TSTP Solution File: REL023-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL023-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 20:01:53 EDT 2022
% Result : Unsatisfiable 0.58s 0.74s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 15
% Syntax : Number of clauses : 130 ( 130 unt; 0 nHn; 130 RR)
% Number of literals : 130 ( 0 equ; 3 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 : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))),composition(sk1,meet(sk2,sk3))),
file('REL023-2.p',unknown),
[] ).
cnf(2,axiom,
equal(join(u,v),join(v,u)),
file('REL023-2.p',unknown),
[] ).
cnf(3,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL023-2.p',unknown),
[] ).
cnf(4,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL023-2.p',unknown),
[] ).
cnf(5,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL023-2.p',unknown),
[] ).
cnf(6,axiom,
equal(composition(composition(u,v),w),composition(u,composition(v,w))),
file('REL023-2.p',unknown),
[] ).
cnf(7,axiom,
equal(composition(u,one),u),
file('REL023-2.p',unknown),
[] ).
cnf(8,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL023-2.p',unknown),
[] ).
cnf(9,axiom,
equal(converse(converse(u)),u),
file('REL023-2.p',unknown),
[] ).
cnf(10,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL023-2.p',unknown),
[] ).
cnf(11,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL023-2.p',unknown),
[] ).
cnf(12,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL023-2.p',unknown),
[] ).
cnf(13,axiom,
equal(join(u,complement(u)),top),
file('REL023-2.p',unknown),
[] ).
cnf(14,axiom,
equal(meet(u,complement(u)),zero),
file('REL023-2.p',unknown),
[] ).
cnf(16,axiom,
equal(join(meet(composition(u,v),w),meet(composition(u,meet(v,composition(converse(u),w))),w)),meet(composition(u,meet(v,composition(converse(u),w))),w)),
file('REL023-2.p',unknown),
[] ).
cnf(18,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[2,12]),
[iquote('0:Rew:2.0,12.0')] ).
cnf(19,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[5,4]),
[iquote('0:Rew:5.0,4.0')] ).
cnf(20,plain,
~ equal(composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))),
inference(rew,[status(thm),theory(equality)],[2,1,8]),
[iquote('0:Rew:2.0,1.0,8.0,1.0')] ).
cnf(31,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[9,11]),
[iquote('0:SpR:9.0,11.0')] ).
cnf(36,plain,
equal(converse(join(u,converse(v))),join(converse(u),v)),
inference(spr,[status(thm),theory(equality)],[9,10]),
[iquote('0:SpR:9.0,10.0')] ).
cnf(37,plain,
equal(converse(join(converse(u),v)),join(u,converse(v))),
inference(spr,[status(thm),theory(equality)],[9,10]),
[iquote('0:SpR:9.0,10.0')] ).
cnf(79,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[13,5]),
[iquote('0:SpR:13.0,5.0')] ).
cnf(80,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[2,5]),
[iquote('0:SpR:2.0,5.0')] ).
cnf(82,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[14,79]),
[iquote('0:Rew:14.0,79.0')] ).
cnf(83,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[5,80]),
[iquote('0:Rew:5.0,80.0')] ).
cnf(85,plain,
equal(join(meet(composition(u,v),w),meet(w,composition(u,meet(v,composition(converse(u),w))))),meet(w,composition(u,meet(v,composition(converse(u),w))))),
inference(rew,[status(thm),theory(equality)],[83,16]),
[iquote('0:Rew:83.0,16.0')] ).
cnf(93,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[13,19]),
[iquote('0:SpR:13.0,19.0')] ).
cnf(96,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[5,19]),
[iquote('0:SpR:5.0,19.0')] ).
cnf(97,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[14,19]),
[iquote('0:SpR:14.0,19.0')] ).
cnf(98,plain,
equal(join(complement(top),meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[2,93]),
[iquote('0:Rew:2.0,93.0')] ).
cnf(99,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[82,98]),
[iquote('0:Rew:82.0,98.0')] ).
