TSTP Solution File: REL012+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL012+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 20:01:38 EDT 2022
% Result : Theorem 285.36s 285.58s
% Output : Refutation 291.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 12
% 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('REL012+1.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL012+1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,complement(u)),top),
file('REL012+1.p',unknown),
[] ).
cnf(4,axiom,
equal(meet(u,complement(u)),zero),
file('REL012+1.p',unknown),
[] ).
cnf(5,axiom,
equal(join(u,v),join(v,u)),
file('REL012+1.p',unknown),
[] ).
cnf(6,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL012+1.p',unknown),
[] ).
cnf(7,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL012+1.p',unknown),
[] ).
cnf(8,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL012+1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL012+1.p',unknown),
[] ).
cnf(12,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL012+1.p',unknown),
[] ).
cnf(13,axiom,
~ equal(join(composition(complement(composition(skc3,skc2)),converse(skc2)),complement(skc3)),complement(skc3)),
file('REL012+1.p',unknown),
[] ).
cnf(14,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL012+1.p',unknown),
[] ).
cnf(15,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[5,12]),
[iquote('0:Rew:5.0,12.0')] ).
cnf(16,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[6,14]),
[iquote('0:Rew:6.0,14.0')] ).
cnf(17,plain,
~ equal(join(complement(skc3),composition(complement(composition(skc3,skc2)),converse(skc2))),complement(skc3)),
inference(rew,[status(thm),theory(equality)],[5,13]),
[iquote('0:Rew:5.0,13.0')] ).
cnf(28,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(29,plain,
equal(converse(composition(u,converse(v))),composition(v,converse(u))),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(34,plain,
equal(converse(join(converse(u),v)),join(u,converse(v))),
inference(spr,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
cnf(72,plain,
equal(join(join(complement(u),complement(v)),meet(u,v)),top),
inference(spr,[status(thm),theory(equality)],[6,3]),
[iquote('0:SpR:6.0,3.0')] ).
cnf(73,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(76,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(77,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[5,6]),
[iquote('0:SpR:5.0,6.0')] ).
cnf(79,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[4,76]),
[iquote('0:Rew:4.0,76.0')] ).
cnf(80,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[6,77]),
[iquote('0:Rew:6.0,77.0')] ).
cnf(83,plain,
equal(join(meet(u,v),join(complement(u),complement(v))),top),
inference(rew,[status(thm),theory(equality)],[5,72]),
[iquote('0:Rew:5.0,72.0')] ).
cnf(87,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)],[6,16]),
[iquote('0:SpR:6.0,16.0')] ).
cnf(88,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[3,16]),
[iquote('0:SpR:3.0,16.0')] ).
cnf(89,plain,
equal(join(meet(u,v),complement(join(v,complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[5,16]),
[iquote('0:SpR:5.0,16.0')] ).
cnf(91,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[6,16]),
[iquote('0:SpR:6.0,16.0')] ).
cnf(92,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[4,16]),
[iquote('0:SpR:4.0,16.0')] ).
cnf(93,plain,
equal(join(complement(top),meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[5,88]),
[iquote('0:Rew:5.0,88.0')] ).
cnf(94,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[79,93]),
[iquote('0:Rew:79.0,93.0')] ).
cnf(95,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[5,91]),
[iquote('0:Rew:5.0,91.0')] ).
cnf(96,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[6,92]),
[iquote('0:Rew:6.0,92.0')] ).
cnf(97,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)],[5,87]),
[iquote('0:Rew:5.0,87.0')] ).
cnf(98,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)],[73,97]),
[iquote('0:Rew:73.0,97.0')] ).
cnf(101,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[79,6]),
[iquote('0:SpR:79.0,6.0')] ).
cnf(102,plain,
equal(join(meet(top,u),complement(join(zero,u))),top),
inference(spr,[status(thm),theory(equality)],[79,16]),
[iquote('0:SpR:79.0,16.0')] ).
cnf(119,plain,
equal(join(meet(u,v),complement(join(complement(v),u))),v),
inference(spr,[status(thm),theory(equality)],[80,16]),
[iquote('0:SpR:80.0,16.0')] ).
