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 : n025.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 20:01:30 EDT 2022
% Result : Theorem 3.49s 3.65s
% Output : Refutation 3.62s
% 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(composition(u,one),u),
file('REL007+1.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL007+1.p',unknown),
[] ).
cnf(3,axiom,
equal(meet(skc2,converse(skc3)),zero),
file('REL007+1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(u,complement(u)),top),
file('REL007+1.p',unknown),
[] ).
cnf(5,axiom,
equal(meet(u,complement(u)),zero),
file('REL007+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(meet(converse(skc2),skc3),zero),
file('REL007+1.p',unknown),
[] ).
cnf(7,axiom,
equal(join(u,v),join(v,u)),
file('REL007+1.p',unknown),
[] ).
cnf(8,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL007+1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL007+1.p',unknown),
[] ).
cnf(10,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL007+1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL007+1.p',unknown),
[] ).
cnf(14,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL007+1.p',unknown),
[] ).
cnf(15,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
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)],[7,14]),
[iquote('0:Rew:7.0,14.0')] ).
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)],[2,10]),
[iquote('0:SpR:2.0,10.0')] ).
cnf(34,plain,
equal(converse(join(u,converse(v))),join(converse(u),v)),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(35,plain,
equal(converse(join(converse(u),v)),join(u,converse(v))),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(40,plain,
equal(meet(join(complement(u),complement(v)),w),complement(join(meet(u,v),complement(w)))),
inference(spr,[status(thm),theory(equality)],[8]),
[iquote('0:SpR:8.0,8.0')] ).
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(44,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[7,8]),
[iquote('0:SpR:7.0,8.0')] ).
cnf(46,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[5,43]),
[iquote('0:Rew:5.0,43.0')] ).
cnf(47,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[8,44]),
[iquote('0:Rew:8.0,44.0')] ).
cnf(48,plain,
~ equal(meet(skc3,converse(skc2)),zero),
inference(rew,[status(thm),theory(equality)],[47,6]),
[iquote('0:Rew:47.0,6.0')] ).
cnf(54,plain,
equal(meet(top,zero),zero),
inference(spr,[status(thm),theory(equality)],[46,5]),
[iquote('0:SpR:46.0,5.0')] ).
cnf(56,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(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)],[8,17]),
[iquote('0:SpR:8.0,17.0')] ).
cnf(68,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(69,plain,
equal(join(meet(u,v),complement(join(v,complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[7,17]),
[iquote('0:SpR:7.0,17.0')] ).
cnf(71,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(72,plain,
equal(join(zero,complement(join(complement(skc2),converse(skc3)))),skc2),
inference(spr,[status(thm),theory(equality)],[3,17]),
[iquote('0:SpR:3.0,17.0')] ).
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(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)],[7,74]),
[iquote('0:Rew:7.0,74.0')] ).
cnf(76,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[7,68,46]),
[iquote('0:Rew:7.0,68.0,46.0,68.0')] ).
cnf(77,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[7,71]),
[iquote('0:Rew:7.0,71.0')] ).
cnf(78,plain,
equal(join(zero,complement(join(converse(skc3),complement(skc2)))),skc2),
inference(rew,[status(thm),theory(equality)],[7,72]),
[iquote('0:Rew:7.0,72.0')] ).
cnf(79,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[8,73]),
[iquote('0:Rew:8.0,73.0')] ).
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)],[7,66]),
[iquote('0:Rew:7.0,66.0')] ).
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)],[56,8]),
[iquote('0:SpR:56.0,8.0')] ).
cnf(97,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,join(zero,complement(v)))),
inference(spr,[status(thm),theory(equality)],[56,8]),
[iquote('0:SpR:56.0,8.0')] ).
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)],[100,5]),
[iquote('0:SpR:100.0,5.0')] ).
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)],[7,140]),
[iquote('0:Rew:7.0,140.0')] ).
cnf(147,plain,
equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[11,146]),
[iquote('0:Rew:11.0,146.0')] ).
cnf(149,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[11,7]),
[iquote('0:SpR:11.0,7.0')] ).
cnf(153,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(159,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(160,plain,
equal(join(zero,join(complement(join(top,complement(zero))),u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[75,11]),
[iquote('0:SpR:75.0,11.0')] ).
cnf(205,plain,
equal(join(complement(u),composition(v,complement(composition(converse(v),u)))),complement(u)),
inference(spr,[status(thm),theory(equality)],[2,16]),
[iquote('0:SpR:2.0,16.0')] ).
cnf(258,plain,
equal(meet(top,join(converse(skc3),complement(skc2))),complement(skc2)),
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)],[1,29]),
[iquote('0:SpR:1.0,29.0')] ).
cnf(318,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[2,315]),
[iquote('0:Rew:2.0,315.0')] ).
cnf(327,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[318,1]),
[iquote('0:SpR:318.0,1.0')] ).
