TSTP Solution File: REL041+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL041+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 20:02:23 EDT 2022
% Result : Theorem 183.47s 183.67s
% Output : Refutation 188.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 17
% Syntax : Number of clauses : 121 ( 121 unt; 0 nHn; 121 RR)
% Number of literals : 121 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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(composition(u,one),u),
file('REL041+2.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL041+2.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,complement(u)),top),
file('REL041+2.p',unknown),
[] ).
cnf(4,axiom,
equal(meet(u,complement(u)),zero),
file('REL041+2.p',unknown),
[] ).
cnf(5,axiom,
equal(join(u,v),join(v,u)),
file('REL041+2.p',unknown),
[] ).
cnf(6,axiom,
equal(join(composition(converse(skc2),skc2),one),one),
file('REL041+2.p',unknown),
[] ).
cnf(7,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL041+2.p',unknown),
[] ).
cnf(8,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL041+2.p',unknown),
[] ).
cnf(9,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL041+2.p',unknown),
[] ).
cnf(10,axiom,
~ equal(meet(composition(skc2,skc3),composition(skc2,complement(skc3))),zero),
file('REL041+2.p',unknown),
[] ).
cnf(11,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL041+2.p',unknown),
[] ).
cnf(12,axiom,
equal(composition(composition(u,v),w),composition(u,composition(v,w))),
file('REL041+2.p',unknown),
[] ).
cnf(13,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL041+2.p',unknown),
[] ).
cnf(14,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL041+2.p',unknown),
[] ).
cnf(15,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL041+2.p',unknown),
[] ).
cnf(17,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('REL041+2.p',unknown),
[] ).
cnf(18,axiom,
equal(join(meet(composition(u,v),w),composition(meet(u,composition(w,converse(v))),meet(v,composition(converse(u),w)))),composition(meet(u,composition(w,converse(v))),meet(v,composition(converse(u),w)))),
file('REL041+2.p',unknown),
[] ).
cnf(19,plain,
equal(join(one,composition(converse(skc2),skc2)),one),
inference(rew,[status(thm),theory(equality)],[5,6]),
[iquote('0:Rew:5.0,6.0')] ).
cnf(20,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[5,14]),
[iquote('0:Rew:5.0,14.0')] ).
cnf(21,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[7,15]),
[iquote('0:Rew:7.0,15.0')] ).
cnf(33,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(38,plain,
equal(converse(join(u,converse(v))),join(converse(u),v)),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(39,plain,
equal(converse(join(converse(u),v)),join(u,converse(v))),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(77,plain,
equal(join(join(complement(u),complement(v)),meet(u,v)),top),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(81,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(82,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[5,7]),
[iquote('0:SpR:5.0,7.0')] ).
cnf(84,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[4,81]),
[iquote('0:Rew:4.0,81.0')] ).
cnf(85,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[7,82]),
[iquote('0:Rew:7.0,82.0')] ).
cnf(86,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)],[85,17]),
[iquote('0:Rew:85.0,17.0')] ).
cnf(90,plain,
equal(join(meet(u,v),join(complement(u),complement(v))),top),
inference(rew,[status(thm),theory(equality)],[5,77]),
[iquote('0:Rew:5.0,77.0')] ).
cnf(93,plain,
equal(meet(top,zero),zero),
inference(spr,[status(thm),theory(equality)],[84,4]),
[iquote('0:SpR:84.0,4.0')] ).
cnf(95,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[84,7]),
[iquote('0:SpR:84.0,7.0')] ).
cnf(98,plain,
equal(meet(zero,top),zero),
inference(rew,[status(thm),theory(equality)],[85,93]),
[iquote('0:Rew:85.0,93.0')] ).
cnf(110,plain,
equal(complement(join(meet(top,u),complement(v))),meet(join(zero,complement(u)),v)),
inference(spr,[status(thm),theory(equality)],[95,7]),
[iquote('0:SpR:95.0,7.0')] ).
cnf(147,plain,
equal(join(meet(top,u),complement(join(zero,u))),top),
inference(spr,[status(thm),theory(equality)],[84,21]),
[iquote('0:SpR:84.0,21.0')] ).
cnf(148,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[3,21]),
[iquote('0:SpR:3.0,21.0')] ).
cnf(152,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[4,21]),
[iquote('0:SpR:4.0,21.0')] ).
cnf(154,plain,
equal(join(zero,complement(join(complement(zero),top))),zero),
inference(spr,[status(thm),theory(equality)],[98,21]),
[iquote('0:SpR:98.0,21.0')] ).