cnf(132,plain,
equal(complement(join(meet(top,u),complement(v))),meet(join(zero,complement(u)),v)),
inference(spr,[status(thm),theory(equality)],[101,6]),
[iquote('0:SpR:101.0,6.0')] ).
cnf(135,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,join(zero,complement(v)))),
inference(spr,[status(thm),theory(equality)],[101,6]),
[iquote('0:SpR:101.0,6.0')] ).
cnf(154,plain,
equal(join(u,join(v,complement(join(u,v)))),top),
inference(spr,[status(thm),theory(equality)],[9,3]),
[iquote('0:SpR:9.0,3.0')] ).
cnf(155,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(161,plain,
equal(join(u,join(complement(u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[3,9]),
[iquote('0:SpR:3.0,9.0')] ).
cnf(165,plain,
equal(join(meet(u,v),join(complement(join(complement(u),v)),w)),join(u,w)),
inference(spr,[status(thm),theory(equality)],[16,9]),
[iquote('0:SpR:16.0,9.0')] ).
cnf(169,plain,
equal(join(complement(u),join(meet(v,u),complement(v))),top),
inference(rew,[status(thm),theory(equality)],[155,83]),
[iquote('0:Rew:155.0,83.0')] ).
cnf(175,plain,
equal(join(complement(u),join(complement(v),meet(v,u))),top),
inference(rew,[status(thm),theory(equality)],[5,169]),
[iquote('0:Rew:5.0,169.0')] ).
cnf(213,plain,
equal(join(complement(converse(u)),composition(converse(converse(v)),complement(converse(composition(u,v))))),complement(converse(u))),
inference(spr,[status(thm),theory(equality)],[8,15]),
[iquote('0:SpR:8.0,15.0')] ).
cnf(215,plain,
equal(join(complement(u),composition(v,complement(composition(converse(v),u)))),complement(u)),
inference(spr,[status(thm),theory(equality)],[2,15]),
[iquote('0:SpR:2.0,15.0')] ).
cnf(223,plain,
equal(join(complement(converse(u)),composition(v,complement(converse(composition(u,v))))),complement(converse(u))),
inference(rew,[status(thm),theory(equality)],[2,213]),
[iquote('0:Rew:2.0,213.0')] ).
cnf(391,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[1,28]),
[iquote('0:SpR:1.0,28.0')] ).
cnf(394,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[2,391]),
[iquote('0:Rew:2.0,391.0')] ).
cnf(403,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[394,1]),
[iquote('0:SpR:394.0,1.0')] ).
cnf(409,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[394,15]),
[iquote('0:SpR:394.0,15.0')] ).
cnf(413,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[403,394]),
[iquote('0:Rew:403.0,394.0')] ).
cnf(420,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[413,409]),
[iquote('0:Rew:413.0,409.0')] ).
cnf(456,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[420,6]),
[iquote('0:SpR:420.0,6.0')] ).
cnf(462,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[79,420]),
[iquote('0:SpR:79.0,420.0')] ).
cnf(480,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[456,96]),
[iquote('0:Rew:456.0,96.0')] ).
cnf(507,plain,
equal(meet(top,complement(u)),complement(u)),
inference(spr,[status(thm),theory(equality)],[480,101]),
[iquote('0:SpR:480.0,101.0')] ).
cnf(512,plain,
equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[6,480]),
[iquote('0:SpR:6.0,480.0')] ).
cnf(536,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[462,9]),
[iquote('0:SpR:462.0,9.0')] ).
cnf(550,plain,
equal(join(complement(u),complement(join(zero,complement(u)))),top),
inference(spr,[status(thm),theory(equality)],[507,102]),
[iquote('0:SpR:507.0,102.0')] ).
cnf(557,plain,
equal(join(complement(u),meet(top,u)),top),
inference(rew,[status(thm),theory(equality)],[101,550]),
[iquote('0:Rew:101.0,550.0')] ).
cnf(575,plain,
equal(join(complement(u),join(meet(top,u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[557,9]),
[iquote('0:SpR:557.0,9.0')] ).
