TSTP Solution File: LAT009-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT009-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 : Sun Jul 17 06:48:34 EDT 2022
% Result : Unsatisfiable 3.75s 3.91s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 10
% Syntax : Number of clauses : 139 ( 139 unt; 0 nHn; 139 RR)
% Number of literals : 139 ( 0 equ; 1 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 : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(join(meet(join(meet(u,v),w),v),meet(w,u)),meet(join(meet(join(u,v),w),v),join(w,u))),
file('LAT009-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(meet(join(a,b),join(a,c)),join(a,meet(b,c))),
file('LAT009-1.p',unknown),
[] ).
cnf(3,axiom,
equal(meet(u,u),u),
file('LAT009-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(u,u),u),
file('LAT009-1.p',unknown),
[] ).
cnf(5,axiom,
equal(meet(u,join(u,v)),u),
file('LAT009-1.p',unknown),
[] ).
cnf(6,axiom,
equal(join(u,meet(u,v)),u),
file('LAT009-1.p',unknown),
[] ).
cnf(7,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT009-1.p',unknown),
[] ).
cnf(8,axiom,
equal(join(u,v),join(v,u)),
file('LAT009-1.p',unknown),
[] ).
cnf(9,axiom,
equal(meet(meet(u,v),w),meet(u,meet(v,w))),
file('LAT009-1.p',unknown),
[] ).
cnf(10,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('LAT009-1.p',unknown),
[] ).
cnf(11,plain,
equal(join(meet(u,v),meet(w,join(meet(v,w),u))),meet(join(u,v),join(w,meet(join(v,w),u)))),
inference(rew,[status(thm),theory(equality)],[8,1,7]),
[iquote('0:Rew:8.0,1.0,7.0,1.0,7.0,1.0,8.0,1.0')] ).
cnf(21,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[8,5]),
[iquote('0:SpR:8.0,5.0')] ).
cnf(29,plain,
equal(join(u,meet(v,u)),u),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(40,plain,
equal(meet(meet(u,v),u),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[6,21]),
[iquote('0:SpR:6.0,21.0')] ).
cnf(43,plain,
equal(meet(u,meet(u,v)),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[7,40]),
[iquote('0:Rew:7.0,40.0')] ).
cnf(47,plain,
equal(meet(meet(u,v),v),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[29,21]),
[iquote('0:SpR:29.0,21.0')] ).
cnf(50,plain,
equal(join(join(u,v),u),join(u,v)),
inference(spr,[status(thm),theory(equality)],[5,29]),
[iquote('0:SpR:5.0,29.0')] ).
cnf(51,plain,
equal(join(join(u,v),v),join(u,v)),
inference(spr,[status(thm),theory(equality)],[21,29]),
[iquote('0:SpR:21.0,29.0')] ).
cnf(53,plain,
equal(meet(u,meet(v,u)),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[7,47]),
[iquote('0:Rew:7.0,47.0')] ).
cnf(54,plain,
equal(join(u,join(u,v)),join(u,v)),
inference(rew,[status(thm),theory(equality)],[8,50]),
[iquote('0:Rew:8.0,50.0')] ).
cnf(55,plain,
equal(join(u,join(v,u)),join(v,u)),
inference(rew,[status(thm),theory(equality)],[8,51]),
[iquote('0:Rew:8.0,51.0')] ).
cnf(66,plain,
equal(join(u,join(v,meet(join(u,v),w))),join(u,v)),
inference(spr,[status(thm),theory(equality)],[10,6]),
[iquote('0:SpR:10.0,6.0')] ).
cnf(68,plain,
equal(meet(join(u,v),join(u,join(v,w))),join(u,v)),
inference(spr,[status(thm),theory(equality)],[10,5]),
[iquote('0:SpR:10.0,5.0')] ).
cnf(69,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[10,8]),
[iquote('0:SpR:10.0,8.0')] ).
cnf(72,plain,
equal(meet(u,join(v,join(w,u))),u),
inference(spr,[status(thm),theory(equality)],[10,21]),
[iquote('0:SpR:10.0,21.0')] ).
cnf(75,plain,
equal(join(u,join(meet(u,v),w)),join(u,w)),
inference(spr,[status(thm),theory(equality)],[6,10]),
[iquote('0:SpR:6.0,10.0')] ).
cnf(141,plain,
equal(meet(u,join(v,join(u,w))),u),
inference(spr,[status(thm),theory(equality)],[8,72]),
[iquote('0:SpR:8.0,72.0')] ).
