TSTP Solution File: LAT010-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT010-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 2.07s 2.28s
% Output : Refutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of clauses : 86 ( 86 unt; 0 nHn; 86 RR)
% Number of literals : 86 ( 0 equ; 5 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(join(meet(u,join(v,meet(u,w))),meet(u,join(meet(u,v),meet(w,x)))),meet(u,join(v,meet(w,join(u,x))))),
file('LAT010-1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(meet(u,join(v,meet(w,u))),meet(v,join(w,u))),meet(join(v,meet(w,u)),join(u,meet(v,w)))),
file('LAT010-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(meet(meet(a,meet(join(b,c),join(b,d))),join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d)))),meet(a,meet(join(b,c),join(b,d)))),
file('LAT010-1.p',unknown),
[] ).
cnf(5,axiom,
equal(meet(u,u),u),
file('LAT010-1.p',unknown),
[] ).
cnf(7,axiom,
equal(meet(u,join(u,v)),u),
file('LAT010-1.p',unknown),
[] ).
cnf(8,axiom,
equal(join(u,meet(u,v)),u),
file('LAT010-1.p',unknown),
[] ).
cnf(9,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT010-1.p',unknown),
[] ).
cnf(10,axiom,
equal(join(u,v),join(v,u)),
file('LAT010-1.p',unknown),
[] ).
cnf(11,axiom,
equal(meet(meet(u,v),w),meet(u,meet(v,w))),
file('LAT010-1.p',unknown),
[] ).
cnf(12,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('LAT010-1.p',unknown),
[] ).
cnf(13,plain,
equal(join(meet(u,join(v,w)),meet(w,join(u,meet(v,w)))),meet(join(u,meet(v,w)),join(w,meet(u,v)))),
inference(rew,[status(thm),theory(equality)],[10,3]),
[iquote('0:Rew:10.0,3.0')] ).
cnf(14,plain,
~ equal(meet(a,meet(join(b,c),meet(join(b,d),join(meet(a,c),join(meet(a,d),meet(a,join(b,meet(c,d)))))))),meet(a,meet(join(b,c),join(b,d)))),
inference(rew,[status(thm),theory(equality)],[11,4,12,10]),
[iquote('0:Rew:11.0,4.0,11.0,4.0,12.0,4.0,10.0,4.0')] ).
cnf(24,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.0')] ).
cnf(32,plain,
equal(join(u,meet(v,u)),u),
inference(spr,[status(thm),theory(equality)],[9,8]),
[iquote('0:SpR:9.0,8.0')] ).
cnf(43,plain,
equal(meet(meet(u,v),u),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[8,24]),
[iquote('0:SpR:8.0,24.0')] ).
cnf(46,plain,
equal(meet(u,meet(u,v)),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[9,43]),
[iquote('0:Rew:9.0,43.0')] ).
cnf(53,plain,
equal(join(join(u,v),u),join(u,v)),
inference(spr,[status(thm),theory(equality)],[7,32]),
[iquote('0:SpR:7.0,32.0')] ).
cnf(54,plain,
equal(join(join(u,v),v),join(u,v)),
inference(spr,[status(thm),theory(equality)],[24,32]),
[iquote('0:SpR:24.0,32.0')] ).
cnf(57,plain,
equal(join(u,join(u,v)),join(u,v)),
inference(rew,[status(thm),theory(equality)],[10,53]),
[iquote('0:Rew:10.0,53.0')] ).
cnf(58,plain,
equal(join(u,join(v,u)),join(v,u)),
inference(rew,[status(thm),theory(equality)],[10,54]),
[iquote('0:Rew:10.0,54.0')] ).
cnf(72,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[12,10]),
[iquote('0:SpR:12.0,10.0')] ).
cnf(75,plain,
equal(meet(u,join(v,join(w,u))),u),
inference(spr,[status(thm),theory(equality)],[12,24]),
[iquote('0:SpR:12.0,24.0')] ).
cnf(78,plain,
equal(join(u,join(meet(u,v),w)),join(u,w)),
inference(spr,[status(thm),theory(equality)],[8,12]),
[iquote('0:SpR:8.0,12.0')] ).
cnf(142,plain,
equal(meet(meet(u,v),join(w,u)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[8,75]),
[iquote('0:SpR:8.0,75.0')] ).
cnf(144,plain,
equal(meet(u,join(v,join(u,w))),u),
inference(spr,[status(thm),theory(equality)],[10,75]),
[iquote('0:SpR:10.0,75.0')] ).