cnf(157,plain,
equal(join(zero,complement(join(top,complement(zero)))),zero),
inference(rew,[status(thm),theory(equality)],[5,154]),
[iquote('0:Rew:5.0,154.0')] ).
cnf(158,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[5,148,84]),
[iquote('0:Rew:5.0,148.0,84.0,148.0')] ).
cnf(160,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[7,152]),
[iquote('0:Rew:7.0,152.0')] ).
cnf(176,plain,
equal(meet(top,join(top,complement(zero))),complement(zero)),
inference(spr,[status(thm),theory(equality)],[157,95]),
[iquote('0:SpR:157.0,95.0')] ).
cnf(211,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[11,5]),
[iquote('0:SpR:11.0,5.0')] ).
cnf(217,plain,
equal(join(u,join(complement(u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[3,11]),
[iquote('0:SpR:3.0,11.0')] ).
cnf(231,plain,
equal(join(complement(u),join(meet(v,u),complement(v))),top),
inference(rew,[status(thm),theory(equality)],[211,90]),
[iquote('0:Rew:211.0,90.0')] ).
cnf(237,plain,
equal(join(complement(u),join(complement(v),meet(v,u))),top),
inference(rew,[status(thm),theory(equality)],[5,231]),
[iquote('0:Rew:5.0,231.0')] ).
cnf(277,plain,
equal(join(zero,composition(converse(u),complement(composition(u,top)))),zero),
inference(spr,[status(thm),theory(equality)],[84,20]),
[iquote('0:SpR:84.0,20.0')] ).
cnf(316,plain,
equal(join(meet(top,u),complement(join(u,zero))),top),
inference(spr,[status(thm),theory(equality)],[5,147]),
[iquote('0:SpR:5.0,147.0')] ).
cnf(353,plain,
equal(join(composition(u,v),join(composition(w,v),x)),join(composition(join(u,w),v),x)),
inference(spr,[status(thm),theory(equality)],[13,11]),
[iquote('0:SpR:13.0,11.0')] ).
cnf(434,plain,
equal(join(complement(zero),complement(join(join(top,complement(zero)),zero))),top),
inference(spr,[status(thm),theory(equality)],[176,316]),
[iquote('0:SpR:176.0,316.0')] ).
cnf(439,plain,
equal(join(complement(zero),complement(join(top,top))),top),
inference(rew,[status(thm),theory(equality)],[3,434,5,11]),
[iquote('0:Rew:3.0,434.0,5.0,434.0,11.0,434.0')] ).
cnf(441,plain,
equal(meet(zero,join(top,top)),complement(top)),
inference(spr,[status(thm),theory(equality)],[439,7]),
[iquote('0:SpR:439.0,7.0')] ).
cnf(446,plain,
equal(meet(zero,join(top,top)),zero),
inference(rew,[status(thm),theory(equality)],[84,441]),
[iquote('0:Rew:84.0,441.0')] ).
cnf(611,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[1,33]),
[iquote('0:SpR:1.0,33.0')] ).
cnf(614,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[2,611]),
[iquote('0:Rew:2.0,611.0')] ).
cnf(656,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[614,1]),
[iquote('0:SpR:614.0,1.0')] ).
cnf(667,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[614,20]),
[iquote('0:SpR:614.0,20.0')] ).
cnf(674,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[656,614]),
[iquote('0:Rew:656.0,614.0')] ).
cnf(689,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[674,667]),
[iquote('0:Rew:674.0,667.0')] ).
cnf(762,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[689,7]),
[iquote('0:SpR:689.0,7.0')] ).
cnf(768,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[84,689]),
[iquote('0:SpR:84.0,689.0')] ).
cnf(789,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[762,160]),
[iquote('0:Rew:762.0,160.0')] ).
cnf(827,plain,
equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[7,789]),
[iquote('0:SpR:7.0,789.0')] ).
cnf(855,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[768,11]),
[iquote('0:SpR:768.0,11.0')] ).
cnf(1050,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[158,855]),
[iquote('0:SpR:158.0,855.0')] ).
cnf(1057,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[1050,789]),
[iquote('0:Rew:1050.0,789.0')] ).
cnf(1063,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[1050,95]),
[iquote('0:Rew:1050.0,95.0')] ).
cnf(1072,plain,
equal(composition(converse(u),complement(composition(u,top))),zero),
inference(rew,[status(thm),theory(equality)],[1050,277]),
[iquote('0:Rew:1050.0,277.0')] ).