cnf(161,plain,
equal(meet(u,meet(v,w)),meet(w,meet(u,v))),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(165,plain,
equal(meet(u,meet(v,join(w,meet(u,v)))),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[9,21]),
[iquote('0:SpR:9.0,21.0')] ).
cnf(170,plain,
equal(join(u,meet(v,meet(w,u))),u),
inference(spr,[status(thm),theory(equality)],[9,29]),
[iquote('0:SpR:9.0,29.0')] ).
cnf(174,plain,
equal(meet(meet(u,v),w),meet(v,meet(u,w))),
inference(spr,[status(thm),theory(equality)],[7,9]),
[iquote('0:SpR:7.0,9.0')] ).
cnf(175,plain,
equal(meet(u,meet(join(u,v),w)),meet(u,w)),
inference(spr,[status(thm),theory(equality)],[5,9]),
[iquote('0:SpR:5.0,9.0')] ).
cnf(176,plain,
equal(meet(u,meet(join(v,u),w)),meet(u,w)),
inference(spr,[status(thm),theory(equality)],[21,9]),
[iquote('0:SpR:21.0,9.0')] ).
cnf(182,plain,
equal(meet(u,meet(v,w)),meet(v,meet(u,w))),
inference(rew,[status(thm),theory(equality)],[9,174]),
[iquote('0:Rew:9.0,174.0')] ).
cnf(230,plain,
equal(join(u,meet(v,meet(u,w))),u),
inference(spr,[status(thm),theory(equality)],[7,170]),
[iquote('0:SpR:7.0,170.0')] ).
cnf(231,plain,
equal(join(join(u,v),meet(w,u)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[5,170]),
[iquote('0:SpR:5.0,170.0')] ).
cnf(248,plain,
equal(join(u,join(v,meet(w,u))),join(u,v)),
inference(rew,[status(thm),theory(equality)],[10,231]),
[iquote('0:Rew:10.0,231.0')] ).
cnf(341,plain,
equal(join(u,join(v,w)),join(w,join(v,u))),
inference(spr,[status(thm),theory(equality)],[8,69]),
[iquote('0:SpR:8.0,69.0')] ).
cnf(397,plain,
equal(meet(meet(u,v),join(u,w)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[75,141]),
[iquote('0:SpR:75.0,141.0')] ).
cnf(416,plain,
equal(join(u,join(v,meet(u,w))),join(u,v)),
inference(spr,[status(thm),theory(equality)],[8,75]),
[iquote('0:SpR:8.0,75.0')] ).
cnf(424,plain,
equal(meet(u,meet(v,join(u,w))),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[9,397]),
[iquote('0:Rew:9.0,397.0')] ).
cnf(682,plain,
equal(join(u,meet(join(u,v),join(w,meet(join(v,w),u)))),join(u,meet(w,join(meet(v,w),u)))),
inference(spr,[status(thm),theory(equality)],[11,75]),
[iquote('0:SpR:11.0,75.0')] ).
cnf(690,plain,
equal(meet(join(u,v),join(join(v,w),meet(join(v,join(v,w)),u))),join(meet(u,v),meet(join(v,w),join(v,u)))),
inference(spr,[status(thm),theory(equality)],[5,11]),
[iquote('0:SpR:5.0,11.0')] ).
cnf(699,plain,
equal(meet(join(meet(u,v),u),join(v,meet(join(u,v),meet(u,v)))),join(meet(meet(u,v),u),meet(v,meet(u,v)))),
inference(spr,[status(thm),theory(equality)],[4,11]),
[iquote('0:SpR:4.0,11.0')] ).
cnf(707,plain,
equal(meet(join(join(u,meet(v,w)),v),join(w,meet(join(v,w),join(u,meet(v,w))))),join(meet(join(u,meet(v,w)),v),meet(w,join(u,meet(v,w))))),
inference(spr,[status(thm),theory(equality)],[55,11]),
[iquote('0:SpR:55.0,11.0')] ).
cnf(715,plain,
equal(meet(join(join(u,v),w),join(v,meet(join(w,v),join(u,v)))),join(meet(join(u,v),w),v)),
inference(spr,[status(thm),theory(equality)],[72,11]),
[iquote('0:SpR:72.0,11.0')] ).
cnf(720,plain,
equal(meet(join(u,join(u,v)),join(w,meet(join(join(u,v),w),u))),join(u,meet(w,join(meet(join(u,v),w),u)))),
inference(spr,[status(thm),theory(equality)],[5,11]),
[iquote('0:SpR:5.0,11.0')] ).
