,5]),
[iquote('0:Rew:6.0,5.0')] ).
cnf(29,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[10,12]),
[iquote('0:SpR:10.0,12.0')] ).
cnf(34,plain,
equal(converse(join(u,converse(v))),join(converse(u),v)),
inference(spr,[status(thm),theory(equality)],[10,11]),
[iquote('0:SpR:10.0,11.0')] ).
cnf(35,plain,
equal(converse(join(converse(u),v)),join(u,converse(v))),
inference(spr,[status(thm),theory(equality)],[10,11]),
[iquote('0:SpR:10.0,11.0')] ).
cnf(40,plain,
equal(meet(join(complement(u),complement(v)),w),complement(join(meet(u,v),complement(w)))),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(43,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[14,6]),
[iquote('0:SpR:14.0,6.0')] ).
cnf(44,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(46,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[15,43]),
[iquote('0:Rew:15.0,43.0')] ).
cnf(47,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[6,44]),
[iquote('0:Rew:6.0,44.0')] ).
cnf(48,plain,
~ equal(meet(sk2,converse(sk1)),zero),
inference(rew,[status(thm),theory(equality)],[47,2]),
[iquote('0:Rew:47.0,2.0')] ).
cnf(54,plain,
equal(meet(top,zero),zero),
inference(spr,[status(thm),theory(equality)],[46,15]),
[iquote('0:SpR:46.0,15.0')] ).
cnf(56,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[46,6]),
[iquote('0:SpR:46.0,6.0')] ).
cnf(59,plain,
equal(meet(zero,top),zero),
inference(rew,[status(thm),theory(equality)],[47,54]),
[iquote('0:Rew:47.0,54.0')] ).
cnf(66,plain,
equal(join(meet(join(complement(u),complement(v)),w),complement(join(meet(u,v),w))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[6,17]),
[iquote('0:SpR:6.0,17.0')] ).
cnf(68,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[14,17]),
[iquote('0:SpR:14.0,17.0')] ).
cnf(69,plain,
equal(join(meet(u,v),complement(join(v,complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[3,17]),
[iquote('0:SpR:3.0,17.0')] ).
cnf(71,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[6,17]),
[iquote('0:SpR:6.0,17.0')] ).
cnf(72,plain,
equal(join(zero,complement(join(complement(sk1),converse(sk2)))),sk1),
inference(spr,[status(thm),theory(equality)],[1,17]),
[iquote('0:SpR:1.0,17.0')] ).
cnf(73,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[15,17]),
[iquote('0:SpR:15.0,17.0')] ).
cnf(74,plain,
equal(join(zero,complement(join(complement(zero),top))),zero),
inference(spr,[status(thm),theory(equality)],[59,17]),
[iquote('0:SpR:59.0,17.0')] ).
cnf(75,plain,
equal(join(zero,complement(join(top,complement(zero)))),zero),
inference(rew,[status(thm),theory(equality)],[3,74]),
[iquote('0:Rew:3.0,74.0')] ).
cnf(76,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[3,68,46]),
[iquote('0:Rew:3.0,68.0,46.0,68.0')] ).
cnf(77,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[3,71]),
[iquote('0:Rew:3.0,71.0')] ).
cnf(78,plain,
equal(join(zero,complement(join(converse(sk2),complement(sk1)))),sk1),
inference(rew,[status(thm),theory(equality)],[3,72]),
[iquote('0:Rew:3.0,72.0')] ).
cnf(79,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[6,73]),
[iquote('0:Rew:6.0,73.0')] ).
cnf(80,plain,
equal(join(complement(join(meet(u,v),w)),meet(join(complement(u),complement(v)),w)),join(complement(u),complement(v))),
inference(rew,[status(thm),theory(equality)],[3,66]),
[iquote('0:Rew:3.0,66.0')] ).