cnf(1081,plain,
equal(join(complement(u),complement(v)),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[1050,827]),
[iquote('0:Rew:1050.0,827.0')] ).
cnf(1085,plain,
equal(complement(join(meet(top,u),complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[1050,110]),
[iquote('0:Rew:1050.0,110.0')] ).
cnf(1088,plain,
equal(meet(u,u),u),
inference(rew,[status(thm),theory(equality)],[1057,762]),
[iquote('0:Rew:1057.0,762.0')] ).
cnf(1102,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[1057,1063]),
[iquote('0:Rew:1057.0,1063.0')] ).
cnf(1103,plain,
equal(join(top,complement(zero)),complement(zero)),
inference(rew,[status(thm),theory(equality)],[1102,176]),
[iquote('0:Rew:1102.0,176.0')] ).
cnf(1129,plain,
equal(complement(meet(zero,join(top,top))),top),
inference(rew,[status(thm),theory(equality)],[1081,439]),
[iquote('0:Rew:1081.0,439.0')] ).
cnf(1136,plain,
equal(complement(zero),top),
inference(rew,[status(thm),theory(equality)],[446,1129]),
[iquote('0:Rew:446.0,1129.0')] ).
cnf(1138,plain,
equal(join(top,top),top),
inference(rew,[status(thm),theory(equality)],[1136,1103]),
[iquote('0:Rew:1136.0,1103.0')] ).
cnf(1163,plain,
equal(complement(join(u,complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[1102,1085]),
[iquote('0:Rew:1102.0,1085.0')] ).
cnf(1204,plain,
equal(join(top,join(top,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[1138,11]),
[iquote('0:SpR:1138.0,11.0')] ).
cnf(1211,plain,
equal(join(u,zero),u),
inference(spr,[status(thm),theory(equality)],[1050,5]),
[iquote('0:SpR:1050.0,5.0')] ).
cnf(1265,plain,
equal(join(converse(zero),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[1050,38]),
[iquote('0:SpR:1050.0,38.0')] ).
cnf(1266,plain,
equal(join(converse(zero),u),u),
inference(rew,[status(thm),theory(equality)],[2,1265]),
[iquote('0:Rew:2.0,1265.0')] ).
cnf(1327,plain,
equal(converse(zero),zero),
inference(spr,[status(thm),theory(equality)],[1266,1211]),
[iquote('0:SpR:1266.0,1211.0')] ).
cnf(1368,plain,
equal(join(u,converse(complement(converse(u)))),converse(top)),
inference(spr,[status(thm),theory(equality)],[3,39]),
[iquote('0:SpR:3.0,39.0')] ).
cnf(1545,plain,
equal(join(top,converse(top)),converse(top)),
inference(spr,[status(thm),theory(equality)],[1368,1204]),
[iquote('0:SpR:1368.0,1204.0')] ).
cnf(1578,plain,
equal(join(converse(top),top),converse(converse(top))),
inference(spr,[status(thm),theory(equality)],[1545,38]),
[iquote('0:SpR:1545.0,38.0')] ).
cnf(1581,plain,
equal(converse(top),top),
inference(rew,[status(thm),theory(equality)],[1545,1578,5,2]),
[iquote('0:Rew:1545.0,1578.0,5.0,1578.0,2.0,1578.0')] ).
cnf(1582,plain,
equal(join(u,converse(complement(converse(u)))),top),
inference(rew,[status(thm),theory(equality)],[1581,1368]),
[iquote('0:Rew:1581.0,1368.0')] ).
cnf(1625,plain,
equal(join(top,converse(u)),converse(join(top,u))),
inference(spr,[status(thm),theory(equality)],[1581,8]),
[iquote('0:SpR:1581.0,8.0')] ).
cnf(1631,plain,
equal(composition(top,complement(composition(top,top))),zero),
inference(spr,[status(thm),theory(equality)],[1581,1072]),
[iquote('0:SpR:1581.0,1072.0')] ).
cnf(1681,plain,
equal(join(meet(zero,u),composition(meet(top,composition(u,converse(complement(composition(top,top))))),meet(complement(composition(top,top)),composition(converse(top),u)))),composition(meet(top,composition(u,converse(complement(composition(top,top))))),meet(complement(composition(top,top)),composition(converse(top),u)))),
inference(spr,[status(thm),theory(equality)],[1631,18]),
[iquote('0:SpR:1631.0,18.0')] ).
cnf(1683,plain,
equal(join(composition(u,complement(composition(top,top))),zero),composition(join(u,top),complement(composition(top,top)))),
inference(spr,[status(thm),theory(equality)],[1631,13]),
[iquote('0:SpR:1631.0,13.0')] ).