cnf(158,plain,
equal(meet(u,meet(v,join(w,u))),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[11,142]),
[iquote('0:Rew:11.0,142.0')] ).
cnf(164,plain,
equal(meet(u,meet(v,w)),meet(w,meet(u,v))),
inference(spr,[status(thm),theory(equality)],[11,9]),
[iquote('0:SpR:11.0,9.0')] ).
cnf(169,plain,
equal(meet(u,meet(v,join(w,join(x,meet(u,v))))),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[11,75]),
[iquote('0:SpR:11.0,75.0')] ).
cnf(173,plain,
equal(join(u,meet(v,meet(w,u))),u),
inference(spr,[status(thm),theory(equality)],[11,32]),
[iquote('0:SpR:11.0,32.0')] ).
cnf(177,plain,
equal(meet(meet(u,v),w),meet(v,meet(u,w))),
inference(spr,[status(thm),theory(equality)],[9,11]),
[iquote('0:SpR:9.0,11.0')] ).
cnf(178,plain,
equal(meet(u,meet(join(u,v),w)),meet(u,w)),
inference(spr,[status(thm),theory(equality)],[7,11]),
[iquote('0:SpR:7.0,11.0')] ).
cnf(179,plain,
equal(meet(u,meet(join(v,u),w)),meet(u,w)),
inference(spr,[status(thm),theory(equality)],[24,11]),
[iquote('0:SpR:24.0,11.0')] ).
cnf(185,plain,
equal(meet(u,meet(v,w)),meet(v,meet(u,w))),
inference(rew,[status(thm),theory(equality)],[11,177]),
[iquote('0:Rew:11.0,177.0')] ).
cnf(234,plain,
equal(join(join(u,v),meet(w,u)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[7,173]),
[iquote('0:SpR:7.0,173.0')] ).
cnf(251,plain,
equal(join(u,join(v,meet(w,u))),join(u,v)),
inference(rew,[status(thm),theory(equality)],[12,234]),
[iquote('0:Rew:12.0,234.0')] ).
cnf(389,plain,
equal(meet(meet(u,join(v,w)),meet(join(u,meet(v,w)),join(w,meet(u,v)))),meet(u,join(v,w))),
inference(spr,[status(thm),theory(equality)],[13,7]),
[iquote('0:SpR:13.0,7.0')] ).
cnf(413,plain,
equal(join(meet(u,join(v,meet(w,u))),meet(meet(w,u),u)),meet(u,join(meet(w,u),meet(u,v)))),
inference(spr,[status(thm),theory(equality)],[173,13]),
[iquote('0:SpR:173.0,13.0')] ).
cnf(436,plain,
equal(meet(join(u,meet(v,join(w,u))),join(join(w,u),meet(u,v))),join(u,meet(join(w,u),join(u,meet(v,join(w,u)))))),
inference(spr,[status(thm),theory(equality)],[75,13]),
[iquote('0:SpR:75.0,13.0')] ).
cnf(448,plain,
equal(join(meet(u,v),meet(v,join(w,meet(u,v)))),meet(v,join(meet(u,v),meet(v,w)))),
inference(rew,[status(thm),theory(equality)],[10,413,5,11]),
[iquote('0:Rew:10.0,413.0,5.0,413.0,11.0,413.0')] ).
cnf(449,plain,
equal(meet(u,meet(join(v,w),meet(join(u,meet(v,w)),join(w,meet(u,v))))),meet(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[11,389]),
[iquote('0:Rew:11.0,389.0')] ).
cnf(459,plain,
equal(join(u,meet(join(v,u),join(u,meet(w,join(v,u))))),meet(join(v,u),join(u,meet(w,join(v,u))))),
inference(rew,[status(thm),theory(equality)],[9,436,8,12]),
[iquote('0:Rew:9.0,436.0,8.0,436.0,12.0,436.0')] ).
cnf(505,plain,
equal(meet(meet(u,v),join(u,w)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[78,144]),
[iquote('0:SpR:78.0,144.0')] ).
cnf(524,plain,
equal(join(u,join(v,meet(u,w))),join(u,v)),
inference(spr,[status(thm),theory(equality)],[10,78]),
[iquote('0:SpR:10.0,78.0')] ).