cnf(100,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[2,96]),
[iquote('0:Rew:2.0,96.0')] ).
cnf(101,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[5,97]),
[iquote('0:Rew:5.0,97.0')] ).
cnf(105,plain,
equal(join(top,zero),top),
inference(spr,[status(thm),theory(equality)],[82,13]),
[iquote('0:SpR:82.0,13.0')] ).
cnf(106,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[82,5]),
[iquote('0:SpR:82.0,5.0')] ).
cnf(107,plain,
equal(join(meet(top,u),complement(join(zero,u))),top),
inference(spr,[status(thm),theory(equality)],[82,19]),
[iquote('0:SpR:82.0,19.0')] ).
cnf(135,plain,
equal(meet(join(zero,complement(u)),meet(top,u)),zero),
inference(spr,[status(thm),theory(equality)],[106,14]),
[iquote('0:SpR:106.0,14.0')] ).
cnf(143,plain,
equal(complement(join(zero,zero)),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[82,106]),
[iquote('0:SpR:82.0,106.0')] ).
cnf(149,plain,
equal(meet(meet(top,u),join(zero,complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[83,135]),
[iquote('0:Rew:83.0,135.0')] ).
cnf(159,plain,
equal(join(u,join(v,complement(join(u,v)))),top),
inference(spr,[status(thm),theory(equality)],[3,13]),
[iquote('0:SpR:3.0,13.0')] ).
cnf(160,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(166,plain,
equal(join(u,join(complement(u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[13,3]),
[iquote('0:SpR:13.0,3.0')] ).
cnf(171,plain,
equal(join(top,join(zero,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[105,3]),
[iquote('0:SpR:105.0,3.0')] ).
cnf(182,plain,
equal(meet(join(zero,zero),meet(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[143,14]),
[iquote('0:SpR:143.0,14.0')] ).
cnf(191,plain,
equal(meet(meet(top,top),join(zero,zero)),zero),
inference(rew,[status(thm),theory(equality)],[83,182]),
[iquote('0:Rew:83.0,182.0')] ).
cnf(198,plain,
equal(join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[191,19]),
[iquote('0:SpR:191.0,19.0')] ).
cnf(204,plain,
equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[3,198,2]),
[iquote('0:Rew:3.0,198.0,2.0,198.0')] ).
cnf(210,plain,
equal(join(top,meet(u,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[101,171]),
[iquote('0:SpR:101.0,171.0')] ).
cnf(227,plain,
equal(join(zero,composition(converse(u),complement(composition(u,top)))),zero),
inference(spr,[status(thm),theory(equality)],[82,18]),
[iquote('0:SpR:82.0,18.0')] ).
cnf(342,plain,
equal(meet(meet(u,top),join(zero,complement(u))),zero),
inference(spr,[status(thm),theory(equality)],[83,149]),
[iquote('0:SpR:83.0,149.0')] ).
cnf(453,plain,
equal(join(zero,complement(join(complement(meet(u,top)),join(zero,complement(u))))),meet(u,top)),
inference(spr,[status(thm),theory(equality)],[342,19]),
[iquote('0:SpR:342.0,19.0')] ).
cnf(472,plain,
equal(join(zero,complement(join(zero,join(complement(u),complement(meet(u,top)))))),meet(u,top)),
inference(rew,[status(thm),theory(equality)],[160,453]),
[iquote('0:Rew:160.0,453.0')] ).
cnf(565,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[7,31]),
[iquote('0:SpR:7.0,31.0')] ).
cnf(568,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[9,565]),
[iquote('0:Rew:9.0,565.0')] ).
cnf(610,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[568,7]),
[iquote('0:SpR:568.0,7.0')] ).
cnf(613,plain,
equal(join(u,composition(v,u)),composition(join(converse(one),v),u)),
inference(spr,[status(thm),theory(equality)],[568,8]),
[iquote('0:SpR:568.0,8.0')] ).
cnf(622,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[568,18]),
[iquote('0:SpR:568.0,18.0')] ).