cnf(732,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[94,536]),
[iquote('0:SpR:94.0,536.0')] ).
cnf(738,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[732,480]),
[iquote('0:Rew:732.0,480.0')] ).
cnf(739,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[732,101]),
[iquote('0:Rew:732.0,101.0')] ).
cnf(754,plain,
equal(join(complement(u),complement(v)),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[732,512]),
[iquote('0:Rew:732.0,512.0')] ).
cnf(756,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[732,135]),
[iquote('0:Rew:732.0,135.0')] ).
cnf(757,plain,
equal(complement(join(meet(top,u),complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[732,132]),
[iquote('0:Rew:732.0,132.0')] ).
cnf(761,plain,
equal(meet(u,u),u),
inference(rew,[status(thm),theory(equality)],[738,456]),
[iquote('0:Rew:738.0,456.0')] ).
cnf(767,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[738,739]),
[iquote('0:Rew:738.0,739.0')] ).
cnf(769,plain,
equal(join(complement(u),join(u,v)),join(top,v)),
inference(rew,[status(thm),theory(equality)],[767,575]),
[iquote('0:Rew:767.0,575.0')] ).
cnf(789,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)],[754,98]),
[iquote('0:Rew:754.0,98.0')] ).
cnf(795,plain,
equal(join(u,join(v,complement(u))),join(top,v)),
inference(rew,[status(thm),theory(equality)],[155,769]),
[iquote('0:Rew:155.0,769.0')] ).
cnf(802,plain,
equal(complement(join(complement(u),v)),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[767,756]),
[iquote('0:Rew:767.0,756.0')] ).
cnf(804,plain,
equal(join(meet(u,v),meet(v,complement(u))),v),
inference(rew,[status(thm),theory(equality)],[802,119]),
[iquote('0:Rew:802.0,119.0')] ).
cnf(805,plain,
equal(join(meet(u,v),join(meet(u,complement(v)),w)),join(u,w)),
inference(rew,[status(thm),theory(equality)],[802,165]),
[iquote('0:Rew:802.0,165.0')] ).
cnf(806,plain,
equal(complement(join(u,complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[767,757]),
[iquote('0:Rew:767.0,757.0')] ).
cnf(807,plain,
equal(join(meet(u,v),meet(complement(v),u)),u),
inference(rew,[status(thm),theory(equality)],[806,89]),
[iquote('0:Rew:806.0,89.0')] ).
cnf(815,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)],[754,789]),
[iquote('0:Rew:754.0,789.0')] ).
cnf(817,plain,
equal(join(u,zero),u),
inference(spr,[status(thm),theory(equality)],[732,5]),
[iquote('0:SpR:732.0,5.0')] ).
cnf(876,plain,
equal(join(u,converse(complement(converse(u)))),converse(top)),
inference(spr,[status(thm),theory(equality)],[3,34]),
[iquote('0:SpR:3.0,34.0')] ).
cnf(1092,plain,
equal(join(top,converse(complement(converse(complement(u))))),join(u,converse(top))),
inference(spr,[status(thm),theory(equality)],[876,161]),
[iquote('0:SpR:876.0,161.0')] ).
cnf(1482,plain,
equal(join(complement(u),join(complement(u),u)),top),
inference(spr,[status(thm),theory(equality)],[761,175]),
[iquote('0:SpR:761.0,175.0')] ).
cnf(1494,plain,
equal(join(top,complement(u)),top),
inference(rew,[status(thm),theory(equality)],[5,1482,3]),
[iquote('0:Rew:5.0,1482.0,3.0,1482.0,5.0,1482.0')] ).
cnf(1505,plain,
equal(join(u,top),top),
inference(spr,[status(thm),theory(equality)],[1494,154]),
[iquote('0:SpR:1494.0,154.0')] ).
cnf(1509,plain,
equal(join(top,u),top),
inference(spr,[status(thm),theory(equality)],[738,1494]),
[iquote('0:SpR:738.0,1494.0')] ).