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)],[344,8]),
[iquote('0:SpR:344.0,8.0')] ).
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)],[4,423]),
[iquote('0:Rew:4.0,423.0')] ).
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)],[8,404]),
[iquote('0:SpR:8.0,404.0')] ).
cnf(448,plain,
equal(complement(join(top,complement(u))),meet(zero,u)),
inference(spr,[status(thm),theory(equality)],[424,8]),
[iquote('0:SpR:424.0,8.0')] ).
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)],[454,11]),
[iquote('0:SpR:454.0,11.0')] ).
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(skc3),complement(skc2)),complement(skc2)),
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(skc3,converse(complement(skc2))),converse(complement(skc2))),
inference(spr,[status(thm),theory(equality)],[731,35]),
[iquote('0:SpR:731.0,35.0')] ).
cnf(1008,plain,
equal(join(u,join(v,complement(u))),join(top,v)),
inference(spr,[status(thm),theory(equality)],[7,153]),
[iquote('0:SpR:7.0,153.0')] ).
cnf(1096,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(1103,plain,
equal(join(u,meet(u,zero)),u),
inference(rew,[status(thm),theory(equality)],[46,1096]),
[iquote('0:Rew:46.0,1096.0')] ).
cnf(1125,plain,
equal(join(u,complement(u)),join(top,meet(complement(u),zero))),
inference(spr,[status(thm),theory(equality)],[1103,153]),
[iquote('0:SpR:1103.0,153.0')] ).
cnf(1135,plain,
equal(join(top,complement(join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[4,1125,759,47]),
[iquote('0:Rew:4.0,1125.0,759.0,1125.0,47.0,1125.0')] ).
cnf(1136,plain,
equal(complement(meet(zero,join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[760,1135]),
[iquote('0:Rew:760.0,1135.0')] ).
cnf(1222,plain,
equal(meet(zero,join(top,u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[1136,703]),
[iquote('0:SpR:1136.0,703.0')] ).
cnf(1252,plain,
equal(meet(zero,join(top,u)),zero),
inference(rew,[status(thm),theory(equality)],[46,1222]),
[iquote('0:Rew:46.0,1222.0')] ).
cnf(1264,plain,
equal(join(zero,meet(zero,complement(join(top,u)))),zero),
inference(spr,[status(thm),theory(equality)],[1252,77]),
[iquote('0:SpR:1252.0,77.0')] ).
cnf(1284,plain,
equal(complement(join(top,u)),zero),
inference(rew,[status(thm),theory(equality)],[697,1264,486,759]),
[iquote('0:Rew:697.0,1264.0,486.0,1264.0,759.0,1264.0')] ).
cnf(1367,plain,
equal(join(top,u),complement(zero)),
inference(spr,[status(thm),theory(equality)],[1284,703]),
[iquote('0:SpR:1284.0,703.0')] ).
cnf(1384,plain,
equal(join(top,u),top),
inference(rew,[status(thm),theory(equality)],[424,1367]),
[iquote('0:Rew:424.0,1367.0')] ).
cnf(1388,plain,
equal(join(u,join(v,complement(u))),top),
inference(rew,[status(thm),theory(equality)],[1384,1008]),
[iquote('0:Rew:1384.0,1008.0')] ).
cnf(1417,plain,
equal(join(converse(top),u),converse(top)),
inference(spr,[status(thm),theory(equality)],[1384,34]),
[iquote('0:SpR:1384.0,34.0')] ).
cnf(1468,plain,
equal(converse(top),top),
inference(spr,[status(thm),theory(equality)],[1417,4]),
[iquote('0:SpR:1417.0,4.0')] ).
cnf(1728,plain,
equal(join(u,join(v,w)),join(w,join(v,u))),
inference(spr,[status(thm),theory(equality)],[7,149]),
[iquote('0:SpR:7.0,149.0')] ).
cnf(2494,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(2897,plain,
equal(join(u,complement(meet(v,u))),top),
inference(spr,[status(thm),theory(equality)],[712,1388]),
[iquote('0:SpR:712.0,1388.0')] ).
cnf(2905,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(2908,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(2945,plain,
equal(complement(meet(u,meet(v,complement(u)))),top),
inference(spr,[status(thm),theory(equality)],[2897,712]),
[iquote('0:SpR:2897.0,712.0')] ).
cnf(3134,plain,
equal(meet(u,meet(v,complement(u))),complement(top)),
inference(spr,[status(thm),theory(equality)],[2945,703]),
[iquote('0:SpR:2945.0,703.0')] ).