cnf(628,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[610,568]),
[iquote('0:Rew:610.0,568.0')] ).
cnf(643,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[628,622]),
[iquote('0:Rew:628.0,622.0')] ).
cnf(644,plain,
equal(join(u,composition(v,u)),composition(join(one,v),u)),
inference(rew,[status(thm),theory(equality)],[610,613]),
[iquote('0:Rew:610.0,613.0')] ).
cnf(715,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[643,5]),
[iquote('0:SpR:643.0,5.0')] ).
cnf(721,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[82,643]),
[iquote('0:SpR:82.0,643.0')] ).
cnf(727,plain,
equal(meet(top,top),complement(zero)),
inference(rew,[status(thm),theory(equality)],[721,143]),
[iquote('0:Rew:721.0,143.0')] ).
cnf(740,plain,
equal(join(zero,complement(join(zero,join(zero,complement(complement(zero)))))),complement(zero)),
inference(rew,[status(thm),theory(equality)],[727,204]),
[iquote('0:Rew:727.0,204.0')] ).
cnf(743,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[715,101]),
[iquote('0:Rew:715.0,101.0')] ).
cnf(744,plain,
equal(join(top,complement(complement(u))),join(top,u)),
inference(rew,[status(thm),theory(equality)],[715,210]),
[iquote('0:Rew:715.0,210.0')] ).
cnf(772,plain,
equal(join(zero,complement(zero)),complement(zero)),
inference(rew,[status(thm),theory(equality)],[721,740,743]),
[iquote('0:Rew:721.0,740.0,743.0,740.0')] ).
cnf(773,plain,
equal(complement(zero),top),
inference(rew,[status(thm),theory(equality)],[13,772]),
[iquote('0:Rew:13.0,772.0')] ).
cnf(796,plain,
equal(meet(top,complement(u)),complement(u)),
inference(spr,[status(thm),theory(equality)],[743,106]),
[iquote('0:SpR:743.0,106.0')] ).
cnf(803,plain,
equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[5,743]),
[iquote('0:SpR:5.0,743.0')] ).
cnf(822,plain,
equal(complement(join(top,complement(u))),meet(zero,u)),
inference(spr,[status(thm),theory(equality)],[773,5]),
[iquote('0:SpR:773.0,5.0')] ).
cnf(832,plain,
equal(join(top,top),top),
inference(spr,[status(thm),theory(equality)],[773,643]),
[iquote('0:SpR:773.0,643.0')] ).
cnf(851,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[721,3]),
[iquote('0:SpR:721.0,3.0')] ).
cnf(869,plain,
equal(join(top,join(top,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[832,3]),
[iquote('0:SpR:832.0,3.0')] ).
cnf(879,plain,
equal(join(complement(u),complement(join(zero,complement(u)))),top),
inference(spr,[status(thm),theory(equality)],[796,107]),
[iquote('0:SpR:796.0,107.0')] ).
cnf(890,plain,
equal(join(complement(u),meet(top,u)),top),
inference(rew,[status(thm),theory(equality)],[106,879]),
[iquote('0:Rew:106.0,879.0')] ).
cnf(975,plain,
equal(join(complement(u),meet(u,top)),top),
inference(spr,[status(thm),theory(equality)],[83,890]),
[iquote('0:SpR:83.0,890.0')] ).
cnf(1002,plain,
equal(join(meet(u,meet(u,top)),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[975,19]),
[iquote('0:SpR:975.0,19.0')] ).
cnf(1014,plain,
equal(join(zero,meet(u,meet(u,top))),u),
inference(rew,[status(thm),theory(equality)],[2,1002,82]),
[iquote('0:Rew:2.0,1002.0,82.0,1002.0')] ).
cnf(1113,plain,
equal(meet(top,join(top,complement(u))),complement(join(zero,meet(zero,u)))),
inference(spr,[status(thm),theory(equality)],[822,106]),
[iquote('0:SpR:822.0,106.0')] ).