cnf(1513,plain,
equal(join(u,converse(top)),top),
inference(rew,[status(thm),theory(equality)],[1509,1092]),
[iquote('0:Rew:1509.0,1092.0')] ).
cnf(1520,plain,
equal(join(u,join(v,complement(u))),top),
inference(rew,[status(thm),theory(equality)],[1509,795]),
[iquote('0:Rew:1509.0,795.0')] ).
cnf(1530,plain,
equal(join(u,converse(top)),converse(top)),
inference(spr,[status(thm),theory(equality)],[1505,34]),
[iquote('0:SpR:1505.0,34.0')] ).
cnf(1535,plain,
equal(converse(top),top),
inference(rew,[status(thm),theory(equality)],[1513,1530]),
[iquote('0:Rew:1513.0,1530.0')] ).
cnf(1536,plain,
equal(join(u,converse(complement(converse(u)))),top),
inference(rew,[status(thm),theory(equality)],[1535,876]),
[iquote('0:Rew:1535.0,876.0')] ).
cnf(2555,plain,
equal(join(u,composition(v,complement(composition(converse(v),complement(u))))),u),
inference(spr,[status(thm),theory(equality)],[738,215]),
[iquote('0:SpR:738.0,215.0')] ).
cnf(3505,plain,
equal(join(u,complement(meet(u,v))),top),
inference(spr,[status(thm),theory(equality)],[805,1520]),
[iquote('0:SpR:805.0,1520.0')] ).
cnf(3544,plain,
equal(join(u,meet(complement(complement(v)),u)),join(meet(u,v),u)),
inference(spr,[status(thm),theory(equality)],[807,805]),
[iquote('0:SpR:807.0,805.0')] ).
cnf(3574,plain,
equal(join(u,meet(v,u)),join(u,meet(u,v))),
inference(rew,[status(thm),theory(equality)],[738,3544,5]),
[iquote('0:Rew:738.0,3544.0,5.0,3544.0')] ).
cnf(6838,plain,
equal(complement(meet(u,join(meet(u,v),complement(meet(u,complement(v)))))),complement(meet(u,v))),
inference(spr,[status(thm),theory(equality)],[95,815]),
[iquote('0:SpR:95.0,815.0')] ).
cnf(7265,plain,
equal(complement(meet(u,meet(complement(u),v))),top),
inference(spr,[status(thm),theory(equality)],[754,3505]),
[iquote('0:SpR:754.0,3505.0')] ).
cnf(7290,plain,
equal(complement(meet(u,complement(v))),join(complement(u),v)),
inference(spr,[status(thm),theory(equality)],[738,754]),
[iquote('0:SpR:738.0,754.0')] ).
cnf(7293,plain,
equal(complement(meet(complement(u),v)),join(u,complement(v))),
inference(spr,[status(thm),theory(equality)],[738,754]),
[iquote('0:SpR:738.0,754.0')] ).
cnf(7303,plain,
equal(complement(meet(u,join(meet(u,v),join(complement(u),v)))),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[7290,6838]),
[iquote('0:Rew:7290.0,6838.0')] ).
cnf(7330,plain,
equal(complement(meet(u,join(complement(u),join(v,meet(u,v))))),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[155,7303]),
[iquote('0:Rew:155.0,7303.0')] ).
cnf(7335,plain,
equal(meet(u,meet(complement(u),v)),complement(top)),
inference(spr,[status(thm),theory(equality)],[7265,738]),
[iquote('0:SpR:7265.0,738.0')] ).
cnf(7379,plain,
equal(meet(u,meet(complement(u),v)),zero),
inference(rew,[status(thm),theory(equality)],[79,7335]),
[iquote('0:Rew:79.0,7335.0')] ).
cnf(7410,plain,
equal(join(zero,meet(u,complement(meet(complement(u),v)))),u),
inference(spr,[status(thm),theory(equality)],[7379,95]),
[iquote('0:SpR:7379.0,95.0')] ).
cnf(7425,plain,
equal(meet(complement(u),meet(u,v)),zero),
inference(spr,[status(thm),theory(equality)],[738,7379]),
[iquote('0:SpR:738.0,7379.0')] ).