cnf(3170,plain,
equal(meet(u,meet(v,complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[46,3134]),
[iquote('0:Rew:46.0,3134.0')] ).
cnf(3264,plain,
equal(join(zero,meet(u,complement(meet(v,complement(u))))),u),
inference(spr,[status(thm),theory(equality)],[3170,77]),
[iquote('0:SpR:3170.0,77.0')] ).
cnf(3276,plain,
equal(meet(complement(u),meet(v,u)),zero),
inference(spr,[status(thm),theory(equality)],[703,3170]),
[iquote('0:SpR:703.0,3170.0')] ).
cnf(3290,plain,
equal(meet(u,complement(meet(v,complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[697,3264]),
[iquote('0:Rew:697.0,3264.0')] ).
cnf(3291,plain,
equal(meet(u,join(complement(v),u)),u),
inference(rew,[status(thm),theory(equality)],[2905,3290]),
[iquote('0:Rew:2905.0,3290.0')] ).
cnf(3617,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[703,3291]),
[iquote('0:SpR:703.0,3291.0')] ).
cnf(3679,plain,
equal(meet(u,join(u,v)),u),
inference(spr,[status(thm),theory(equality)],[7,3617]),
[iquote('0:SpR:7.0,3617.0')] ).
cnf(3739,plain,
equal(meet(complement(join(u,v)),u),zero),
inference(spr,[status(thm),theory(equality)],[3679,3276]),
[iquote('0:SpR:3679.0,3276.0')] ).
cnf(3778,plain,
equal(meet(skc3,converse(complement(skc2))),skc3),
inference(spr,[status(thm),theory(equality)],[920,3679]),
[iquote('0:SpR:920.0,3679.0')] ).
cnf(3786,plain,
equal(meet(u,complement(join(u,v))),zero),
inference(rew,[status(thm),theory(equality)],[47,3739]),
[iquote('0:Rew:47.0,3739.0')] ).
cnf(3839,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(3879,plain,
equal(join(u,meet(v,u)),join(u,meet(u,v))),
inference(rew,[status(thm),theory(equality)],[703,3839,7]),
[iquote('0:Rew:703.0,3839.0,7.0,3839.0')] ).
cnf(3939,plain,
equal(join(converse(complement(skc2)),complement(skc3)),top),
inference(spr,[status(thm),theory(equality)],[3778,2897]),
[iquote('0:SpR:3778.0,2897.0')] ).
cnf(3943,plain,
equal(join(complement(skc3),converse(complement(skc2))),top),
inference(rew,[status(thm),theory(equality)],[7,3939]),
[iquote('0:Rew:7.0,3939.0')] ).
cnf(3978,plain,
equal(join(converse(complement(skc3)),complement(skc2)),converse(top)),
inference(spr,[status(thm),theory(equality)],[3943,34]),
[iquote('0:SpR:3943.0,34.0')] ).
cnf(3984,plain,
equal(join(complement(skc2),converse(complement(skc3))),top),
inference(rew,[status(thm),theory(equality)],[7,3978,1468]),
[iquote('0:Rew:7.0,3978.0,1468.0,3978.0')] ).
cnf(6833,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(6854,plain,
equal(complement(meet(u,join(complement(u),join(v,meet(u,v))))),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[1728,6833,2908]),
[iquote('0:Rew:1728.0,6833.0,2908.0,6833.0')] ).
cnf(12258,plain,
equal(converse(join(converse(u),meet(converse(u),v))),join(u,converse(meet(v,converse(u))))),
inference(spr,[status(thm),theory(equality)],[3879,35]),
[iquote('0:SpR:3879.0,35.0')] ).
cnf(12373,plain,
equal(join(u,converse(meet(converse(u),v))),join(u,converse(meet(v,converse(u))))),
inference(rew,[status(thm),theory(equality)],[35,12258]),
[iquote('0:Rew:35.0,12258.0')] ).
cnf(17096,plain,
equal(join(u,complement(composition(converse(one),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[337,2494]),
[iquote('0:SpR:337.0,2494.0')] ).
cnf(17106,plain,
equal(join(u,u),u),
inference(rew,[status(thm),theory(equality)],[703,17096,337,327]),
[iquote('0:Rew:703.0,17096.0,337.0,17096.0,327.0,17096.0')] ).
cnf(17325,plain,
equal(join(meet(u,v),meet(u,complement(v))),join(u,meet(u,complement(v)))),
inference(spr,[status(thm),theory(equality)],[17106,771]),
[iquote('0:SpR:17106.0,771.0')] ).