cnf(721,plain,
equal(meet(join(u,join(v,u)),join(w,meet(join(join(v,u),w),u))),join(u,meet(w,join(meet(join(v,u),w),u)))),
inference(spr,[status(thm),theory(equality)],[21,11]),
[iquote('0:SpR:21.0,11.0')] ).
cnf(725,plain,
equal(meet(join(u,meet(v,u)),join(w,meet(join(meet(v,u),w),u))),join(meet(v,u),meet(w,join(meet(meet(v,u),w),u)))),
inference(spr,[status(thm),theory(equality)],[53,11]),
[iquote('0:SpR:53.0,11.0')] ).
cnf(727,plain,
equal(join(meet(u,v),meet(w,join(meet(u,w),v))),meet(join(v,u),join(w,meet(join(u,w),v)))),
inference(spr,[status(thm),theory(equality)],[7,11]),
[iquote('0:SpR:7.0,11.0')] ).
cnf(737,plain,
equal(meet(join(u,join(v,w)),join(v,meet(join(w,v),join(u,v)))),join(v,meet(join(u,v),w))),
inference(rew,[status(thm),theory(equality)],[10,715,8]),
[iquote('0:Rew:10.0,715.0,8.0,715.0')] ).
cnf(738,plain,
equal(join(u,meet(v,join(u,meet(join(w,u),v)))),meet(join(w,u),join(v,u))),
inference(rew,[status(thm),theory(equality)],[55,721,141,7,10,8]),
[iquote('0:Rew:55.0,721.0,141.0,721.0,7.0,721.0,10.0,721.0,8.0,721.0')] ).
cnf(739,plain,
equal(join(u,meet(v,join(u,meet(join(u,w),v)))),meet(join(u,w),join(v,u))),
inference(rew,[status(thm),theory(equality)],[54,720,5,7,10,8]),
[iquote('0:Rew:54.0,720.0,5.0,720.0,7.0,720.0,10.0,720.0,8.0,720.0')] ).
cnf(740,plain,
equal(join(meet(u,v),meet(v,u)),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[6,699,8,29,21,9,7,53]),
[iquote('0:Rew:6.0,699.0,8.0,699.0,29.0,699.0,21.0,699.0,9.0,699.0,7.0,699.0,53.0,699.0,9.0,699.0,53.0,699.0')] ).
cnf(745,plain,
equal(meet(join(u,v),join(v,join(w,meet(join(v,w),u)))),join(meet(u,v),meet(join(v,w),join(v,u)))),
inference(rew,[status(thm),theory(equality)],[10,690,54]),
[iquote('0:Rew:10.0,690.0,54.0,690.0')] ).
cnf(746,plain,
equal(join(meet(u,v),meet(join(v,w),join(v,u))),meet(join(u,v),join(v,w))),
inference(rew,[status(thm),theory(equality)],[66,745]),
[iquote('0:Rew:66.0,745.0')] ).
cnf(750,plain,
equal(meet(u,join(v,meet(u,join(meet(w,u),v)))),join(meet(w,u),meet(v,u))),
inference(rew,[status(thm),theory(equality)],[29,725,7,230,8,9]),
[iquote('0:Rew:29.0,725.0,7.0,725.0,230.0,725.0,8.0,725.0,9.0,725.0')] ).
cnf(780,plain,
equal(join(meet(u,join(v,meet(u,w))),meet(w,join(v,meet(u,w)))),meet(join(v,u),join(w,meet(join(u,w),join(v,meet(u,w)))))),
inference(rew,[status(thm),theory(equality)],[6,707,8,10,7]),
[iquote('0:Rew:6.0,707.0,8.0,707.0,10.0,707.0,7.0,707.0')] ).
cnf(930,plain,
equal(meet(u,meet(v,w)),meet(w,meet(v,u))),
inference(spr,[status(thm),theory(equality)],[7,161]),
[iquote('0:SpR:7.0,161.0')] ).
cnf(1129,plain,
equal(meet(u,meet(v,meet(join(u,w),x))),meet(v,meet(u,x))),
inference(spr,[status(thm),theory(equality)],[175,182]),
[iquote('0:SpR:175.0,182.0')] ).
cnf(1207,plain,
equal(join(meet(u,v),join(meet(v,u),w)),join(meet(v,u),w)),
inference(spr,[status(thm),theory(equality)],[740,10]),
[iquote('0:SpR:740.0,10.0')] ).