cnf(7441,plain,
equal(meet(u,complement(meet(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[732,7410]),
[iquote('0:Rew:732.0,7410.0')] ).
cnf(7442,plain,
equal(meet(u,join(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[7293,7441]),
[iquote('0:Rew:7293.0,7441.0')] ).
cnf(7459,plain,
equal(meet(complement(u),meet(v,u)),zero),
inference(spr,[status(thm),theory(equality)],[80,7425]),
[iquote('0:SpR:80.0,7425.0')] ).
cnf(7713,plain,
equal(meet(u,join(u,v)),u),
inference(spr,[status(thm),theory(equality)],[738,7442]),
[iquote('0:SpR:738.0,7442.0')] ).
cnf(7756,plain,
equal(join(meet(join(complement(u),v),u),complement(u)),join(complement(u),v)),
inference(spr,[status(thm),theory(equality)],[7713,807]),
[iquote('0:SpR:7713.0,807.0')] ).
cnf(7764,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[5,7713]),
[iquote('0:SpR:5.0,7713.0')] ).
cnf(7832,plain,
equal(join(complement(u),meet(u,join(complement(u),v))),join(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[5,7756,80]),
[iquote('0:Rew:5.0,7756.0,80.0,7756.0')] ).
cnf(8042,plain,
equal(meet(complement(join(u,v)),v),zero),
inference(spr,[status(thm),theory(equality)],[7764,7459]),
[iquote('0:SpR:7764.0,7459.0')] ).
cnf(8112,plain,
equal(meet(u,complement(join(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[80,8042]),
[iquote('0:Rew:80.0,8042.0')] ).
cnf(8605,plain,
equal(meet(converse(u),complement(converse(join(v,u)))),zero),
inference(spr,[status(thm),theory(equality)],[7,8112]),
[iquote('0:SpR:7.0,8112.0')] ).
cnf(13141,plain,
equal(converse(join(converse(u),meet(converse(u),v))),join(u,converse(meet(v,converse(u))))),
inference(spr,[status(thm),theory(equality)],[3574,34]),
[iquote('0:SpR:3574.0,34.0')] ).
cnf(13252,plain,
equal(join(u,converse(meet(converse(u),v))),join(u,converse(meet(v,converse(u))))),
inference(rew,[status(thm),theory(equality)],[34,13141]),
[iquote('0:Rew:34.0,13141.0')] ).
cnf(15627,plain,
equal(meet(converse(composition(u,complement(converse(composition(v,u))))),complement(converse(complement(converse(v))))),zero),
inference(spr,[status(thm),theory(equality)],[223,8605]),
[iquote('0:SpR:223.0,8605.0')] ).
cnf(15780,plain,
equal(meet(complement(converse(complement(converse(u)))),converse(composition(v,complement(converse(composition(u,v)))))),zero),
inference(rew,[status(thm),theory(equality)],[80,15627]),
[iquote('0:Rew:80.0,15627.0')] ).
cnf(18114,plain,
equal(join(u,complement(composition(converse(one),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[413,2555]),
[iquote('0:SpR:413.0,2555.0')] ).
cnf(18124,plain,
equal(join(u,u),u),
inference(rew,[status(thm),theory(equality)],[738,18114,413,403]),
[iquote('0:Rew:738.0,18114.0,413.0,18114.0,403.0,18114.0')] ).
cnf(18307,plain,
equal(join(meet(u,v),meet(u,complement(v))),join(u,meet(u,complement(v)))),
inference(spr,[status(thm),theory(equality)],[18124,805]),
[iquote('0:SpR:18124.0,805.0')] ).
cnf(18411,plain,
equal(join(u,meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[95,18307]),
[iquote('0:Rew:95.0,18307.0')] ).
cnf(18471,plain,
equal(join(u,meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[738,18411]),
[iquote('0:SpR:738.0,18411.0')] ).
cnf(18497,plain,
equal(join(u,meet(v,u)),u),
inference(rew,[status(thm),theory(equality)],[18471,3574]),
[iquote('0:Rew:18471.0,3574.0')] ).
