TSTP Solution File: LAT026-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT026-1 : TPTP v8.1.0. Released v2.2.0.
% 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 : Sun Jul 17 06:48:39 EDT 2022
% Result : Timeout 294.12s 294.37s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of clauses : 94 ( 94 unt; 0 nHn; 94 RR)
% Number of literals : 94 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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(meet(u,join(v,join(u,w))),u),
file('LAT026-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(meet(meet(a,b),c),meet(a,meet(b,c))),
file('LAT026-1.p',unknown),
[] ).
cnf(3,axiom,
equal(meet(u,u),u),
file('LAT026-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(u,u),u),
file('LAT026-1.p',unknown),
[] ).
cnf(5,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT026-1.p',unknown),
[] ).
cnf(6,axiom,
equal(join(u,v),join(v,u)),
file('LAT026-1.p',unknown),
[] ).
cnf(7,axiom,
equal(meet(meet(join(u,v),join(w,v)),v),v),
file('LAT026-1.p',unknown),
[] ).
cnf(8,axiom,
equal(join(join(meet(u,v),meet(w,v)),v),v),
file('LAT026-1.p',unknown),
[] ).
cnf(9,plain,
equal(join(u,join(meet(v,u),meet(w,u))),u),
inference(rew,[status(thm),theory(equality)],[6,8]),
[iquote('0:Rew:6.0,8.0')] ).
cnf(10,plain,
equal(meet(u,meet(join(v,u),join(w,u))),u),
inference(rew,[status(thm),theory(equality)],[5,7]),
[iquote('0:Rew:5.0,7.0')] ).
cnf(11,plain,
~ equal(meet(c,meet(a,b)),meet(a,meet(b,c))),
inference(rew,[status(thm),theory(equality)],[5,2]),
[iquote('0:Rew:5.0,2.0')] ).
cnf(27,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(28,plain,
equal(meet(u,join(v,join(w,u))),u),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(30,plain,
equal(meet(u,join(u,v)),u),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(31,plain,
equal(meet(u,join(join(u,v),w)),u),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(50,plain,
equal(meet(u,join(join(v,u),w)),u),
inference(spr,[status(thm),theory(equality)],[6,28]),
[iquote('0:SpR:6.0,28.0')] ).
cnf(72,plain,
equal(join(u,join(meet(v,u),meet(u,w))),u),
inference(spr,[status(thm),theory(equality)],[5,9]),
[iquote('0:SpR:5.0,9.0')] ).
cnf(76,plain,
equal(join(join(u,v),join(meet(w,join(u,v)),v)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[27,9]),
[iquote('0:SpR:27.0,9.0')] ).
cnf(80,plain,
equal(join(u,join(meet(u,v),meet(w,u))),u),
inference(spr,[status(thm),theory(equality)],[5,9]),
[iquote('0:SpR:5.0,9.0')] ).
cnf(82,plain,
equal(join(join(u,join(v,w)),join(v,meet(x,join(u,join(v,w))))),join(u,join(v,w))),
inference(spr,[status(thm),theory(equality)],[1,9]),
[iquote('0:SpR:1.0,9.0')] ).
cnf(87,plain,
equal(join(u,meet(v,u)),u),
inference(spr,[status(thm),theory(equality)],[4,9]),
[iquote('0:SpR:4.0,9.0')] ).
cnf(95,plain,
equal(join(join(u,v),join(v,meet(w,join(u,v)))),join(u,v)),
inference(rew,[status(thm),theory(equality)],[6,76]),
[iquote('0:Rew:6.0,76.0')] ).
cnf(102,plain,
equal(meet(meet(u,v),join(w,v)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[87,28]),
[iquote('0:SpR:87.0,28.0')] ).
cnf(109,plain,
equal(join(u,meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[5,87]),
[iquote('0:SpR:5.0,87.0')] ).
cnf(115,plain,
equal(join(join(join(u,v),w),u),join(join(u,v),w)),
inference(spr,[status(thm),theory(equality)],[31,87]),
[iquote('0:SpR:31.0,87.0')] ).
cnf(121,plain,
equal(join(u,join(join(u,v),w)),join(join(u,v),w)),
inference(rew,[status(thm),theory(equality)],[6,115]),
[iquote('0:Rew:6.0,115.0')] ).