cnf(1657,plain,
equal(meet(join(u,meet(v,w)),join(w,u)),join(u,meet(v,w))),
inference(spr,[status(thm),theory(equality)],[248,21]),
[iquote('0:SpR:248.0,21.0')] ).
cnf(1723,plain,
equal(meet(join(u,v),join(v,meet(w,u))),join(v,meet(w,u))),
inference(rew,[status(thm),theory(equality)],[7,1657]),
[iquote('0:Rew:7.0,1657.0')] ).
cnf(1765,plain,
equal(meet(join(u,meet(join(v,u),w)),meet(join(v,u),x)),meet(join(u,meet(join(v,u),w)),x)),
inference(spr,[status(thm),theory(equality)],[66,176]),
[iquote('0:SpR:66.0,176.0')] ).
cnf(1873,plain,
equal(meet(join(u,v),meet(w,join(v,meet(join(u,v),x)))),meet(join(v,meet(join(u,v),x)),w)),
inference(rew,[status(thm),theory(equality)],[161,1765]),
[iquote('0:Rew:161.0,1765.0')] ).
cnf(2349,plain,
equal(join(meet(u,v),join(meet(v,u),w)),join(w,meet(u,v))),
inference(spr,[status(thm),theory(equality)],[740,341]),
[iquote('0:SpR:740.0,341.0')] ).
cnf(2443,plain,
equal(join(meet(u,v),w),join(w,meet(v,u))),
inference(rew,[status(thm),theory(equality)],[1207,2349]),
[iquote('0:Rew:1207.0,2349.0')] ).
cnf(2529,plain,
equal(meet(join(u,v),join(v,u)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[55,68]),
[iquote('0:SpR:55.0,68.0')] ).
cnf(2751,plain,
equal(meet(join(u,meet(v,w)),join(v,u)),join(u,meet(v,w))),
inference(spr,[status(thm),theory(equality)],[416,21]),
[iquote('0:SpR:416.0,21.0')] ).
cnf(2753,plain,
equal(meet(join(u,meet(v,w)),meet(join(v,u),x)),meet(join(u,meet(v,w)),x)),
inference(spr,[status(thm),theory(equality)],[416,176]),
[iquote('0:SpR:416.0,176.0')] ).
cnf(2805,plain,
equal(join(u,meet(join(v,w),join(u,meet(join(w,u),v)))),join(u,meet(v,w))),
inference(spr,[status(thm),theory(equality)],[11,416]),
[iquote('0:SpR:11.0,416.0')] ).
cnf(2833,plain,
equal(meet(join(u,v),join(v,meet(u,w))),join(v,meet(u,w))),
inference(rew,[status(thm),theory(equality)],[7,2751]),
[iquote('0:Rew:7.0,2751.0')] ).
cnf(2851,plain,
equal(meet(join(u,v),meet(w,join(v,meet(u,x)))),meet(join(v,meet(u,x)),w)),
inference(rew,[status(thm),theory(equality)],[161,2753]),
[iquote('0:Rew:161.0,2753.0')] ).
cnf(3631,plain,
equal(meet(join(u,v),meet(join(v,u),w)),meet(join(u,v),w)),
inference(spr,[status(thm),theory(equality)],[2529,9]),
[iquote('0:SpR:2529.0,9.0')] ).
cnf(3647,plain,
equal(meet(join(u,v),meet(join(v,u),w)),meet(w,join(v,u))),
inference(spr,[status(thm),theory(equality)],[2529,930]),
[iquote('0:SpR:2529.0,930.0')] ).
cnf(3750,plain,
equal(meet(join(u,v),w),meet(w,join(v,u))),
inference(rew,[status(thm),theory(equality)],[3631,3647]),
[iquote('0:Rew:3631.0,3647.0')] ).
cnf(7663,plain,
equal(join(u,meet(v,join(u,meet(meet(join(u,w),join(x,u)),v)))),meet(meet(join(u,w),join(x,u)),join(v,u))),
inference(spr,[status(thm),theory(equality)],[739]),
[iquote('0:SpR:739.0,739.0')] ).
cnf(7665,plain,
equal(meet(meet(u,join(v,meet(join(v,w),u))),meet(join(v,w),join(u,v))),meet(u,join(v,meet(join(v,w),u)))),
inference(spr,[status(thm),theory(equality)],[739,21]),
[iquote('0:SpR:739.0,21.0')] ).
