TSTP Solution File: REL044+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL044+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 20:02:27 EDT 2022
% Result : Theorem 13.17s 13.37s
% Output : Refutation 13.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 16
% Syntax : Number of clauses : 121 ( 121 unt; 0 nHn; 121 RR)
% Number of literals : 121 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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('REL044+2.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL044+2.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,complement(u)),top),
file('REL044+2.p',unknown),
[] ).
cnf(4,axiom,
equal(meet(u,complement(u)),zero),
file('REL044+2.p',unknown),
[] ).
cnf(5,axiom,
equal(join(u,v),join(v,u)),
file('REL044+2.p',unknown),
[] ).
cnf(6,axiom,
~ equal(join(composition(skc5,converse(skc4)),skc3),skc3),
file('REL044+2.p',unknown),
[] ).
cnf(7,axiom,
equal(join(composition(complement(skc3),skc4),complement(skc5)),complement(skc5)),
file('REL044+2.p',unknown),
[] ).
cnf(8,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL044+2.p',unknown),
[] ).
cnf(9,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL044+2.p',unknown),
[] ).
cnf(10,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL044+2.p',unknown),
[] ).
cnf(11,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL044+2.p',unknown),
[] ).
cnf(13,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL044+2.p',unknown),
[] ).
cnf(14,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL044+2.p',unknown),
[] ).
cnf(15,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL044+2.p',unknown),
[] ).
cnf(16,axiom,
equal(join(meet(composition(u,v),w),meet(composition(meet(u,composition(w,converse(v))),v),w)),meet(composition(meet(u,composition(w,converse(v))),v),w)),
file('REL044+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('REL044+2.p',unknown),
[] ).
cnf(19,plain,
~ equal(join(skc3,composition(skc5,converse(skc4))),skc3),
inference(rew,[status(thm),theory(equality)],[5,6]),
[iquote('0:Rew:5.0,6.0')] ).
cnf(20,plain,
equal(join(complement(skc5),composition(complement(skc3),skc4)),complement(skc5)),
inference(rew,[status(thm),theory(equality)],[5,7]),
[iquote('0:Rew:5.0,7.0')] ).
cnf(21,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(22,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(34,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(39,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(40,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(48,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpR:3.0,8.0')] ).
cnf(49,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[5,8]),
[iquote('0:SpR:5.0,8.0')] ).
cnf(51,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[4,48]),
[iquote('0:Rew:4.0,48.0')] ).
cnf(52,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[8,49]),
[iquote('0:Rew:8.0,49.0')] ).
cnf(54,plain,
equal(join(meet(composition(u,v),w),meet(w,composition(meet(u,composition(w,converse(v))),v))),meet(w,composition(meet(u,composition(w,converse(v))),v))),
inference(rew,[status(thm),theory(equality)],[52,16]),
[iquote('0:Rew:52.0,16.0')] ).
cnf(62,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[51,8]),
[iquote('0:SpR:51.0,8.0')] ).
cnf(75,plain,
equal(join(meet(top,u),complement(join(zero,u))),top),
inference(spr,[status(thm),theory(equality)],[51,22]),
[iquote('0:SpR:51.0,22.0')] ).
cnf(76,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[3,22]),
[iquote('0:SpR:3.0,22.0')] ).
cnf(80,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[8,22]),
[iquote('0:SpR:8.0,22.0')] ).
cnf(81,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[4,22]),
[iquote('0:SpR:4.0,22.0')] ).
cnf(86,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[5,76,51]),
[iquote('0:Rew:5.0,76.0,51.0,76.0')] ).
cnf(87,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[5,80]),
[iquote('0:Rew:5.0,80.0')] ).
cnf(88,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[8,81]),
[iquote('0:Rew:8.0,81.0')] ).
cnf(98,plain,
equal(meet(join(zero,complement(u)),meet(top,u)),zero),
inference(spr,[status(thm),theory(equality)],[62,4]),
[iquote('0:SpR:62.0,4.0')] ).
cnf(103,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,join(zero,complement(v)))),
inference(spr,[status(thm),theory(equality)],[62,8]),
[iquote('0:SpR:62.0,8.0')] ).
cnf(112,plain,
equal(meet(meet(top,u),join(zero,complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[52,98]),
[iquote('0:Rew:52.0,98.0')] ).
cnf(162,plain,
equal(join(u,join(v,complement(join(u,v)))),top),
inference(spr,[status(thm),theory(equality)],[11,3]),
[iquote('0:SpR:11.0,3.0')] ).