cnf(81,plain,
equal(join(complement(join(meet(u,v),w)),complement(join(meet(u,v),complement(w)))),join(complement(u),complement(v))),
inference(rew,[status(thm),theory(equality)],[40,80]),
[iquote('0:Rew:40.0,80.0')] ).
cnf(94,plain,
equal(complement(join(meet(top,u),complement(v))),meet(join(zero,complement(u)),v)),
inference(spr,[status(thm),theory(equality)],[56,6]),
[iquote('0:SpR:56.0,6.0')] ).
cnf(97,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,join(zero,complement(v)))),
inference(spr,[status(thm),theory(equality)],[56,6]),
[iquote('0:SpR:56.0,6.0')] ).
cnf(100,plain,
equal(complement(join(zero,zero)),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[46,56]),
[iquote('0:SpR:46.0,56.0')] ).
cnf(116,plain,
equal(meet(join(zero,zero),meet(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[100,15]),
[iquote('0:SpR:100.0,15.0')] ).
cnf(125,plain,
equal(meet(meet(top,top),join(zero,zero)),zero),
inference(rew,[status(thm),theory(equality)],[47,116]),
[iquote('0:Rew:47.0,116.0')] ).
cnf(140,plain,
equal(join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[125,17]),
[iquote('0:SpR:125.0,17.0')] ).
cnf(146,plain,
equal(join(zero,complement(join(join(zero,zero),complement(meet(top,top))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[3,140]),
[iquote('0:Rew:3.0,140.0')] ).
cnf(147,plain,
equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[4,146]),
[iquote('0:Rew:4.0,146.0')] ).
cnf(149,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(153,plain,
equal(join(u,join(complement(u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[14,4]),
[iquote('0:SpR:14.0,4.0')] ).
cnf(159,plain,
equal(join(meet(u,v),join(complement(join(complement(u),v)),w)),join(u,w)),
inference(spr,[status(thm),theory(equality)],[17,4]),
[iquote('0:SpR:17.0,4.0')] ).
cnf(160,plain,
equal(join(zero,join(complement(join(top,complement(zero))),u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[75,4]),
[iquote('0:SpR:75.0,4.0')] ).
cnf(205,plain,
equal(join(complement(u),composition(v,complement(composition(converse(v),u)))),complement(u)),
inference(spr,[status(thm),theory(equality)],[10,16]),
[iquote('0:SpR:10.0,16.0')] ).
cnf(258,plain,
equal(meet(top,join(converse(sk2),complement(sk1))),complement(sk1)),
inference(spr,[status(thm),theory(equality)],[78,56]),
[iquote('0:SpR:78.0,56.0')] ).
cnf(315,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[8,29]),
[iquote('0:SpR:8.0,29.0')] ).
cnf(318,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[10,315]),
[iquote('0:Rew:10.0,315.0')] ).
cnf(327,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[318,8]),
[iquote('0:SpR:318.0,8.0')] ).
cnf(333,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[318,16]),
[iquote('0:SpR:318.0,16.0')] ).
cnf(337,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[327,318]),
[iquote('0:Rew:327.0,318.0')] ).
cnf(344,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[337,333]),
[iquote('0:Rew:337.0,333.0')] ).
cnf(381,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[344,6]),
[iquote('0:SpR:344.0,6.0')] ).
cnf(387,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[46,344]),
[iquote('0:SpR:46.0,344.0')] ).
cnf(392,plain,
equal(meet(top,top),complement(zero)),
inference(rew,[status(thm),theory(equality)],[387,100]),
[iquote('0:Rew:387.0,100.0')] ).
cnf(403,plain,
equal(join(zero,complement(join(zero,join(zero,complement(complement(zero)))))),complement(zero)),
inference(rew,[status(thm),theory(equality)],[392,147]),
[iquote('0:Rew:392.0,147.0')] ).
cnf(404,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[381,79]),
[iquote('0:Rew:381.0,79.0')] ).
cnf(423,plain,
equal(join(zero,complement(zero)),complement(zero)),
inference(rew,[status(thm),theory(equality)],[387,403,404]),
[iquote('0:Rew:387.0,403.0,404.0,403.0')] ).