cnf(7745,plain,
equal(join(u,meet(meet(join(u,v),w),join(u,meet(join(u,v),w)))),meet(join(u,v),join(meet(join(u,v),w),u))),
inference(spr,[status(thm),theory(equality)],[43,739]),
[iquote('0:SpR:43.0,739.0')] ).
cnf(7771,plain,
equal(join(u,meet(v,join(u,meet(v,join(w,u))))),meet(join(u,w),join(v,u))),
inference(spr,[status(thm),theory(equality)],[3750,739]),
[iquote('0:SpR:3750.0,739.0')] ).
cnf(7850,plain,
equal(meet(join(u,v),join(u,meet(w,join(u,v)))),join(u,meet(join(u,v),w))),
inference(rew,[status(thm),theory(equality)],[165,7745,9,2443]),
[iquote('0:Rew:165.0,7745.0,9.0,7745.0,2443.0,7745.0')] ).
cnf(7854,plain,
equal(meet(u,join(v,meet(join(v,w),u))),meet(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[424,7665,930,165]),
[iquote('0:Rew:424.0,7665.0,930.0,7665.0,165.0,7665.0,930.0,7665.0')] ).
cnf(7855,plain,
equal(join(u,meet(v,join(u,w))),meet(join(u,w),join(v,u))),
inference(rew,[status(thm),theory(equality)],[7854,739]),
[iquote('0:Rew:7854.0,739.0')] ).
cnf(7871,plain,
equal(meet(join(u,v),meet(join(u,v),join(w,u))),join(u,meet(join(u,v),w))),
inference(rew,[status(thm),theory(equality)],[7855,7850]),
[iquote('0:Rew:7855.0,7850.0')] ).
cnf(7876,plain,
equal(meet(join(u,meet(join(v,u),w)),join(join(w,v),u)),join(u,meet(w,v))),
inference(rew,[status(thm),theory(equality)],[7855,2805]),
[iquote('0:Rew:7855.0,2805.0')] ).
cnf(7878,plain,
equal(meet(join(u,meet(v,join(w,u))),join(v,u)),meet(join(u,w),join(v,u))),
inference(rew,[status(thm),theory(equality)],[7855,7771]),
[iquote('0:Rew:7855.0,7771.0')] ).
cnf(7885,plain,
equal(meet(join(u,meet(join(v,u),w)),join(w,u)),meet(join(v,u),join(w,u))),
inference(rew,[status(thm),theory(equality)],[7855,738]),
[iquote('0:Rew:7855.0,738.0')] ).
cnf(7894,plain,
equal(join(u,meet(join(u,v),w)),meet(join(u,v),join(w,u))),
inference(rew,[status(thm),theory(equality)],[43,7871]),
[iquote('0:Rew:43.0,7871.0')] ).
cnf(7909,plain,
equal(meet(join(u,v),join(join(w,meet(join(v,w),u)),u)),join(u,meet(w,join(meet(v,w),u)))),
inference(rew,[status(thm),theory(equality)],[7894,682]),
[iquote('0:Rew:7894.0,682.0')] ).
cnf(7914,plain,
equal(meet(join(u,join(v,w)),join(w,meet(u,join(v,w)))),join(w,meet(u,v))),
inference(rew,[status(thm),theory(equality)],[2443,7876,3750,10]),
[iquote('0:Rew:2443.0,7876.0,3750.0,7876.0,10.0,7876.0')] ).
cnf(7915,plain,
equal(meet(join(u,v),join(v,meet(join(w,v),u))),meet(join(v,w),join(u,v))),
inference(rew,[status(thm),theory(equality)],[2443,7878,3750]),
[iquote('0:Rew:2443.0,7878.0,3750.0,7878.0')] ).
cnf(7916,plain,
equal(join(u,meet(join(v,u),w)),meet(join(u,v),join(w,u))),
inference(rew,[status(thm),theory(equality)],[1723,7915]),
[iquote('0:Rew:1723.0,7915.0')] ).
cnf(7917,plain,
equal(join(meet(u,v),meet(w,join(meet(v,w),u))),meet(join(u,v),meet(join(w,v),join(u,w)))),
inference(rew,[status(thm),theory(equality)],[7916,11]),
[iquote('0:Rew:7916.0,11.0')] ).
cnf(7992,plain,
equal(join(meet(u,join(v,meet(u,w))),meet(w,join(v,meet(u,w)))),meet(join(v,u),meet(join(w,u),join(join(v,meet(u,w)),w)))),
inference(rew,[status(thm),theory(equality)],[7916,780]),
[iquote('0:Rew:7916.0,780.0')] ).