cnf(163,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(170,plain,
equal(join(complement(skc5),join(composition(complement(skc3),skc4),u)),join(complement(skc5),u)),
inference(spr,[status(thm),theory(equality)],[20,11]),
[iquote('0:SpR:20.0,11.0')] ).
cnf(221,plain,
equal(join(zero,composition(converse(u),complement(composition(u,top)))),zero),
inference(spr,[status(thm),theory(equality)],[51,21]),
[iquote('0:SpR:51.0,21.0')] ).
cnf(345,plain,
equal(meet(meet(u,top),join(zero,complement(u))),zero),
inference(spr,[status(thm),theory(equality)],[52,112]),
[iquote('0:SpR:52.0,112.0')] ).
cnf(456,plain,
equal(join(zero,complement(join(complement(meet(u,top)),join(zero,complement(u))))),meet(u,top)),
inference(spr,[status(thm),theory(equality)],[345,22]),
[iquote('0:SpR:345.0,22.0')] ).
cnf(476,plain,
equal(join(zero,complement(join(zero,join(complement(u),complement(meet(u,top)))))),meet(u,top)),
inference(rew,[status(thm),theory(equality)],[163,456]),
[iquote('0:Rew:163.0,456.0')] ).
cnf(479,plain,
equal(join(meet(composition(u,converse(v)),w),meet(w,composition(meet(u,composition(w,v)),converse(v)))),meet(w,composition(meet(u,composition(w,v)),converse(v)))),
inference(spr,[status(thm),theory(equality)],[2,54]),
[iquote('0:SpR:2.0,54.0')] ).
cnf(601,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[1,34]),
[iquote('0:SpR:1.0,34.0')] ).
cnf(604,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[2,601]),
[iquote('0:Rew:2.0,601.0')] ).
cnf(615,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[604,1]),
[iquote('0:SpR:604.0,1.0')] ).
cnf(627,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[604,21]),
[iquote('0:SpR:604.0,21.0')] ).
cnf(633,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[615,604]),
[iquote('0:Rew:615.0,604.0')] ).
cnf(648,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[633,627]),
[iquote('0:Rew:633.0,627.0')] ).
cnf(758,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[648,8]),
[iquote('0:SpR:648.0,8.0')] ).
cnf(764,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[51,648]),
[iquote('0:SpR:51.0,648.0')] ).
cnf(786,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[758,88]),
[iquote('0:Rew:758.0,88.0')] ).
cnf(821,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[764,11]),
[iquote('0:SpR:764.0,11.0')] ).
cnf(838,plain,
equal(meet(top,complement(u)),complement(u)),
inference(spr,[status(thm),theory(equality)],[786,62]),
[iquote('0:SpR:786.0,62.0')] ).
cnf(845,plain,
equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[8,786]),
[iquote('0:SpR:8.0,786.0')] ).
cnf(878,plain,
equal(join(complement(u),complement(join(zero,complement(u)))),top),
inference(spr,[status(thm),theory(equality)],[838,75]),
[iquote('0:SpR:838.0,75.0')] ).
cnf(886,plain,
equal(join(complement(u),meet(top,u)),top),
inference(rew,[status(thm),theory(equality)],[62,878]),
[iquote('0:Rew:62.0,878.0')] ).
cnf(972,plain,
equal(join(complement(u),meet(u,top)),top),
inference(spr,[status(thm),theory(equality)],[52,886]),
[iquote('0:SpR:52.0,886.0')] ).
cnf(997,plain,
equal(join(meet(u,meet(u,top)),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[972,22]),
[iquote('0:SpR:972.0,22.0')] ).
cnf(1007,plain,
equal(join(zero,meet(u,meet(u,top))),u),
inference(rew,[status(thm),theory(equality)],[5,997,51]),
[iquote('0:Rew:5.0,997.0,51.0,997.0')] ).
cnf(1056,plain,
equal(join(u,converse(complement(converse(u)))),converse(top)),
inference(spr,[status(thm),theory(equality)],[3,40]),
[iquote('0:SpR:3.0,40.0')] ).
cnf(1114,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[86,821]),
[iquote('0:SpR:86.0,821.0')] ).
cnf(1121,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[1114,786]),
[iquote('0:Rew:1114.0,786.0')] ).
cnf(1122,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[1114,62]),
[iquote('0:Rew:1114.0,62.0')] ).
cnf(1128,plain,
equal(composition(converse(u),complement(composition(u,top))),zero),
inference(rew,[status(thm),theory(equality)],[1114,221]),
[iquote('0:Rew:1114.0,221.0')] ).