cnf(424,plain,
equal(complement(zero),top),
inference(rew,[status(thm),theory(equality)],[14,423]),
[iquote('0:Rew:14.0,423.0')] ).
cnf(430,plain,
equal(join(zero,join(complement(join(top,top)),u)),join(zero,u)),
inference(rew,[status(thm),theory(equality)],[424,160]),
[iquote('0:Rew:424.0,160.0')] ).
cnf(441,plain,
equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[6,404]),
[iquote('0:SpR:6.0,404.0')] ).
cnf(448,plain,
equal(complement(join(top,complement(u))),meet(zero,u)),
inference(spr,[status(thm),theory(equality)],[424,6]),
[iquote('0:SpR:424.0,6.0')] ).
cnf(454,plain,
equal(join(top,top),top),
inference(spr,[status(thm),theory(equality)],[424,344]),
[iquote('0:SpR:424.0,344.0')] ).
cnf(462,plain,
equal(join(zero,join(complement(top),u)),join(zero,u)),
inference(rew,[status(thm),theory(equality)],[454,430]),
[iquote('0:Rew:454.0,430.0')] ).
cnf(475,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(rew,[status(thm),theory(equality)],[46,462]),
[iquote('0:Rew:46.0,462.0')] ).
cnf(486,plain,
equal(join(top,join(top,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[454,4]),
[iquote('0:SpR:454.0,4.0')] ).
cnf(660,plain,
equal(meet(top,join(top,complement(u))),complement(join(zero,meet(zero,u)))),
inference(spr,[status(thm),theory(equality)],[448,56]),
[iquote('0:SpR:448.0,56.0')] ).
cnf(672,plain,
equal(meet(zero,join(zero,complement(u))),complement(join(top,meet(top,u)))),
inference(spr,[status(thm),theory(equality)],[56,448]),
[iquote('0:SpR:56.0,448.0')] ).
cnf(697,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[76,475]),
[iquote('0:SpR:76.0,475.0')] ).
cnf(703,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[697,404]),
[iquote('0:Rew:697.0,404.0')] ).
cnf(704,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[697,56]),
[iquote('0:Rew:697.0,56.0')] ).
cnf(712,plain,
equal(join(complement(u),complement(v)),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[697,441]),
[iquote('0:Rew:697.0,441.0')] ).
cnf(713,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[697,97]),
[iquote('0:Rew:697.0,97.0')] ).
cnf(716,plain,
equal(complement(join(meet(top,u),complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[697,94]),
[iquote('0:Rew:697.0,94.0')] ).
cnf(720,plain,
equal(complement(join(top,meet(top,u))),meet(zero,complement(u))),
inference(rew,[status(thm),theory(equality)],[697,672]),
[iquote('0:Rew:697.0,672.0')] ).
cnf(726,plain,
equal(meet(top,join(top,complement(u))),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[697,660]),
[iquote('0:Rew:697.0,660.0')] ).
cnf(730,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[703,704]),
[iquote('0:Rew:703.0,704.0')] ).
cnf(731,plain,
equal(join(converse(sk2),complement(sk1)),complement(sk1)),
inference(rew,[status(thm),theory(equality)],[730,258]),
[iquote('0:Rew:730.0,258.0')] ).
cnf(749,plain,
equal(complement(meet(join(meet(u,v),w),join(meet(u,v),complement(w)))),join(complement(u),complement(v))),
inference(rew,[status(thm),theory(equality)],[712,81]),
[iquote('0:Rew:712.0,81.0')] ).
cnf(759,plain,
equal(meet(zero,complement(u)),complement(join(top,u))),
inference(rew,[status(thm),theory(equality)],[730,720]),
[iquote('0:Rew:730.0,720.0')] ).
cnf(760,plain,
equal(join(top,complement(u)),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[730,726]),
[iquote('0:Rew:730.0,726.0')] ).