cnf(7993,plain,
equal(join(meet(u,v),meet(w,join(meet(u,w),v))),meet(join(v,u),meet(join(w,u),join(v,w)))),
inference(rew,[status(thm),theory(equality)],[7916,727]),
[iquote('0:Rew:7916.0,727.0')] ).
cnf(8020,plain,
equal(meet(join(u,v),meet(w,meet(join(v,u),join(x,v)))),meet(meet(join(v,u),join(x,v)),w)),
inference(rew,[status(thm),theory(equality)],[7916,1873]),
[iquote('0:Rew:7916.0,1873.0')] ).
cnf(8026,plain,
equal(meet(join(u,join(v,w)),meet(join(v,w),join(join(u,v),v))),join(v,meet(join(u,v),w))),
inference(rew,[status(thm),theory(equality)],[7916,737]),
[iquote('0:Rew:7916.0,737.0')] ).
cnf(8041,plain,
equal(meet(join(u,v),join(v,meet(u,join(w,v)))),meet(join(w,v),join(u,v))),
inference(rew,[status(thm),theory(equality)],[2443,7885,3750]),
[iquote('0:Rew:2443.0,7885.0,3750.0,7885.0')] ).
cnf(8042,plain,
equal(join(u,meet(v,join(w,u))),meet(join(w,u),join(v,u))),
inference(rew,[status(thm),theory(equality)],[2833,8041]),
[iquote('0:Rew:2833.0,8041.0')] ).
cnf(8047,plain,
equal(meet(join(u,join(v,w)),meet(join(v,w),join(u,w))),join(w,meet(u,v))),
inference(rew,[status(thm),theory(equality)],[8042,7914]),
[iquote('0:Rew:8042.0,7914.0')] ).
cnf(8057,plain,
equal(meet(u,meet(join(meet(v,u),w),join(u,w))),join(meet(v,u),meet(w,u))),
inference(rew,[status(thm),theory(equality)],[8042,750]),
[iquote('0:Rew:8042.0,750.0')] ).
cnf(8077,plain,
equal(meet(join(u,v),join(w,v)),join(v,meet(u,w))),
inference(rew,[status(thm),theory(equality)],[21,8047,930]),
[iquote('0:Rew:21.0,8047.0,930.0,8047.0')] ).
cnf(8080,plain,
equal(join(u,meet(v,join(w,u))),join(u,meet(w,v))),
inference(rew,[status(thm),theory(equality)],[8077,8042]),
[iquote('0:Rew:8077.0,8042.0')] ).
cnf(8111,plain,
equal(join(meet(u,v),meet(w,v)),meet(v,join(w,meet(u,v)))),
inference(rew,[status(thm),theory(equality)],[175,8057,3750]),
[iquote('0:Rew:175.0,8057.0,3750.0,8057.0')] ).
cnf(8162,plain,
equal(join(u,meet(v,join(meet(w,v),u))),meet(join(u,w),join(v,u))),
inference(rew,[status(thm),theory(equality)],[6,7909,2443,10]),
[iquote('0:Rew:6.0,7909.0,2443.0,7909.0,10.0,7909.0')] ).
cnf(8163,plain,
equal(join(u,meet(meet(v,w),w)),meet(join(u,v),join(w,u))),
inference(rew,[status(thm),theory(equality)],[8080,8162]),
[iquote('0:Rew:8080.0,8162.0')] ).
cnf(8164,plain,
equal(meet(join(u,v),join(w,u)),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[3,8163,9]),
[iquote('0:Rew:3.0,8163.0,9.0,8163.0')] ).
cnf(8171,plain,
equal(join(u,meet(join(u,v),w)),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[8164,7894]),
[iquote('0:Rew:8164.0,7894.0')] ).
cnf(8172,plain,
equal(join(u,meet(join(v,u),w)),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[8164,7916]),
[iquote('0:Rew:8164.0,7916.0')] ).
cnf(8174,plain,
equal(join(u,meet(v,join(u,w))),join(u,meet(w,v))),
inference(rew,[status(thm),theory(equality)],[8164,7855]),
[iquote('0:Rew:8164.0,7855.0')] ).
cnf(8224,plain,
equal(join(meet(u,v),meet(w,join(meet(v,w),u))),meet(join(u,v),join(w,meet(v,u)))),
inference(rew,[status(thm),theory(equality)],[8164,7917]),
[iquote('0:Rew:8164.0,7917.0')] ).