cnf(1132,plain,
equal(join(zero,complement(join(complement(u),complement(meet(u,top))))),meet(u,top)),
inference(rew,[status(thm),theory(equality)],[1114,476]),
[iquote('0:Rew:1114.0,476.0')] ).
cnf(1134,plain,
equal(join(complement(u),complement(v)),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[1114,845]),
[iquote('0:Rew:1114.0,845.0')] ).
cnf(1136,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[1114,103]),
[iquote('0:Rew:1114.0,103.0')] ).
cnf(1143,plain,
equal(meet(u,meet(u,top)),u),
inference(rew,[status(thm),theory(equality)],[1114,1007]),
[iquote('0:Rew:1114.0,1007.0')] ).
cnf(1159,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[1121,1122]),
[iquote('0:Rew:1121.0,1122.0')] ).
cnf(1200,plain,
equal(complement(join(complement(u),v)),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[1159,1136]),
[iquote('0:Rew:1159.0,1136.0')] ).
cnf(1209,plain,
equal(meet(u,top),u),
inference(rew,[status(thm),theory(equality)],[1114,1132,1121,1143,1134]),
[iquote('0:Rew:1114.0,1132.0,1121.0,1132.0,1143.0,1132.0,1134.0,1132.0')] ).
cnf(1230,plain,
equal(complement(zero),top),
inference(spr,[status(thm),theory(equality)],[1114,3]),
[iquote('0:SpR:1114.0,3.0')] ).
cnf(1231,plain,
equal(join(u,zero),u),
inference(spr,[status(thm),theory(equality)],[1114,5]),
[iquote('0:SpR:1114.0,5.0')] ).
cnf(1235,plain,
equal(join(converse(zero),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[1114,39]),
[iquote('0:SpR:1114.0,39.0')] ).
cnf(1248,plain,
equal(join(converse(zero),u),u),
inference(rew,[status(thm),theory(equality)],[2,1235]),
[iquote('0:Rew:2.0,1235.0')] ).
cnf(1324,plain,
equal(converse(zero),zero),
inference(spr,[status(thm),theory(equality)],[1248,1231]),
[iquote('0:SpR:1248.0,1231.0')] ).
cnf(1414,plain,
equal(join(meet(composition(u,v),w),join(meet(w,composition(meet(u,composition(w,converse(v))),v)),complement(meet(w,composition(meet(u,composition(w,converse(v))),v))))),top),
inference(spr,[status(thm),theory(equality)],[54,162]),
[iquote('0:SpR:54.0,162.0')] ).
cnf(1440,plain,
equal(join(top,meet(composition(u,v),w)),top),
inference(rew,[status(thm),theory(equality)],[5,1414,3]),
[iquote('0:Rew:5.0,1414.0,3.0,1414.0')] ).
cnf(1458,plain,
equal(composition(converse(complement(composition(u,top))),u),converse(zero)),
inference(spr,[status(thm),theory(equality)],[1128,34]),
[iquote('0:SpR:1128.0,34.0')] ).
cnf(1461,plain,
equal(composition(u,complement(composition(converse(u),top))),zero),
inference(spr,[status(thm),theory(equality)],[2,1128]),
[iquote('0:SpR:2.0,1128.0')] ).
cnf(1473,plain,
equal(composition(converse(complement(composition(u,top))),u),zero),
inference(rew,[status(thm),theory(equality)],[1324,1458]),
[iquote('0:Rew:1324.0,1458.0')] ).
cnf(1836,plain,
equal(composition(complement(composition(top,top)),complement(zero)),zero),
inference(spr,[status(thm),theory(equality)],[1473,1461]),
[iquote('0:SpR:1473.0,1461.0')] ).
cnf(1845,plain,
equal(composition(complement(composition(top,top)),top),zero),
inference(rew,[status(thm),theory(equality)],[1230,1836]),
[iquote('0:Rew:1230.0,1836.0')] ).
cnf(1864,plain,
equal(join(meet(zero,u),composition(meet(complement(composition(top,top)),composition(u,converse(top))),meet(top,composition(converse(complement(composition(top,top))),u)))),composition(meet(complement(composition(top,top)),composition(u,converse(top))),meet(top,composition(converse(complement(composition(top,top))),u)))),
inference(spr,[status(thm),theory(equality)],[1845,18]),
[iquote('0:SpR:1845.0,18.0')] ).
cnf(1876,plain,
equal(join(meet(zero,u),composition(meet(complement(composition(top,top)),composition(u,converse(top))),composition(converse(complement(composition(top,top))),u))),composition(meet(complement(composition(top,top)),composition(u,converse(top))),composition(converse(complement(composition(top,top))),u))),
inference(rew,[status(thm),theory(equality)],[1159,1864]),
[iquote('0:Rew:1159.0,1864.0')] ).