cnf(769,plain,
equal(complement(join(complement(u),v)),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[730,713]),
[iquote('0:Rew:730.0,713.0')] ).
cnf(771,plain,
equal(join(meet(u,v),join(meet(u,complement(v)),w)),join(u,w)),
inference(rew,[status(thm),theory(equality)],[769,159]),
[iquote('0:Rew:769.0,159.0')] ).
cnf(773,plain,
equal(complement(join(u,complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[730,716]),
[iquote('0:Rew:730.0,716.0')] ).
cnf(774,plain,
equal(join(meet(u,v),meet(complement(v),u)),u),
inference(rew,[status(thm),theory(equality)],[773,69]),
[iquote('0:Rew:773.0,69.0')] ).
cnf(783,plain,
equal(complement(meet(join(meet(u,v),w),join(meet(u,v),complement(w)))),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[712,749]),
[iquote('0:Rew:712.0,749.0')] ).
cnf(808,plain,
equal(meet(u,top),u),
inference(spr,[status(thm),theory(equality)],[730,47]),
[iquote('0:SpR:730.0,47.0')] ).
cnf(920,plain,
equal(join(sk2,converse(complement(sk1))),converse(complement(sk1))),
inference(spr,[status(thm),theory(equality)],[731,35]),
[iquote('0:SpR:731.0,35.0')] ).
cnf(1007,plain,
equal(join(u,join(v,complement(u))),join(top,v)),
inference(spr,[status(thm),theory(equality)],[3,153]),
[iquote('0:SpR:3.0,153.0')] ).
cnf(1095,plain,
equal(join(u,meet(u,complement(top))),u),
inference(spr,[status(thm),theory(equality)],[808,77]),
[iquote('0:SpR:808.0,77.0')] ).
cnf(1102,plain,
equal(join(u,meet(u,zero)),u),
inference(rew,[status(thm),theory(equality)],[46,1095]),
[iquote('0:Rew:46.0,1095.0')] ).
cnf(1124,plain,
equal(join(u,complement(u)),join(top,meet(complement(u),zero))),
inference(spr,[status(thm),theory(equality)],[1102,153]),
[iquote('0:SpR:1102.0,153.0')] ).
cnf(1134,plain,
equal(join(top,complement(join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[14,1124,759,47]),
[iquote('0:Rew:14.0,1124.0,759.0,1124.0,47.0,1124.0')] ).
cnf(1135,plain,
equal(complement(meet(zero,join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[760,1134]),
[iquote('0:Rew:760.0,1134.0')] ).
cnf(1221,plain,
equal(meet(zero,join(top,u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[1135,703]),
[iquote('0:SpR:1135.0,703.0')] ).
cnf(1249,plain,
equal(meet(zero,join(top,u)),zero),
inference(rew,[status(thm),theory(equality)],[46,1221]),
[iquote('0:Rew:46.0,1221.0')] ).
cnf(1261,plain,
equal(join(zero,meet(zero,complement(join(top,u)))),zero),
inference(spr,[status(thm),theory(equality)],[1249,77]),
[iquote('0:SpR:1249.0,77.0')] ).
cnf(1280,plain,
equal(complement(join(top,u)),zero),
inference(rew,[status(thm),theory(equality)],[697,1261,486,759]),
[iquote('0:Rew:697.0,1261.0,486.0,1261.0,759.0,1261.0')] ).
cnf(1363,plain,
equal(join(top,u),complement(zero)),
inference(spr,[status(thm),theory(equality)],[1280,703]),
[iquote('0:SpR:1280.0,703.0')] ).
cnf(1379,plain,
equal(join(top,u),top),
inference(rew,[status(thm),theory(equality)],[424,1363]),
[iquote('0:Rew:424.0,1363.0')] ).
cnf(1383,plain,
equal(join(u,join(v,complement(u))),top),
inference(rew,[status(thm),theory(equality)],[1379,1007]),
[iquote('0:Rew:1379.0,1007.0')] ).