cnf(525,plain,
equal(join(u,join(v,join(meet(u,w),x))),join(u,join(x,v))),
inference(spr,[status(thm),theory(equality)],[72,78]),
[iquote('0:SpR:72.0,78.0')] ).
cnf(533,plain,
equal(meet(u,meet(v,join(u,w))),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[11,505]),
[iquote('0:Rew:11.0,505.0')] ).
cnf(745,plain,
equal(join(meet(u,join(v,w)),meet(w,u)),meet(u,join(v,w))),
inference(spr,[status(thm),theory(equality)],[158,32]),
[iquote('0:SpR:158.0,32.0')] ).
cnf(787,plain,
equal(join(meet(u,v),meet(v,join(w,u))),meet(v,join(w,u))),
inference(rew,[status(thm),theory(equality)],[10,745]),
[iquote('0:Rew:10.0,745.0')] ).
cnf(1291,plain,
equal(meet(u,meet(v,meet(join(u,w),x))),meet(v,meet(u,x))),
inference(spr,[status(thm),theory(equality)],[178,185]),
[iquote('0:SpR:178.0,185.0')] ).
cnf(1345,plain,
equal(meet(join(u,v),meet(w,join(v,meet(w,u)))),meet(w,join(u,v))),
inference(rew,[status(thm),theory(equality)],[1291,449]),
[iquote('0:Rew:1291.0,449.0')] ).
cnf(1402,plain,
equal(join(meet(u,join(v,meet(u,w))),meet(u,join(meet(u,v),meet(x,meet(w,y))))),meet(u,join(v,meet(w,join(u,meet(x,y)))))),
inference(spr,[status(thm),theory(equality)],[185,1]),
[iquote('0:SpR:185.0,1.0')] ).
cnf(1441,plain,
equal(join(meet(u,join(v,meet(u,w))),meet(u,join(meet(u,v),meet(meet(u,w),x)))),meet(u,join(v,meet(meet(u,w),join(u,x))))),
inference(spr,[status(thm),theory(equality)],[46,1]),
[iquote('0:SpR:46.0,1.0')] ).
cnf(1500,plain,
equal(join(meet(u,join(v,meet(u,w))),meet(u,join(meet(u,v),meet(u,meet(w,x))))),meet(u,join(v,meet(u,meet(w,join(u,x)))))),
inference(rew,[status(thm),theory(equality)],[11,1441]),
[iquote('0:Rew:11.0,1441.0,11.0,1441.0')] ).
cnf(1501,plain,
equal(join(meet(u,join(v,meet(u,w))),meet(u,join(meet(u,v),meet(u,meet(w,x))))),meet(u,join(v,meet(u,w)))),
inference(rew,[status(thm),theory(equality)],[533,1500]),
[iquote('0:Rew:533.0,1500.0')] ).
cnf(1503,plain,
equal(meet(u,join(v,meet(w,join(u,meet(u,x))))),meet(u,join(v,meet(u,w)))),
inference(rew,[status(thm),theory(equality)],[1402,1501]),
[iquote('0:Rew:1402.0,1501.0')] ).
cnf(1504,plain,
equal(meet(u,join(v,meet(w,u))),meet(u,join(v,meet(u,w)))),
inference(rew,[status(thm),theory(equality)],[8,1503]),
[iquote('0:Rew:8.0,1503.0')] ).
cnf(1925,plain,
equal(meet(join(u,meet(v,w)),meet(join(w,u),x)),meet(join(u,meet(v,w)),x)),
inference(spr,[status(thm),theory(equality)],[251,179]),
[iquote('0:SpR:251.0,179.0')] ).
cnf(1970,plain,
equal(join(join(u,meet(v,w)),meet(join(u,meet(v,w)),join(w,meet(u,v)))),join(join(u,meet(v,w)),meet(u,join(v,w)))),
inference(spr,[status(thm),theory(equality)],[13,251]),
[iquote('0:SpR:13.0,251.0')] ).
cnf(2004,plain,
equal(meet(join(u,v),meet(w,join(v,meet(x,u)))),meet(join(v,meet(x,u)),w)),
inference(rew,[status(thm),theory(equality)],[164,1925]),
[iquote('0:Rew:164.0,1925.0')] ).
cnf(2005,plain,
equal(meet(join(u,meet(v,w)),v),meet(v,join(w,u))),
inference(rew,[status(thm),theory(equality)],[2004,1345]),
[iquote('0:Rew:2004.0,1345.0')] ).