cnf(8235,plain,
equal(join(meet(u,v),meet(w,join(meet(u,w),v))),meet(join(v,u),join(w,meet(u,v)))),
inference(rew,[status(thm),theory(equality)],[8164,7993]),
[iquote('0:Rew:8164.0,7993.0')] ).
cnf(8243,plain,
equal(meet(join(u,v),meet(w,meet(join(v,u),join(x,v)))),meet(join(v,u),meet(join(x,v),w))),
inference(rew,[status(thm),theory(equality)],[9,8020]),
[iquote('0:Rew:9.0,8020.0')] ).
cnf(8244,plain,
equal(meet(join(u,v),meet(join(w,u),x)),meet(join(u,meet(v,w)),x)),
inference(rew,[status(thm),theory(equality)],[2851,8243,8164]),
[iquote('0:Rew:2851.0,8243.0,8164.0,8243.0')] ).
cnf(8249,plain,
equal(join(u,meet(join(v,u),w)),meet(join(v,u),join(u,w))),
inference(rew,[status(thm),theory(equality)],[21,8026,930,4,10]),
[iquote('0:Rew:21.0,8026.0,930.0,8026.0,4.0,8026.0,10.0,8026.0')] ).
cnf(8250,plain,
equal(meet(join(u,v),join(v,w)),join(v,meet(u,w))),
inference(rew,[status(thm),theory(equality)],[8172,8249]),
[iquote('0:Rew:8172.0,8249.0')] ).
cnf(8260,plain,
equal(join(meet(u,v),meet(join(v,w),join(v,u))),join(v,meet(u,w))),
inference(rew,[status(thm),theory(equality)],[8250,746]),
[iquote('0:Rew:8250.0,746.0')] ).
cnf(8308,plain,
equal(join(u,meet(v,join(u,meet(join(u,w),meet(join(x,u),v))))),meet(join(u,w),meet(join(x,u),join(v,u)))),
inference(rew,[status(thm),theory(equality)],[9,7663]),
[iquote('0:Rew:9.0,7663.0,9.0,7663.0')] ).
cnf(8309,plain,
equal(join(u,meet(meet(meet(v,w),x),x)),meet(join(u,v),join(u,meet(w,x)))),
inference(rew,[status(thm),theory(equality)],[8174,8308,8171,8244,8077]),
[iquote('0:Rew:8174.0,8308.0,8171.0,8308.0,8244.0,8308.0,8077.0,8308.0')] ).
cnf(8310,plain,
equal(meet(join(u,v),join(u,meet(w,x))),join(u,meet(v,meet(w,x)))),
inference(rew,[status(thm),theory(equality)],[3,8309,9]),
[iquote('0:Rew:3.0,8309.0,9.0,8309.0,9.0,8309.0,9.0,8309.0')] ).
cnf(8514,plain,
equal(join(meet(u,join(v,meet(u,w))),meet(w,join(v,meet(u,w)))),meet(join(v,u),meet(join(w,u),join(v,w)))),
inference(rew,[status(thm),theory(equality)],[6,7992,2443,10]),
[iquote('0:Rew:6.0,7992.0,2443.0,7992.0,10.0,7992.0')] ).
cnf(8515,plain,
equal(meet(join(u,meet(v,w)),join(w,meet(v,join(u,meet(v,w))))),meet(join(u,v),join(w,meet(v,u)))),
inference(rew,[status(thm),theory(equality)],[8111,8514,8164]),
[iquote('0:Rew:8111.0,8514.0,8164.0,8514.0')] ).
cnf(9683,plain,
equal(join(u,meet(join(u,v),join(w,meet(v,u)))),join(u,meet(w,join(meet(v,w),u)))),
inference(spr,[status(thm),theory(equality)],[8224,75]),
[iquote('0:SpR:8224.0,75.0')] ).
cnf(9692,plain,
equal(meet(u,meet(join(meet(v,u),w),meet(join(w,v),join(u,meet(v,w))))),meet(u,join(meet(v,u),w))),
inference(spr,[status(thm),theory(equality)],[8224,165]),
[iquote('0:SpR:8224.0,165.0')] ).
cnf(9841,plain,
equal(join(u,meet(v,join(w,meet(v,u)))),join(u,meet(meet(v,w),w))),
inference(rew,[status(thm),theory(equality)],[8171,9683,8080]),
[iquote('0:Rew:8171.0,9683.0,8080.0,9683.0')] ).
cnf(9842,plain,
equal(join(u,meet(v,join(w,meet(v,u)))),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[3,9841,9]),
[iquote('0:Rew:3.0,9841.0,9.0,9841.0')] ).