cnf(1132,plain,
equal(meet(zero,complement(u)),complement(join(top,u))),
inference(spr,[status(thm),theory(equality)],[744,822]),
[iquote('0:SpR:744.0,822.0')] ).
cnf(1160,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[99,851]),
[iquote('0:SpR:99.0,851.0')] ).
cnf(1167,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[1160,743]),
[iquote('0:Rew:1160.0,743.0')] ).
cnf(1168,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[1160,106]),
[iquote('0:Rew:1160.0,106.0')] ).
cnf(1175,plain,
equal(composition(converse(u),complement(composition(u,top))),zero),
inference(rew,[status(thm),theory(equality)],[1160,227]),
[iquote('0:Rew:1160.0,227.0')] ).
cnf(1178,plain,
equal(join(zero,complement(join(complement(u),complement(meet(u,top))))),meet(u,top)),
inference(rew,[status(thm),theory(equality)],[1160,472]),
[iquote('0:Rew:1160.0,472.0')] ).
cnf(1181,plain,
equal(meet(u,meet(u,top)),u),
inference(rew,[status(thm),theory(equality)],[1160,1014]),
[iquote('0:Rew:1160.0,1014.0')] ).
cnf(1185,plain,
equal(meet(top,join(top,complement(u))),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[1160,1113]),
[iquote('0:Rew:1160.0,1113.0')] ).
cnf(1187,plain,
equal(join(complement(u),complement(v)),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[1160,803]),
[iquote('0:Rew:1160.0,803.0')] ).
cnf(1207,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[1167,1168]),
[iquote('0:Rew:1167.0,1168.0')] ).
cnf(1239,plain,
equal(join(top,complement(u)),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[1207,1185]),
[iquote('0:Rew:1207.0,1185.0')] ).
cnf(1266,plain,
equal(meet(u,top),u),
inference(rew,[status(thm),theory(equality)],[1160,1178,1167,1181,1187]),
[iquote('0:Rew:1160.0,1178.0,1167.0,1178.0,1181.0,1178.0,1187.0,1178.0')] ).
cnf(1377,plain,
equal(join(u,converse(complement(converse(u)))),converse(top)),
inference(spr,[status(thm),theory(equality)],[13,37]),
[iquote('0:SpR:13.0,37.0')] ).
cnf(1616,plain,
equal(join(u,complement(meet(zero,join(u,top)))),top),
inference(spr,[status(thm),theory(equality)],[1239,159]),
[iquote('0:SpR:1239.0,159.0')] ).
cnf(1638,plain,
equal(join(top,converse(top)),converse(top)),
inference(spr,[status(thm),theory(equality)],[1377,869]),
[iquote('0:SpR:1377.0,869.0')] ).
cnf(1671,plain,
equal(join(converse(top),top),converse(converse(top))),
inference(spr,[status(thm),theory(equality)],[1638,36]),
[iquote('0:SpR:1638.0,36.0')] ).
cnf(1674,plain,
equal(converse(top),top),
inference(rew,[status(thm),theory(equality)],[1638,1671,2,9]),
[iquote('0:Rew:1638.0,1671.0,2.0,1671.0,9.0,1671.0')] ).
cnf(1696,plain,
equal(composition(top,complement(composition(top,top))),zero),
inference(spr,[status(thm),theory(equality)],[1674,1175]),
[iquote('0:SpR:1674.0,1175.0')] ).
cnf(1699,plain,
equal(join(complement(u),composition(top,complement(composition(top,u)))),complement(u)),
inference(spr,[status(thm),theory(equality)],[1674,18]),
[iquote('0:SpR:1674.0,18.0')] ).
cnf(1733,plain,
equal(join(u,meet(u,complement(top))),u),
inference(spr,[status(thm),theory(equality)],[1266,100]),
[iquote('0:SpR:1266.0,100.0')] ).
cnf(1740,plain,
equal(join(u,meet(u,zero)),u),
inference(rew,[status(thm),theory(equality)],[82,1733]),
[iquote('0:Rew:82.0,1733.0')] ).