cnf(2006,plain,
equal(meet(u,join(v,meet(u,w))),meet(u,join(w,v))),
inference(rew,[status(thm),theory(equality)],[9,2005]),
[iquote('0:Rew:9.0,2005.0')] ).
cnf(2010,plain,
equal(join(meet(u,v),meet(v,join(w,meet(u,v)))),meet(v,join(w,meet(u,v)))),
inference(rew,[status(thm),theory(equality)],[2006,448]),
[iquote('0:Rew:2006.0,448.0')] ).
cnf(2034,plain,
equal(meet(u,join(v,meet(w,u))),meet(u,join(w,v))),
inference(rew,[status(thm),theory(equality)],[2006,1504]),
[iquote('0:Rew:2006.0,1504.0')] ).
cnf(2048,plain,
equal(meet(join(u,meet(v,w)),join(w,meet(u,v))),join(meet(u,join(v,w)),meet(w,join(v,u)))),
inference(rew,[status(thm),theory(equality)],[2034,13]),
[iquote('0:Rew:2034.0,13.0')] ).
cnf(2065,plain,
equal(join(u,meet(join(v,u),join(w,u))),meet(join(v,u),join(w,u))),
inference(rew,[status(thm),theory(equality)],[2034,459]),
[iquote('0:Rew:2034.0,459.0')] ).
cnf(2086,plain,
equal(join(meet(u,v),meet(v,join(u,w))),meet(v,join(u,w))),
inference(rew,[status(thm),theory(equality)],[2034,2010]),
[iquote('0:Rew:2034.0,2010.0')] ).
cnf(2114,plain,
equal(join(u,join(meet(v,w),meet(join(u,meet(v,w)),join(w,meet(u,v))))),join(u,join(meet(v,w),meet(u,join(v,w))))),
inference(rew,[status(thm),theory(equality)],[12,1970]),
[iquote('0:Rew:12.0,1970.0,12.0,1970.0')] ).
cnf(2115,plain,
equal(join(u,join(meet(v,join(w,u)),meet(w,v))),join(u,meet(w,v))),
inference(rew,[status(thm),theory(equality)],[525,2114,2048,524]),
[iquote('0:Rew:525.0,2114.0,2048.0,2114.0,524.0,2114.0')] ).
cnf(2116,plain,
equal(join(u,join(meet(v,w),meet(w,join(v,u)))),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[10,2115]),
[iquote('0:Rew:10.0,2115.0')] ).
cnf(2117,plain,
equal(join(u,meet(v,join(w,u))),join(u,meet(w,v))),
inference(rew,[status(thm),theory(equality)],[2086,2116]),
[iquote('0:Rew:2086.0,2116.0')] ).
cnf(2123,plain,
equal(meet(join(u,v),join(w,v)),join(v,meet(w,join(u,v)))),
inference(rew,[status(thm),theory(equality)],[2117,2065]),
[iquote('0:Rew:2117.0,2065.0')] ).
cnf(2163,plain,
equal(meet(join(u,v),join(w,v)),join(v,meet(u,w))),
inference(rew,[status(thm),theory(equality)],[2117,2123]),
[iquote('0:Rew:2117.0,2123.0')] ).
cnf(2258,plain,
equal(join(meet(u,join(v,join(v,w))),meet(join(v,w),join(v,u))),meet(join(u,v),join(join(v,w),meet(u,v)))),
inference(spr,[status(thm),theory(equality)],[7,2048]),
[iquote('0:SpR:7.0,2048.0')] ).
cnf(2259,plain,
equal(join(meet(u,join(v,join(w,v))),meet(join(w,v),join(v,u))),meet(join(u,v),join(join(w,v),meet(u,v)))),
inference(spr,[status(thm),theory(equality)],[24,2048]),
[iquote('0:SpR:24.0,2048.0')] ).
cnf(2356,plain,
equal(join(meet(u,join(v,w)),meet(join(v,w),join(w,u))),meet(join(u,w),join(v,w))),
inference(rew,[status(thm),theory(equality)],[58,2259,32,12]),
[iquote('0:Rew:58.0,2259.0,32.0,2259.0,12.0,2259.0')] ).
cnf(2357,plain,
equal(meet(join(u,v),join(v,w)),join(v,meet(w,u))),
inference(rew,[status(thm),theory(equality)],[787,2356,2163]),
[iquote('0:Rew:787.0,2356.0,2163.0,2356.0')] ).