cnf(17378,plain,
equal(join(u,meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[77,17325]),
[iquote('0:Rew:77.0,17325.0')] ).
cnf(17445,plain,
equal(join(u,meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[703,17378]),
[iquote('0:SpR:703.0,17378.0')] ).
cnf(17478,plain,
equal(join(u,meet(v,u)),u),
inference(rew,[status(thm),theory(equality)],[17445,3879]),
[iquote('0:Rew:17445.0,3879.0')] ).
cnf(17493,plain,
equal(complement(meet(u,join(complement(u),v))),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[17478,6854]),
[iquote('0:Rew:17478.0,6854.0')] ).
cnf(17549,plain,
equal(join(u,converse(meet(converse(u),v))),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[17445,35]),
[iquote('0:SpR:17445.0,35.0')] ).
cnf(17666,plain,
equal(join(u,converse(meet(converse(u),v))),u),
inference(rew,[status(thm),theory(equality)],[2,17549]),
[iquote('0:Rew:2.0,17549.0')] ).
cnf(17667,plain,
equal(join(u,converse(meet(v,converse(u)))),u),
inference(rew,[status(thm),theory(equality)],[17666,12373]),
[iquote('0:Rew:17666.0,12373.0')] ).
cnf(20033,plain,
equal(complement(meet(skc2,converse(complement(skc3)))),complement(meet(skc2,top))),
inference(spr,[status(thm),theory(equality)],[3984,17493]),
[iquote('0:SpR:3984.0,17493.0')] ).
cnf(20092,plain,
equal(complement(meet(skc2,converse(complement(skc3)))),complement(skc2)),
inference(rew,[status(thm),theory(equality)],[730,20033,47]),
[iquote('0:Rew:730.0,20033.0,47.0,20033.0')] ).
cnf(21571,plain,
equal(meet(skc2,converse(complement(skc3))),complement(complement(skc2))),
inference(spr,[status(thm),theory(equality)],[20092,703]),
[iquote('0:SpR:20092.0,703.0')] ).
cnf(21623,plain,
equal(meet(skc2,converse(complement(skc3))),skc2),
inference(rew,[status(thm),theory(equality)],[703,21571]),
[iquote('0:Rew:703.0,21571.0')] ).
cnf(21704,plain,
equal(join(complement(skc3),converse(skc2)),complement(skc3)),
inference(spr,[status(thm),theory(equality)],[21623,17667]),
[iquote('0:SpR:21623.0,17667.0')] ).
cnf(21735,plain,
equal(join(converse(skc2),complement(skc3)),complement(skc3)),
inference(rew,[status(thm),theory(equality)],[7,21704]),
[iquote('0:Rew:7.0,21704.0')] ).
cnf(22060,plain,
equal(meet(converse(skc2),complement(complement(skc3))),zero),
inference(spr,[status(thm),theory(equality)],[21735,3786]),
[iquote('0:SpR:21735.0,3786.0')] ).
cnf(22086,plain,
equal(meet(skc3,converse(skc2)),zero),
inference(rew,[status(thm),theory(equality)],[47,22060,703]),
[iquote('0:Rew:47.0,22060.0,703.0,22060.0')] ).
cnf(22087,plain,
$false,
inference(mrr,[status(thm)],[22086,48]),
[iquote('0:MRR:22086.0,48.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : REL007+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.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 13:50:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.49/3.65
% 3.49/3.65 SPASS V 3.9
% 3.49/3.65 SPASS beiseite: Proof found.
% 3.49/3.65 % SZS status Theorem
% 3.49/3.65 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.49/3.65 SPASS derived 13607 clauses, backtracked 0 clauses, performed 0 splits and kept 1952 clauses.
% 3.49/3.65 SPASS allocated 104707 KBytes.
% 3.49/3.65 SPASS spent 0:00:03.29 on the problem.
% 3.49/3.65 0:00:00.04 for the input.
% 3.49/3.65 0:00:00.02 for the FLOTTER CNF translation.
% 3.49/3.65 0:00:00.09 for inferences.
% 3.49/3.65 0:00:00.00 for the backtracking.
% 3.49/3.65 0:00:03.10 for the reduction.
% 3.49/3.65
% 3.49/3.65
% 3.49/3.65 Here is a proof with depth 15, length 158 :
% 3.49/3.65 % SZS output start Refutation
% See solution above
% 3.62/3.79 Formulae used in the proof : composition_identity converse_idempotence goals def_top def_zero maddux1_join_commutativity maddux4_definiton_of_meet converse_additivity converse_multiplicativity maddux2_join_associativity converse_cancellativity maddux3_a_kind_of_de_Morgan
% 3.62/3.79
%------------------------------------------------------------------------------