cnf(1412,plain,
equal(join(converse(top),u),converse(top)),
inference(spr,[status(thm),theory(equality)],[1379,34]),
[iquote('0:SpR:1379.0,34.0')] ).
cnf(1463,plain,
equal(converse(top),top),
inference(spr,[status(thm),theory(equality)],[1412,14]),
[iquote('0:SpR:1412.0,14.0')] ).
cnf(1723,plain,
equal(join(u,join(v,w)),join(w,join(v,u))),
inference(spr,[status(thm),theory(equality)],[3,149]),
[iquote('0:SpR:3.0,149.0')] ).
cnf(2489,plain,
equal(join(u,composition(v,complement(composition(converse(v),complement(u))))),u),
inference(spr,[status(thm),theory(equality)],[703,205]),
[iquote('0:SpR:703.0,205.0')] ).
cnf(2892,plain,
equal(join(u,complement(meet(v,u))),top),
inference(spr,[status(thm),theory(equality)],[712,1383]),
[iquote('0:SpR:712.0,1383.0')] ).
cnf(2900,plain,
equal(complement(meet(u,complement(v))),join(complement(u),v)),
inference(spr,[status(thm),theory(equality)],[703,712]),
[iquote('0:SpR:703.0,712.0')] ).
cnf(2903,plain,
equal(complement(meet(complement(u),v)),join(u,complement(v))),
inference(spr,[status(thm),theory(equality)],[703,712]),
[iquote('0:SpR:703.0,712.0')] ).
cnf(2940,plain,
equal(complement(meet(u,meet(v,complement(u)))),top),
inference(spr,[status(thm),theory(equality)],[2892,712]),
[iquote('0:SpR:2892.0,712.0')] ).
cnf(3129,plain,
equal(meet(u,meet(v,complement(u))),complement(top)),
inference(spr,[status(thm),theory(equality)],[2940,703]),
[iquote('0:SpR:2940.0,703.0')] ).
cnf(3165,plain,
equal(meet(u,meet(v,complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[46,3129]),
[iquote('0:Rew:46.0,3129.0')] ).
cnf(3259,plain,
equal(join(zero,meet(u,complement(meet(v,complement(u))))),u),
inference(spr,[status(thm),theory(equality)],[3165,77]),
[iquote('0:SpR:3165.0,77.0')] ).
cnf(3271,plain,
equal(meet(complement(u),meet(v,u)),zero),
inference(spr,[status(thm),theory(equality)],[703,3165]),
[iquote('0:SpR:703.0,3165.0')] ).
cnf(3285,plain,
equal(meet(u,complement(meet(v,complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[697,3259]),
[iquote('0:Rew:697.0,3259.0')] ).
cnf(3286,plain,
equal(meet(u,join(complement(v),u)),u),
inference(rew,[status(thm),theory(equality)],[2900,3285]),
[iquote('0:Rew:2900.0,3285.0')] ).
cnf(3612,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[703,3286]),
[iquote('0:SpR:703.0,3286.0')] ).
cnf(3674,plain,
equal(meet(u,join(u,v)),u),
inference(spr,[status(thm),theory(equality)],[3,3612]),
[iquote('0:SpR:3.0,3612.0')] ).
cnf(3734,plain,
equal(meet(complement(join(u,v)),u),zero),
inference(spr,[status(thm),theory(equality)],[3674,3271]),
[iquote('0:SpR:3674.0,3271.0')] ).
cnf(3773,plain,
equal(meet(sk2,converse(complement(sk1))),sk2),
inference(spr,[status(thm),theory(equality)],[920,3674]),
[iquote('0:SpR:920.0,3674.0')] ).
cnf(3781,plain,
equal(meet(u,complement(join(u,v))),zero),
inference(rew,[status(thm),theory(equality)],[47,3734]),
[iquote('0:Rew:47.0,3734.0')] ).