cnf(2372,plain,
equal(join(meet(u,join(v,w)),meet(join(v,w),join(v,u))),meet(join(u,v),join(v,w))),
inference(rew,[status(thm),theory(equality)],[57,2258,251,12]),
[iquote('0:Rew:57.0,2258.0,251.0,2258.0,12.0,2258.0')] ).
cnf(2373,plain,
equal(meet(join(u,v),join(u,w)),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[787,2372,2357]),
[iquote('0:Rew:787.0,2372.0,2357.0,2372.0')] ).
cnf(2404,plain,
~ equal(meet(a,meet(join(b,c),meet(join(b,d),join(meet(a,c),join(meet(a,d),meet(a,join(b,meet(c,d)))))))),meet(a,join(b,meet(c,d)))),
inference(rew,[status(thm),theory(equality)],[2373,14]),
[iquote('0:Rew:2373.0,14.0')] ).
cnf(5648,plain,
equal(meet(u,meet(v,join(w,meet(meet(u,v),x)))),meet(meet(u,v),join(x,w))),
inference(spr,[status(thm),theory(equality)],[2006,11]),
[iquote('0:SpR:2006.0,11.0')] ).
cnf(5671,plain,
equal(meet(u,join(v,meet(w,meet(u,x)))),meet(u,join(meet(w,x),v))),
inference(spr,[status(thm),theory(equality)],[185,2006]),
[iquote('0:SpR:185.0,2006.0')] ).
cnf(5780,plain,
equal(meet(u,meet(v,join(w,meet(u,meet(v,x))))),meet(u,meet(v,join(x,w)))),
inference(rew,[status(thm),theory(equality)],[11,5648]),
[iquote('0:Rew:11.0,5648.0,11.0,5648.0')] ).
cnf(5781,plain,
equal(meet(u,meet(v,join(meet(u,w),x))),meet(u,meet(v,join(w,x)))),
inference(rew,[status(thm),theory(equality)],[5671,5780]),
[iquote('0:Rew:5671.0,5780.0')] ).
cnf(6719,plain,
equal(meet(join(u,v),meet(join(u,w),x)),meet(join(u,meet(v,w)),x)),
inference(spr,[status(thm),theory(equality)],[2373,11]),
[iquote('0:SpR:2373.0,11.0')] ).
cnf(6887,plain,
~ equal(meet(a,meet(join(b,meet(c,d)),join(meet(a,c),join(meet(a,d),meet(a,join(b,meet(c,d))))))),meet(a,join(b,meet(c,d)))),
inference(rew,[status(thm),theory(equality)],[6719,2404]),
[iquote('0:Rew:6719.0,2404.0')] ).
cnf(7047,plain,
~ equal(meet(a,join(b,meet(c,d))),meet(a,join(b,meet(c,d)))),
inference(rew,[status(thm),theory(equality)],[169,6887,5781]),
[iquote('0:Rew:169.0,6887.0,5781.0,6887.0')] ).
cnf(7048,plain,
$false,
inference(obv,[status(thm),theory(equality)],[7047]),
[iquote('0:Obv:7047.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT010-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n004.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 : Thu Jun 30 01:13:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.07/2.28
% 2.07/2.28 SPASS V 3.9
% 2.07/2.28 SPASS beiseite: Proof found.
% 2.07/2.28 % SZS status Theorem
% 2.07/2.28 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.07/2.28 SPASS derived 4362 clauses, backtracked 0 clauses, performed 0 splits and kept 924 clauses.
% 2.07/2.28 SPASS allocated 70940 KBytes.
% 2.07/2.28 SPASS spent 0:00:01.92 on the problem.
% 2.07/2.28 0:00:00.03 for the input.
% 2.07/2.28 0:00:00.00 for the FLOTTER CNF translation.
% 2.07/2.28 0:00:00.03 for inferences.
% 2.07/2.28 0:00:00.00 for the backtracking.
% 2.07/2.28 0:00:01.83 for the reduction.
% 2.07/2.28
% 2.07/2.28
% 2.07/2.28 Here is a proof with depth 4, length 86 :
% 2.07/2.28 % SZS output start Refutation
% See solution above
% 2.13/2.32 Formulae used in the proof : n5_1 nr_3 prove_this idempotence_of_meet absorption1 absorption2 commutativity_of_meet commutativity_of_join associativity_of_meet associativity_of_join
% 2.13/2.32
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