cnf(1881,plain,
equal(join(top,meet(u,v)),top),
inference(spr,[status(thm),theory(equality)],[1,1440]),
[iquote('0:SpR:1.0,1440.0')] ).
cnf(1937,plain,
equal(join(top,u),top),
inference(spr,[status(thm),theory(equality)],[1209,1881]),
[iquote('0:SpR:1209.0,1881.0')] ).
cnf(1959,plain,
equal(converse(top),top),
inference(spr,[status(thm),theory(equality)],[1937,1056]),
[iquote('0:SpR:1937.0,1056.0')] ).
cnf(1976,plain,
equal(join(meet(zero,u),composition(meet(complement(composition(top,top)),composition(u,top)),composition(converse(complement(composition(top,top))),u))),composition(meet(complement(composition(top,top)),composition(u,top)),composition(converse(complement(composition(top,top))),u))),
inference(rew,[status(thm),theory(equality)],[1959,1876]),
[iquote('0:Rew:1959.0,1876.0')] ).
cnf(1993,plain,
equal(composition(top,complement(composition(top,top))),zero),
inference(spr,[status(thm),theory(equality)],[1959,1128]),
[iquote('0:SpR:1959.0,1128.0')] ).
cnf(2082,plain,
equal(join(zero,composition(u,complement(composition(top,top)))),composition(join(top,u),complement(composition(top,top)))),
inference(spr,[status(thm),theory(equality)],[1993,13]),
[iquote('0:SpR:1993.0,13.0')] ).
cnf(2089,plain,
equal(composition(u,complement(composition(top,top))),zero),
inference(rew,[status(thm),theory(equality)],[1114,2082,1993,1937]),
[iquote('0:Rew:1114.0,2082.0,1993.0,2082.0,1937.0,2082.0')] ).
cnf(2183,plain,
equal(composition(converse(complement(composition(top,top))),u),converse(zero)),
inference(spr,[status(thm),theory(equality)],[2089,34]),
[iquote('0:SpR:2089.0,34.0')] ).
cnf(2184,plain,
equal(complement(composition(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[2089,633]),
[iquote('0:SpR:2089.0,633.0')] ).
cnf(2186,plain,
equal(composition(u,zero),zero),
inference(rew,[status(thm),theory(equality)],[2184,2089]),
[iquote('0:Rew:2184.0,2089.0')] ).
cnf(2192,plain,
equal(join(meet(zero,u),composition(meet(zero,composition(u,top)),composition(converse(zero),u))),composition(meet(zero,composition(u,top)),composition(converse(zero),u))),
inference(rew,[status(thm),theory(equality)],[2184,1976]),
[iquote('0:Rew:2184.0,1976.0')] ).
cnf(2282,plain,
equal(composition(converse(complement(composition(top,top))),u),zero),
inference(rew,[status(thm),theory(equality)],[1324,2183]),
[iquote('0:Rew:1324.0,2183.0')] ).
cnf(2283,plain,
equal(composition(converse(zero),u),zero),
inference(rew,[status(thm),theory(equality)],[2184,2282]),
[iquote('0:Rew:2184.0,2282.0')] ).
cnf(2284,plain,
equal(composition(zero,u),zero),
inference(rew,[status(thm),theory(equality)],[1324,2283]),
[iquote('0:Rew:1324.0,2283.0')] ).
cnf(2359,plain,
equal(join(meet(zero,u),composition(meet(zero,composition(u,top)),composition(zero,u))),composition(meet(zero,composition(u,top)),composition(zero,u))),
inference(rew,[status(thm),theory(equality)],[1324,2192]),
[iquote('0:Rew:1324.0,2192.0')] ).
cnf(2360,plain,
equal(join(meet(zero,u),zero),zero),
inference(rew,[status(thm),theory(equality)],[2186,2359,2284]),
[iquote('0:Rew:2186.0,2359.0,2284.0,2359.0')] ).
cnf(2361,plain,
equal(meet(zero,u),zero),
inference(rew,[status(thm),theory(equality)],[1114,2360,5]),
[iquote('0:Rew:1114.0,2360.0,5.0,2360.0')] ).
cnf(3847,plain,
equal(join(complement(skc5),complement(composition(complement(skc3),skc4))),join(complement(skc5),top)),
inference(spr,[status(thm),theory(equality)],[3,170]),
[iquote('0:SpR:3.0,170.0')] ).