cnf(3834,plain,
equal(join(u,meet(complement(complement(v)),u)),join(meet(u,v),u)),
inference(spr,[status(thm),theory(equality)],[774,771]),
[iquote('0:SpR:774.0,771.0')] ).
cnf(3874,plain,
equal(join(u,meet(v,u)),join(u,meet(u,v))),
inference(rew,[status(thm),theory(equality)],[703,3834,3]),
[iquote('0:Rew:703.0,3834.0,3.0,3834.0')] ).
cnf(3934,plain,
equal(join(converse(complement(sk1)),complement(sk2)),top),
inference(spr,[status(thm),theory(equality)],[3773,2892]),
[iquote('0:SpR:3773.0,2892.0')] ).
cnf(3938,plain,
equal(join(complement(sk2),converse(complement(sk1))),top),
inference(rew,[status(thm),theory(equality)],[3,3934]),
[iquote('0:Rew:3.0,3934.0')] ).
cnf(3973,plain,
equal(join(converse(complement(sk2)),complement(sk1)),converse(top)),
inference(spr,[status(thm),theory(equality)],[3938,34]),
[iquote('0:SpR:3938.0,34.0')] ).
cnf(3979,plain,
equal(join(complement(sk1),converse(complement(sk2))),top),
inference(rew,[status(thm),theory(equality)],[3,3973,1463]),
[iquote('0:Rew:3.0,3973.0,1463.0,3973.0')] ).
cnf(6828,plain,
equal(complement(meet(u,join(meet(u,v),complement(meet(complement(v),u))))),complement(meet(u,v))),
inference(spr,[status(thm),theory(equality)],[774,783]),
[iquote('0:SpR:774.0,783.0')] ).
cnf(6849,plain,
equal(complement(meet(u,join(complement(u),join(v,meet(u,v))))),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[1723,6828,2903]),
[iquote('0:Rew:1723.0,6828.0,2903.0,6828.0')] ).
cnf(12253,plain,
equal(converse(join(converse(u),meet(converse(u),v))),join(u,converse(meet(v,converse(u))))),
inference(spr,[status(thm),theory(equality)],[3874,35]),
[iquote('0:SpR:3874.0,35.0')] ).
cnf(12368,plain,
equal(join(u,converse(meet(converse(u),v))),join(u,converse(meet(v,converse(u))))),
inference(rew,[status(thm),theory(equality)],[35,12253]),
[iquote('0:Rew:35.0,12253.0')] ).
cnf(17091,plain,
equal(join(u,complement(composition(converse(one),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[337,2489]),
[iquote('0:SpR:337.0,2489.0')] ).
cnf(17101,plain,
equal(join(u,u),u),
inference(rew,[status(thm),theory(equality)],[703,17091,337,327]),
[iquote('0:Rew:703.0,17091.0,337.0,17091.0,327.0,17091.0')] ).
cnf(17320,plain,
equal(join(meet(u,v),meet(u,complement(v))),join(u,meet(u,complement(v)))),
inference(spr,[status(thm),theory(equality)],[17101,771]),
[iquote('0:SpR:17101.0,771.0')] ).
cnf(17373,plain,
equal(join(u,meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[77,17320]),
[iquote('0:Rew:77.0,17320.0')] ).
cnf(17440,plain,
equal(join(u,meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[703,17373]),
[iquote('0:SpR:703.0,17373.0')] ).
cnf(17473,plain,
equal(join(u,meet(v,u)),u),
inference(rew,[status(thm),theory(equality)],[17440,3874]),
[iquote('0:Rew:17440.0,3874.0')] ).
cnf(17488,plain,
equal(complement(meet(u,join(complement(u),v))),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[17473,6849]),
[iquote('0:Rew:17473.0,6849.0')] ).
cnf(17544,plain,
equal(join(u,converse(meet(converse(u),v))),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[17440,35]),
[iquote('0:SpR:17440.0,35.0')] ).