cnf(9843,plain,
equal(meet(join(u,meet(v,w)),join(w,meet(v,u))),meet(join(u,v),join(w,meet(v,u)))),
inference(rew,[status(thm),theory(equality)],[9842,8515]),
[iquote('0:Rew:9842.0,8515.0')] ).
cnf(9871,plain,
equal(meet(u,meet(join(v,w),meet(join(u,meet(w,v)),join(v,meet(w,u))))),meet(u,join(meet(w,u),v))),
inference(rew,[status(thm),theory(equality)],[3750,9692,161,930]),
[iquote('0:Rew:3750.0,9692.0,161.0,9692.0,930.0,9692.0')] ).
cnf(9872,plain,
equal(meet(join(u,v),meet(w,join(u,meet(v,w)))),meet(w,join(meet(v,w),u))),
inference(rew,[status(thm),theory(equality)],[1129,9871,9843]),
[iquote('0:Rew:1129.0,9871.0,9843.0,9871.0')] ).
cnf(11168,plain,
equal(meet(meet(u,join(v,w)),join(v,meet(w,u))),meet(u,join(v,w))),
inference(spr,[status(thm),theory(equality)],[8174,21]),
[iquote('0:SpR:8174.0,21.0')] ).
cnf(11277,plain,
equal(meet(u,meet(join(v,w),join(v,meet(w,u)))),meet(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[9,11168]),
[iquote('0:Rew:9.0,11168.0')] ).
cnf(11278,plain,
equal(meet(u,join(v,meet(w,meet(w,u)))),meet(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[8310,11277]),
[iquote('0:Rew:8310.0,11277.0')] ).
cnf(11279,plain,
equal(meet(u,join(v,meet(w,u))),meet(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[43,11278]),
[iquote('0:Rew:43.0,11278.0')] ).
cnf(11315,plain,
equal(meet(join(u,v),meet(w,join(u,v))),meet(w,join(meet(v,w),u))),
inference(rew,[status(thm),theory(equality)],[11279,9872]),
[iquote('0:Rew:11279.0,9872.0')] ).
cnf(11389,plain,
equal(meet(u,join(meet(v,u),w)),meet(u,join(w,v))),
inference(rew,[status(thm),theory(equality)],[53,11315]),
[iquote('0:Rew:53.0,11315.0')] ).
cnf(11426,plain,
equal(join(meet(u,v),meet(w,join(v,u))),meet(join(v,u),join(w,meet(u,v)))),
inference(rew,[status(thm),theory(equality)],[11389,8235]),
[iquote('0:Rew:11389.0,8235.0')] ).
cnf(11469,plain,
equal(meet(join(u,v),join(join(u,w),meet(v,u))),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[11426,8260]),
[iquote('0:Rew:11426.0,8260.0')] ).
cnf(11472,plain,
equal(meet(join(u,v),join(u,w)),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[248,11469,10]),
[iquote('0:Rew:248.0,11469.0,10.0,11469.0')] ).
cnf(11473,plain,
$false,
inference(unc,[status(thm)],[11472,2]),
[iquote('0:UnC:11472.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT009-1 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 29 22:20:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.75/3.91
% 3.75/3.91 SPASS V 3.9
% 3.75/3.91 SPASS beiseite: Proof found.
% 3.75/3.91 % SZS status Theorem
% 3.75/3.91 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.75/3.91 SPASS derived 7002 clauses, backtracked 0 clauses, performed 0 splits and kept 1233 clauses.
% 3.75/3.91 SPASS allocated 74272 KBytes.
% 3.75/3.91 SPASS spent 0:00:03.56 on the problem.
% 3.75/3.91 0:00:00.04 for the input.
% 3.75/3.91 0:00:00.00 for the FLOTTER CNF translation.
% 3.75/3.91 0:00:00.05 for inferences.
% 3.75/3.91 0:00:00.00 for the backtracking.
% 3.75/3.91 0:00:03.45 for the reduction.
% 3.75/3.91
% 3.75/3.91
% 3.75/3.91 Here is a proof with depth 5, length 139 :
% 3.75/3.91 % SZS output start Refutation
% See solution above
% 3.75/3.96 Formulae used in the proof : distributivity_dual prove_distributivity idempotence_of_meet idempotence_of_join absorption1 absorption2 commutativity_of_meet commutativity_of_join associativity_of_meet associativity_of_join
% 3.75/3.96
%------------------------------------------------------------------------------