cnf(18521,plain,
equal(complement(meet(u,join(complement(u),v))),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[18497,7330]),
[iquote('0:Rew:18497.0,7330.0')] ).
cnf(18572,plain,
equal(join(u,converse(meet(converse(u),v))),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[18471,34]),
[iquote('0:SpR:18471.0,34.0')] ).
cnf(18665,plain,
equal(join(u,converse(meet(converse(u),v))),u),
inference(rew,[status(thm),theory(equality)],[2,18572]),
[iquote('0:Rew:2.0,18572.0')] ).
cnf(18666,plain,
equal(join(u,converse(meet(v,converse(u)))),u),
inference(rew,[status(thm),theory(equality)],[18665,13252]),
[iquote('0:Rew:18665.0,13252.0')] ).
cnf(19393,plain,
equal(meet(converse(meet(u,converse(v))),complement(v)),zero),
inference(spr,[status(thm),theory(equality)],[18666,8112]),
[iquote('0:SpR:18666.0,8112.0')] ).
cnf(19474,plain,
equal(meet(complement(u),converse(meet(v,converse(u)))),zero),
inference(rew,[status(thm),theory(equality)],[80,19393]),
[iquote('0:Rew:80.0,19393.0')] ).
cnf(21664,plain,
equal(meet(u,join(complement(u),v)),complement(complement(meet(u,v)))),
inference(spr,[status(thm),theory(equality)],[18521,738]),
[iquote('0:SpR:18521.0,738.0')] ).
cnf(21827,plain,
equal(meet(u,join(complement(u),v)),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[738,21664]),
[iquote('0:Rew:738.0,21664.0')] ).
cnf(21829,plain,
equal(join(complement(u),meet(u,v)),join(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[21827,7832]),
[iquote('0:Rew:21827.0,7832.0')] ).
cnf(26526,plain,
equal(meet(u,converse(meet(v,converse(complement(u))))),zero),
inference(spr,[status(thm),theory(equality)],[738,19474]),
[iquote('0:SpR:738.0,19474.0')] ).
cnf(32987,plain,
equal(meet(u,complement(converse(complement(converse(complement(u)))))),complement(top)),
inference(spr,[status(thm),theory(equality)],[1536,802]),
[iquote('0:SpR:1536.0,802.0')] ).
cnf(33125,plain,
equal(meet(u,complement(converse(complement(converse(complement(u)))))),zero),
inference(rew,[status(thm),theory(equality)],[79,32987]),
[iquote('0:Rew:79.0,32987.0')] ).
cnf(33307,plain,
equal(join(meet(u,converse(complement(converse(complement(u))))),zero),u),
inference(spr,[status(thm),theory(equality)],[33125,95]),
[iquote('0:SpR:33125.0,95.0')] ).
cnf(33390,plain,
equal(meet(u,converse(complement(converse(complement(u))))),u),
inference(rew,[status(thm),theory(equality)],[732,33307,5]),
[iquote('0:Rew:732.0,33307.0,5.0,33307.0')] ).
cnf(33433,plain,
equal(join(u,meet(converse(complement(converse(complement(u)))),complement(u))),converse(complement(converse(complement(u))))),
inference(spr,[status(thm),theory(equality)],[33390,804]),
[iquote('0:SpR:33390.0,804.0')] ).
cnf(33474,plain,
equal(meet(converse(complement(u)),converse(u)),zero),
inference(spr,[status(thm),theory(equality)],[33390,26526]),
[iquote('0:SpR:33390.0,26526.0')] ).
cnf(33497,plain,
equal(meet(converse(u),converse(complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[80,33474]),
[iquote('0:Rew:80.0,33474.0')] ).
cnf(33526,plain,
equal(join(u,meet(complement(u),converse(complement(converse(complement(u)))))),converse(complement(converse(complement(u))))),
inference(rew,[status(thm),theory(equality)],[80,33433]),
[iquote('0:Rew:80.0,33433.0')] ).