cnf(17661,plain,
equal(join(u,converse(meet(converse(u),v))),u),
inference(rew,[status(thm),theory(equality)],[10,17544]),
[iquote('0:Rew:10.0,17544.0')] ).
cnf(17662,plain,
equal(join(u,converse(meet(v,converse(u)))),u),
inference(rew,[status(thm),theory(equality)],[17661,12368]),
[iquote('0:Rew:17661.0,12368.0')] ).
cnf(20028,plain,
equal(complement(meet(sk1,converse(complement(sk2)))),complement(meet(sk1,top))),
inference(spr,[status(thm),theory(equality)],[3979,17488]),
[iquote('0:SpR:3979.0,17488.0')] ).
cnf(20087,plain,
equal(complement(meet(sk1,converse(complement(sk2)))),complement(sk1)),
inference(rew,[status(thm),theory(equality)],[808,20028]),
[iquote('0:Rew:808.0,20028.0')] ).
cnf(21566,plain,
equal(meet(sk1,converse(complement(sk2))),complement(complement(sk1))),
inference(spr,[status(thm),theory(equality)],[20087,703]),
[iquote('0:SpR:20087.0,703.0')] ).
cnf(21618,plain,
equal(meet(sk1,converse(complement(sk2))),sk1),
inference(rew,[status(thm),theory(equality)],[703,21566]),
[iquote('0:Rew:703.0,21566.0')] ).
cnf(21699,plain,
equal(join(complement(sk2),converse(sk1)),complement(sk2)),
inference(spr,[status(thm),theory(equality)],[21618,17662]),
[iquote('0:SpR:21618.0,17662.0')] ).
cnf(21730,plain,
equal(join(converse(sk1),complement(sk2)),complement(sk2)),
inference(rew,[status(thm),theory(equality)],[3,21699]),
[iquote('0:Rew:3.0,21699.0')] ).
cnf(22055,plain,
equal(meet(converse(sk1),complement(complement(sk2))),zero),
inference(spr,[status(thm),theory(equality)],[21730,3781]),
[iquote('0:SpR:21730.0,3781.0')] ).
cnf(22081,plain,
equal(meet(sk2,converse(sk1)),zero),
inference(rew,[status(thm),theory(equality)],[47,22055,703]),
[iquote('0:Rew:47.0,22055.0,703.0,22055.0')] ).
cnf(22082,plain,
$false,
inference(mrr,[status(thm)],[22081,48]),
[iquote('0:MRR:22081.0,48.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : REL007-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 11:53:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 4.37/4.55
% 4.37/4.55 SPASS V 3.9
% 4.37/4.55 SPASS beiseite: Proof found.
% 4.37/4.55 % SZS status Theorem
% 4.37/4.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.37/4.55 SPASS derived 13603 clauses, backtracked 0 clauses, performed 0 splits and kept 1952 clauses.
% 4.37/4.55 SPASS allocated 82731 KBytes.
% 4.37/4.55 SPASS spent 0:00:04.19 on the problem.
% 4.37/4.55 0:00:00.04 for the input.
% 4.37/4.55 0:00:00.00 for the FLOTTER CNF translation.
% 4.37/4.55 0:00:00.12 for inferences.
% 4.37/4.55 0:00:00.00 for the backtracking.
% 4.37/4.55 0:00:03.99 for the reduction.
% 4.37/4.55
% 4.37/4.55
% 4.37/4.55 Here is a proof with depth 15, length 158 :
% 4.37/4.55 % SZS output start Refutation
% See solution above
% 4.50/4.73 Formulae used in the proof : goals_14 goals_15 maddux1_join_commutativity_1 maddux2_join_associativity_2 maddux3_a_kind_of_de_Morgan_3 maddux4_definiton_of_meet_4 composition_identity_6 converse_idempotence_8 converse_additivity_9 converse_multiplicativity_10 converse_cancellativity_11 def_top_12 def_zero_13
% 4.50/4.73
%------------------------------------------------------------------------------