cnf(123,plain,
equal(meet(meet(u,v),join(w,u)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[109,28]),
[iquote('0:SpR:109.0,28.0')] ).
cnf(153,plain,
equal(meet(meet(u,v),join(v,w)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[87,50]),
[iquote('0:SpR:87.0,50.0')] ).
cnf(189,plain,
equal(join(meet(join(u,v),join(w,v)),join(meet(x,meet(join(u,v),join(w,v))),v)),meet(join(u,v),join(w,v))),
inference(spr,[status(thm),theory(equality)],[10,9]),
[iquote('0:SpR:10.0,9.0')] ).
cnf(193,plain,
equal(meet(u,meet(join(v,u),join(u,w))),u),
inference(spr,[status(thm),theory(equality)],[6,10]),
[iquote('0:SpR:6.0,10.0')] ).
cnf(196,plain,
equal(meet(meet(u,v),meet(join(w,meet(u,v)),v)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[87,10]),
[iquote('0:SpR:87.0,10.0')] ).
cnf(201,plain,
equal(meet(join(meet(u,v),meet(w,v)),meet(v,join(x,join(meet(u,v),meet(w,v))))),join(meet(u,v),meet(w,v))),
inference(spr,[status(thm),theory(equality)],[9,10]),
[iquote('0:SpR:9.0,10.0')] ).
cnf(213,plain,
equal(meet(meet(u,v),meet(v,join(w,meet(u,v)))),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[5,196]),
[iquote('0:Rew:5.0,196.0')] ).
cnf(217,plain,
equal(join(meet(join(u,v),join(w,v)),join(v,meet(x,meet(join(u,v),join(w,v))))),meet(join(u,v),join(w,v))),
inference(rew,[status(thm),theory(equality)],[6,189]),
[iquote('0:Rew:6.0,189.0')] ).
cnf(294,plain,
equal(meet(join(meet(u,v),meet(v,w)),meet(join(x,join(meet(u,v),meet(v,w))),v)),join(meet(u,v),meet(v,w))),
inference(spr,[status(thm),theory(equality)],[72,10]),
[iquote('0:SpR:72.0,10.0')] ).
cnf(318,plain,
equal(join(u,join(meet(u,v),meet(u,w))),u),
inference(spr,[status(thm),theory(equality)],[5,72]),
[iquote('0:SpR:5.0,72.0')] ).
cnf(348,plain,
equal(meet(join(meet(u,v),meet(v,w)),meet(v,join(x,join(meet(u,v),meet(v,w))))),join(meet(u,v),meet(v,w))),
inference(rew,[status(thm),theory(equality)],[5,294]),
[iquote('0:Rew:5.0,294.0')] ).
cnf(354,plain,
equal(meet(join(meet(u,v),meet(w,u)),meet(join(x,join(meet(u,v),meet(w,u))),u)),join(meet(u,v),meet(w,u))),
inference(spr,[status(thm),theory(equality)],[80,10]),
[iquote('0:SpR:80.0,10.0')] ).
cnf(416,plain,
equal(meet(join(meet(u,v),meet(w,u)),meet(u,join(x,join(meet(u,v),meet(w,u))))),join(meet(u,v),meet(w,u))),
inference(rew,[status(thm),theory(equality)],[5,354]),
[iquote('0:Rew:5.0,354.0')] ).
cnf(419,plain,
equal(join(join(u,v),meet(w,v)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[102,87]),
[iquote('0:SpR:102.0,87.0')] ).
cnf(443,plain,
equal(meet(meet(u,meet(v,w)),v),meet(u,meet(v,w))),
inference(spr,[status(thm),theory(equality)],[109,102]),
[iquote('0:SpR:109.0,102.0')] ).
cnf(458,plain,
equal(meet(u,meet(v,meet(u,w))),meet(v,meet(u,w))),
inference(rew,[status(thm),theory(equality)],[5,443]),
[iquote('0:Rew:5.0,443.0')] ).
cnf(468,plain,
equal(join(join(u,v),meet(v,w)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[123,87]),
[iquote('0:SpR:123.0,87.0')] ).