cnf(1687,plain,
equal(composition(join(u,top),complement(composition(top,top))),composition(u,complement(composition(top,top)))),
inference(rew,[status(thm),theory(equality)],[1050,1683,5]),
[iquote('0:Rew:1050.0,1683.0,5.0,1683.0')] ).
cnf(1690,plain,
equal(join(meet(zero,u),composition(u,composition(converse(complement(composition(top,top))),meet(complement(composition(top,top)),composition(top,u))))),composition(u,composition(converse(complement(composition(top,top))),meet(complement(composition(top,top)),composition(top,u))))),
inference(rew,[status(thm),theory(equality)],[12,1681,1102,1581]),
[iquote('0:Rew:12.0,1681.0,1102.0,1681.0,1581.0,1681.0')] ).
cnf(1697,plain,
equal(join(top,converse(complement(converse(complement(u))))),join(u,top)),
inference(spr,[status(thm),theory(equality)],[1582,217]),
[iquote('0:SpR:1582.0,217.0')] ).
cnf(1724,plain,
equal(converse(join(top,complement(converse(complement(u))))),join(u,top)),
inference(rew,[status(thm),theory(equality)],[1625,1697]),
[iquote('0:Rew:1625.0,1697.0')] ).
cnf(2084,plain,
equal(join(complement(u),join(complement(u),u)),top),
inference(spr,[status(thm),theory(equality)],[1088,237]),
[iquote('0:SpR:1088.0,237.0')] ).
cnf(2096,plain,
equal(join(top,complement(u)),top),
inference(rew,[status(thm),theory(equality)],[5,2084,3]),
[iquote('0:Rew:5.0,2084.0,3.0,2084.0,5.0,2084.0')] ).
cnf(2097,plain,
equal(join(u,top),converse(top)),
inference(rew,[status(thm),theory(equality)],[2096,1724]),
[iquote('0:Rew:2096.0,1724.0')] ).
cnf(2098,plain,
equal(join(u,top),top),
inference(rew,[status(thm),theory(equality)],[1581,2097]),
[iquote('0:Rew:1581.0,2097.0')] ).
cnf(2113,plain,
equal(composition(top,complement(composition(top,top))),composition(u,complement(composition(top,top)))),
inference(rew,[status(thm),theory(equality)],[2098,1687]),
[iquote('0:Rew:2098.0,1687.0')] ).
cnf(2121,plain,
equal(composition(u,complement(composition(top,top))),zero),
inference(rew,[status(thm),theory(equality)],[1631,2113]),
[iquote('0:Rew:1631.0,2113.0')] ).
cnf(2128,plain,
equal(join(top,u),top),
inference(spr,[status(thm),theory(equality)],[2098,5]),
[iquote('0:SpR:2098.0,5.0')] ).
cnf(2198,plain,
equal(composition(converse(complement(composition(top,top))),u),converse(zero)),
inference(spr,[status(thm),theory(equality)],[2121,33]),
[iquote('0:SpR:2121.0,33.0')] ).
cnf(2199,plain,
equal(complement(composition(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[2121,674]),
[iquote('0:SpR:2121.0,674.0')] ).
cnf(2200,plain,
equal(composition(u,zero),zero),
inference(rew,[status(thm),theory(equality)],[2199,2121]),
[iquote('0:Rew:2199.0,2121.0')] ).
cnf(2203,plain,
equal(join(meet(zero,u),composition(u,composition(converse(zero),meet(zero,composition(top,u))))),composition(u,composition(converse(zero),meet(zero,composition(top,u))))),
inference(rew,[status(thm),theory(equality)],[2199,1690]),
[iquote('0:Rew:2199.0,1690.0')] ).
cnf(2279,plain,
equal(composition(converse(complement(composition(top,top))),u),zero),
inference(rew,[status(thm),theory(equality)],[1327,2198]),
[iquote('0:Rew:1327.0,2198.0')] ).
cnf(2280,plain,
equal(composition(converse(zero),u),zero),
inference(rew,[status(thm),theory(equality)],[2199,2279]),
[iquote('0:Rew:2199.0,2279.0')] ).
cnf(2281,plain,
equal(composition(zero,u),zero),
inference(rew,[status(thm),theory(equality)],[1327,2280]),
[iquote('0:Rew:1327.0,2280.0')] ).