cnf(3869,plain,
equal(join(complement(skc5),complement(composition(complement(skc3),skc4))),top),
inference(rew,[status(thm),theory(equality)],[1937,3847,5]),
[iquote('0:Rew:1937.0,3847.0,5.0,3847.0')] ).
cnf(3870,plain,
equal(complement(meet(skc5,composition(complement(skc3),skc4))),top),
inference(rew,[status(thm),theory(equality)],[1134,3869]),
[iquote('0:Rew:1134.0,3869.0')] ).
cnf(3893,plain,
equal(meet(skc5,composition(complement(skc3),skc4)),complement(top)),
inference(spr,[status(thm),theory(equality)],[3870,1121]),
[iquote('0:SpR:3870.0,1121.0')] ).
cnf(3905,plain,
equal(meet(skc5,composition(complement(skc3),skc4)),zero),
inference(rew,[status(thm),theory(equality)],[51,3893]),
[iquote('0:Rew:51.0,3893.0')] ).
cnf(10918,plain,
equal(join(meet(composition(skc5,converse(skc4)),complement(skc3)),meet(complement(skc3),composition(zero,converse(skc4)))),meet(complement(skc3),composition(zero,converse(skc4)))),
inference(spr,[status(thm),theory(equality)],[3905,479]),
[iquote('0:SpR:3905.0,479.0')] ).
cnf(10958,plain,
equal(meet(complement(skc3),composition(skc5,converse(skc4))),zero),
inference(rew,[status(thm),theory(equality)],[1114,10918,5,52,2361,2284]),
[iquote('0:Rew:1114.0,10918.0,5.0,10918.0,52.0,10918.0,2361.0,10918.0,52.0,10918.0,2284.0,10918.0')] ).
cnf(10996,plain,
equal(join(zero,meet(complement(skc3),complement(composition(skc5,converse(skc4))))),complement(skc3)),
inference(spr,[status(thm),theory(equality)],[10958,87]),
[iquote('0:SpR:10958.0,87.0')] ).
cnf(11034,plain,
equal(meet(complement(skc3),complement(composition(skc5,converse(skc4)))),complement(skc3)),
inference(rew,[status(thm),theory(equality)],[1114,10996]),
[iquote('0:Rew:1114.0,10996.0')] ).
cnf(35208,plain,
equal(meet(complement(u),complement(v)),complement(join(u,v))),
inference(spr,[status(thm),theory(equality)],[1121,1200]),
[iquote('0:SpR:1121.0,1200.0')] ).
cnf(35338,plain,
equal(complement(join(skc3,composition(skc5,converse(skc4)))),complement(skc3)),
inference(rew,[status(thm),theory(equality)],[35208,11034]),
[iquote('0:Rew:35208.0,11034.0')] ).
cnf(35502,plain,
equal(join(skc3,composition(skc5,converse(skc4))),complement(complement(skc3))),
inference(spr,[status(thm),theory(equality)],[35338,1121]),
[iquote('0:SpR:35338.0,1121.0')] ).
cnf(35562,plain,
equal(join(skc3,composition(skc5,converse(skc4))),skc3),
inference(rew,[status(thm),theory(equality)],[1121,35502]),
[iquote('0:Rew:1121.0,35502.0')] ).
cnf(35563,plain,
$false,
inference(mrr,[status(thm)],[35562,19]),
[iquote('0:MRR:35562.0,19.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : REL044+2 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.15 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Fri Jul 8 10:28:23 EDT 2022
% 0.14/0.37 % CPUTime :
% 13.17/13.37
% 13.17/13.37 SPASS V 3.9
% 13.17/13.37 SPASS beiseite: Proof found.
% 13.17/13.37 % SZS status Theorem
% 13.17/13.37 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.17/13.37 SPASS derived 21869 clauses, backtracked 0 clauses, performed 0 splits and kept 4147 clauses.
% 13.17/13.37 SPASS allocated 129186 KBytes.
% 13.17/13.37 SPASS spent 0:0:12.96 on the problem.
% 13.17/13.37 0:00:00.04 for the input.
% 13.17/13.37 0:00:00.02 for the FLOTTER CNF translation.
% 13.17/13.37 0:00:00.18 for inferences.
% 13.17/13.37 0:00:00.00 for the backtracking.
% 13.17/13.37 0:0:12.66 for the reduction.
% 13.17/13.37
% 13.17/13.37
% 13.17/13.37 Here is a proof with depth 10, length 121 :
% 13.17/13.37 % SZS output start Refutation
% See solution above
% 13.55/13.77 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_distributivity converse_cancellativity maddux3_a_kind_of_de_Morgan modular_law_2 dedekind_law
% 13.55/13.77
%------------------------------------------------------------------------------