cnf(33584,plain,
equal(meet(u,converse(complement(converse(u)))),zero),
inference(spr,[status(thm),theory(equality)],[2,33497]),
[iquote('0:SpR:2.0,33497.0')] ).
cnf(33625,plain,
equal(converse(complement(converse(complement(u)))),join(u,zero)),
inference(rew,[status(thm),theory(equality)],[33584,33526]),
[iquote('0:Rew:33584.0,33526.0')] ).
cnf(33633,plain,
equal(converse(complement(converse(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[817,33625]),
[iquote('0:Rew:817.0,33625.0')] ).
cnf(34539,plain,
equal(complement(converse(complement(u))),converse(u)),
inference(spr,[status(thm),theory(equality)],[33633,2]),
[iquote('0:SpR:33633.0,2.0')] ).
cnf(34628,plain,
equal(meet(converse(converse(u)),converse(composition(v,complement(converse(composition(u,v)))))),zero),
inference(rew,[status(thm),theory(equality)],[34539,15780]),
[iquote('0:Rew:34539.0,15780.0')] ).
cnf(34851,plain,
equal(meet(u,converse(composition(v,complement(converse(composition(u,v)))))),zero),
inference(rew,[status(thm),theory(equality)],[2,34628]),
[iquote('0:Rew:2.0,34628.0')] ).
cnf(34892,plain,
equal(converse(complement(u)),complement(converse(u))),
inference(spr,[status(thm),theory(equality)],[34539,738]),
[iquote('0:SpR:34539.0,738.0')] ).
cnf(35351,plain,
equal(converse(composition(u,complement(converse(v)))),composition(complement(v),converse(u))),
inference(spr,[status(thm),theory(equality)],[34892,29]),
[iquote('0:SpR:34892.0,29.0')] ).
cnf(35605,plain,
equal(meet(u,composition(complement(composition(u,v)),converse(v))),zero),
inference(rew,[status(thm),theory(equality)],[35351,34851]),
[iquote('0:Rew:35351.0,34851.0')] ).
cnf(215916,plain,
equal(join(complement(u),composition(complement(composition(u,v)),converse(v))),join(complement(u),zero)),
inference(spr,[status(thm),theory(equality)],[35605,21829]),
[iquote('0:SpR:35605.0,21829.0')] ).
cnf(216261,plain,
equal(join(complement(u),composition(complement(composition(u,v)),converse(v))),complement(u)),
inference(rew,[status(thm),theory(equality)],[732,215916,5]),
[iquote('0:Rew:732.0,215916.0,5.0,215916.0')] ).
cnf(216262,plain,
$false,
inference(unc,[status(thm)],[216261,17]),
[iquote('0:UnC:216261.0,17.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : REL012+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n013.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 10:01:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 285.36/285.58
% 285.36/285.58 SPASS V 3.9
% 285.36/285.58 SPASS beiseite: Proof found.
% 285.36/285.58 % SZS status Theorem
% 285.36/285.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 285.36/285.58 SPASS derived 127559 clauses, backtracked 0 clauses, performed 0 splits and kept 15203 clauses.
% 285.36/285.58 SPASS allocated 273644 KBytes.
% 285.36/285.58 SPASS spent 0:4:44.97 on the problem.
% 285.36/285.58 0:00:00.04 for the input.
% 285.36/285.58 0:00:00.02 for the FLOTTER CNF translation.
% 285.36/285.58 0:00:01.04 for inferences.
% 285.36/285.58 0:00:00.00 for the backtracking.
% 285.36/285.58 0:4:43.66 for the reduction.
% 285.36/285.58
% 285.36/285.58
% 285.36/285.58 Here is a proof with depth 16, length 158 :
% 285.36/285.58 % SZS output start Refutation
% See solution above
% 291.63/291.90 Formulae used in the proof : composition_identity converse_idempotence def_top def_zero maddux1_join_commutativity maddux4_definiton_of_meet converse_additivity converse_multiplicativity maddux2_join_associativity converse_cancellativity goals maddux3_a_kind_of_de_Morgan
% 291.63/291.90
%------------------------------------------------------------------------------