cnf(1755,plain,
equal(join(u,complement(u)),join(top,meet(complement(u),zero))),
inference(spr,[status(thm),theory(equality)],[1740,166]),
[iquote('0:SpR:1740.0,166.0')] ).
cnf(1766,plain,
equal(complement(meet(zero,join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[13,1755,1239,1132,83]),
[iquote('0:Rew:13.0,1755.0,1239.0,1755.0,1132.0,1755.0,83.0,1755.0')] ).
cnf(1875,plain,
equal(join(composition(u,complement(composition(top,top))),zero),composition(join(u,top),complement(composition(top,top)))),
inference(spr,[status(thm),theory(equality)],[1696,8]),
[iquote('0:SpR:1696.0,8.0')] ).
cnf(1879,plain,
equal(composition(join(u,top),complement(composition(top,top))),composition(u,complement(composition(top,top)))),
inference(rew,[status(thm),theory(equality)],[1160,1875,2]),
[iquote('0:Rew:1160.0,1875.0,2.0,1875.0')] ).
cnf(1894,plain,
equal(complement(meet(zero,join(u,top))),top),
inference(spr,[status(thm),theory(equality)],[2,1766]),
[iquote('0:SpR:2.0,1766.0')] ).
cnf(1916,plain,
equal(join(u,top),top),
inference(rew,[status(thm),theory(equality)],[1894,1616]),
[iquote('0:Rew:1894.0,1616.0')] ).
cnf(1930,plain,
equal(composition(top,complement(composition(top,top))),composition(u,complement(composition(top,top)))),
inference(rew,[status(thm),theory(equality)],[1916,1879]),
[iquote('0:Rew:1916.0,1879.0')] ).
cnf(1949,plain,
equal(composition(u,complement(composition(top,top))),zero),
inference(rew,[status(thm),theory(equality)],[1696,1930]),
[iquote('0:Rew:1696.0,1930.0')] ).
cnf(2128,plain,
equal(complement(composition(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[1949,628]),
[iquote('0:SpR:1949.0,628.0')] ).
cnf(2271,plain,
equal(composition(top,top),complement(zero)),
inference(spr,[status(thm),theory(equality)],[2128,1167]),
[iquote('0:SpR:2128.0,1167.0')] ).
cnf(2279,plain,
equal(composition(top,top),top),
inference(rew,[status(thm),theory(equality)],[773,2271]),
[iquote('0:Rew:773.0,2271.0')] ).
cnf(2292,plain,
equal(composition(top,composition(top,u)),composition(top,u)),
inference(spr,[status(thm),theory(equality)],[2279,6]),
[iquote('0:SpR:2279.0,6.0')] ).
cnf(2295,plain,
equal(join(meet(top,u),meet(u,composition(top,meet(top,composition(converse(top),u))))),meet(u,composition(top,meet(top,composition(converse(top),u))))),
inference(spr,[status(thm),theory(equality)],[2279,85]),
[iquote('0:SpR:2279.0,85.0')] ).
cnf(2305,plain,
equal(join(u,meet(u,composition(top,composition(top,u)))),meet(u,composition(top,composition(top,u)))),
inference(rew,[status(thm),theory(equality)],[1207,2295,1674]),
[iquote('0:Rew:1207.0,2295.0,1207.0,2295.0,1674.0,2295.0')] ).
cnf(2306,plain,
equal(join(u,meet(u,composition(top,u))),meet(u,composition(top,u))),
inference(rew,[status(thm),theory(equality)],[2292,2305]),
[iquote('0:Rew:2292.0,2305.0')] ).
cnf(2755,plain,
equal(join(complement(composition(top,u)),composition(converse(top),complement(composition(top,u)))),complement(composition(top,u))),
inference(spr,[status(thm),theory(equality)],[2292,18]),
[iquote('0:SpR:2292.0,18.0')] ).