cnf(2342,plain,
equal(join(meet(zero,u),composition(u,composition(zero,meet(zero,composition(top,u))))),composition(u,composition(zero,meet(zero,composition(top,u))))),
inference(rew,[status(thm),theory(equality)],[1327,2203]),
[iquote('0:Rew:1327.0,2203.0')] ).
cnf(2343,plain,
equal(join(meet(zero,u),zero),zero),
inference(rew,[status(thm),theory(equality)],[2200,2342,2281]),
[iquote('0:Rew:2200.0,2342.0,2281.0,2342.0')] ).
cnf(2344,plain,
equal(meet(zero,u),zero),
inference(rew,[status(thm),theory(equality)],[1050,2343,5]),
[iquote('0:Rew:1050.0,2343.0,5.0,2343.0')] ).
cnf(6563,plain,
equal(join(composition(join(u,v),w),complement(composition(v,w))),join(composition(u,w),top)),
inference(spr,[status(thm),theory(equality)],[3,353]),
[iquote('0:SpR:3.0,353.0')] ).
cnf(6631,plain,
equal(join(complement(composition(u,v)),composition(join(w,u),v)),top),
inference(rew,[status(thm),theory(equality)],[5,6563,2128]),
[iquote('0:Rew:5.0,6563.0,2128.0,6563.0,5.0,6563.0')] ).
cnf(42607,plain,
equal(join(complement(composition(composition(converse(skc2),skc2),u)),composition(one,u)),top),
inference(spr,[status(thm),theory(equality)],[19,6631]),
[iquote('0:SpR:19.0,6631.0')] ).
cnf(42776,plain,
equal(join(u,complement(composition(converse(skc2),composition(skc2,u)))),top),
inference(rew,[status(thm),theory(equality)],[5,42607,12,674]),
[iquote('0:Rew:5.0,42607.0,12.0,42607.0,674.0,42607.0')] ).
cnf(131881,plain,
equal(meet(complement(u),composition(converse(skc2),composition(skc2,u))),complement(top)),
inference(spr,[status(thm),theory(equality)],[42776,1163]),
[iquote('0:SpR:42776.0,1163.0')] ).
cnf(132068,plain,
equal(meet(complement(u),composition(converse(skc2),composition(skc2,u))),zero),
inference(rew,[status(thm),theory(equality)],[84,131881]),
[iquote('0:Rew:84.0,131881.0')] ).
cnf(166998,plain,
equal(join(meet(composition(skc2,complement(u)),composition(skc2,u)),meet(composition(skc2,u),composition(skc2,zero))),meet(composition(skc2,u),composition(skc2,zero))),
inference(spr,[status(thm),theory(equality)],[132068,86]),
[iquote('0:SpR:132068.0,86.0')] ).
cnf(167138,plain,
equal(meet(composition(skc2,u),composition(skc2,complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[1050,166998,5,85,2344,2200]),
[iquote('0:Rew:1050.0,166998.0,5.0,166998.0,85.0,166998.0,2344.0,166998.0,85.0,166998.0,2200.0,166998.0')] ).
cnf(167139,plain,
$false,
inference(unc,[status(thm)],[167138,10]),
[iquote('0:UnC:167138.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL041+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 13:04:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 183.47/183.67
% 183.47/183.67 SPASS V 3.9
% 183.47/183.67 SPASS beiseite: Proof found.
% 183.47/183.67 % SZS status Theorem
% 183.47/183.67 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 183.47/183.67 SPASS derived 100590 clauses, backtracked 0 clauses, performed 0 splits and kept 13280 clauses.
% 183.47/183.67 SPASS allocated 252430 KBytes.
% 183.47/183.67 SPASS spent 0:03:03.13 on the problem.
% 183.47/183.67 0:00:00.03 for the input.
% 183.47/183.67 0:00:00.03 for the FLOTTER CNF translation.
% 183.47/183.67 0:00:00.81 for inferences.
% 183.47/183.67 0:00:00.00 for the backtracking.
% 183.47/183.67 0:03:02.03 for the reduction.
% 183.47/183.67
% 183.47/183.67
% 183.47/183.67 Here is a proof with depth 10, length 121 :
% 183.47/183.67 % SZS output start Refutation
% See solution above
% 188.14/188.31 Formulae used in the proof : composition_identity converse_idempotence def_top def_zero maddux1_join_commutativity goals maddux4_definiton_of_meet converse_additivity converse_multiplicativity maddux2_join_associativity composition_associativity composition_distributivity converse_cancellativity maddux3_a_kind_of_de_Morgan modular_law_1 dedekind_law
% 188.14/188.31
%------------------------------------------------------------------------------