cnf(2772,plain,
equal(join(complement(composition(top,u)),composition(top,complement(composition(top,u)))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[1674,2755]),
[iquote('0:Rew:1674.0,2755.0')] ).
cnf(2773,plain,
equal(composition(join(one,top),complement(composition(top,u))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[644,2772]),
[iquote('0:Rew:644.0,2772.0')] ).
cnf(2774,plain,
equal(composition(top,complement(composition(top,u))),complement(composition(top,u))),
inference(rew,[status(thm),theory(equality)],[1916,2773]),
[iquote('0:Rew:1916.0,2773.0')] ).
cnf(2775,plain,
equal(join(complement(u),complement(composition(top,u))),complement(u)),
inference(rew,[status(thm),theory(equality)],[2774,1699]),
[iquote('0:Rew:2774.0,1699.0')] ).
cnf(2776,plain,
equal(complement(meet(u,composition(top,u))),complement(u)),
inference(rew,[status(thm),theory(equality)],[1187,2775]),
[iquote('0:Rew:1187.0,2775.0')] ).
cnf(2972,plain,
equal(meet(u,composition(top,u)),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[2776,1167]),
[iquote('0:SpR:2776.0,1167.0')] ).
cnf(2994,plain,
equal(meet(u,composition(top,u)),u),
inference(rew,[status(thm),theory(equality)],[1167,2972]),
[iquote('0:Rew:1167.0,2972.0')] ).
cnf(2996,plain,
equal(join(u,u),u),
inference(rew,[status(thm),theory(equality)],[2994,2306]),
[iquote('0:Rew:2994.0,2306.0')] ).
cnf(3061,plain,
equal(join(u,join(u,v)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[2996,3]),
[iquote('0:SpR:2996.0,3.0')] ).
cnf(3265,plain,
equal(join(meet(u,v),u),u),
inference(spr,[status(thm),theory(equality)],[100,3061]),
[iquote('0:SpR:100.0,3061.0')] ).
cnf(3272,plain,
equal(join(u,meet(u,v)),u),
inference(rew,[status(thm),theory(equality)],[2,3265]),
[iquote('0:Rew:2.0,3265.0')] ).
cnf(3273,plain,
~ equal(composition(sk1,meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))),
inference(rew,[status(thm),theory(equality)],[3272,20]),
[iquote('0:Rew:3272.0,20.0')] ).
cnf(3289,plain,
$false,
inference(obv,[status(thm),theory(equality)],[3273]),
[iquote('0:Obv:3273.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL023-2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 12:38:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.58/0.74
% 0.58/0.74 SPASS V 3.9
% 0.58/0.74 SPASS beiseite: Proof found.
% 0.58/0.74 % SZS status Theorem
% 0.58/0.74 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.58/0.74 SPASS derived 2079 clauses, backtracked 0 clauses, performed 0 splits and kept 627 clauses.
% 0.58/0.74 SPASS allocated 66980 KBytes.
% 0.58/0.74 SPASS spent 0:00:00.40 on the problem.
% 0.58/0.74 0:00:00.04 for the input.
% 0.58/0.74 0:00:00.00 for the FLOTTER CNF translation.
% 0.58/0.74 0:00:00.02 for inferences.
% 0.58/0.74 0:00:00.00 for the backtracking.
% 0.58/0.74 0:00:00.32 for the reduction.
% 0.58/0.74
% 0.58/0.74
% 0.58/0.74 Here is a proof with depth 16, length 130 :
% 0.58/0.74 % SZS output start Refutation
% See solution above
% 0.58/0.76 Formulae used in the proof : goals_17 maddux1_join_commutativity_1 maddux2_join_associativity_2 maddux3_a_kind_of_de_Morgan_3 maddux4_definiton_of_meet_4 composition_associativity_5 composition_identity_6 composition_distributivity_7 converse_idempotence_8 converse_additivity_9 converse_multiplicativity_10 converse_cancellativity_11 def_top_12 def_zero_13 modular_law_1_15
% 0.58/0.76
%------------------------------------------------------------------------------