cnf(518,plain,
equal(meet(join(u,v),meet(w,u)),meet(w,u)),
inference(spr,[status(thm),theory(equality)],[153,5]),
[iquote('0:SpR:153.0,5.0')] ).
cnf(597,plain,
equal(meet(u,meet(join(u,v),join(u,w))),u),
inference(spr,[status(thm),theory(equality)],[6,193]),
[iquote('0:SpR:6.0,193.0')] ).
cnf(972,plain,
equal(join(join(u,join(v,w)),join(v,u)),join(u,join(v,w))),
inference(spr,[status(thm),theory(equality)],[30,82]),
[iquote('0:SpR:30.0,82.0')] ).
cnf(1003,plain,
equal(join(join(u,v),join(v,join(u,w))),join(v,join(u,w))),
inference(rew,[status(thm),theory(equality)],[6,972]),
[iquote('0:Rew:6.0,972.0')] ).
cnf(1019,plain,
equal(join(meet(u,v),join(w,v)),join(w,v)),
inference(spr,[status(thm),theory(equality)],[419,6]),
[iquote('0:SpR:419.0,6.0')] ).
cnf(1074,plain,
equal(join(u,meet(v,meet(w,u))),u),
inference(spr,[status(thm),theory(equality)],[87,419]),
[iquote('0:SpR:87.0,419.0')] ).
cnf(1075,plain,
equal(join(u,meet(v,meet(u,w))),u),
inference(spr,[status(thm),theory(equality)],[109,419]),
[iquote('0:SpR:109.0,419.0')] ).
cnf(1141,plain,
equal(join(u,meet(meet(v,u),w)),u),
inference(spr,[status(thm),theory(equality)],[5,1074]),
[iquote('0:SpR:5.0,1074.0')] ).
cnf(1210,plain,
equal(join(u,meet(meet(u,v),w)),u),
inference(spr,[status(thm),theory(equality)],[5,1075]),
[iquote('0:SpR:5.0,1075.0')] ).
cnf(1385,plain,
equal(meet(join(meet(u,v),meet(u,v)),meet(v,u)),join(meet(u,v),meet(u,v))),
inference(spr,[status(thm),theory(equality)],[318,201]),
[iquote('0:SpR:318.0,201.0')] ).
cnf(1442,plain,
equal(meet(meet(u,v),meet(v,u)),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[4,1385]),
[iquote('0:Rew:4.0,1385.0')] ).
cnf(2200,plain,
equal(join(meet(u,v),join(w,u)),join(w,u)),
inference(spr,[status(thm),theory(equality)],[468,6]),
[iquote('0:SpR:468.0,6.0')] ).
cnf(2446,plain,
equal(join(meet(join(u,v),join(u,v)),join(v,u)),meet(join(u,v),join(u,v))),
inference(spr,[status(thm),theory(equality)],[597,217]),
[iquote('0:SpR:597.0,217.0')] ).
cnf(2541,plain,
equal(join(join(u,v),join(v,u)),join(u,v)),
inference(rew,[status(thm),theory(equality)],[3,2446]),
[iquote('0:Rew:3.0,2446.0')] ).
cnf(4194,plain,
equal(meet(join(meet(u,v),w),meet(v,u)),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[1442,518]),
[iquote('0:SpR:1442.0,518.0')] ).
cnf(4209,plain,
equal(join(meet(u,v),join(w,meet(v,u))),join(w,meet(v,u))),
inference(spr,[status(thm),theory(equality)],[1442,1019]),
[iquote('0:SpR:1442.0,1019.0')] ).
cnf(4309,plain,
equal(meet(meet(u,v),join(meet(v,u),w)),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[5,4194]),
[iquote('0:Rew:5.0,4194.0')] ).
cnf(4411,plain,
equal(meet(u,meet(join(join(u,v),w),join(u,x))),u),
inference(spr,[status(thm),theory(equality)],[121,597]),
[iquote('0:SpR:121.0,597.0')] ).
cnf(5256,plain,
equal(join(u,join(meet(meet(u,v),w),meet(x,u))),u),
inference(spr,[status(thm),theory(equality)],[1210,95]),
[iquote('0:SpR:1210.0,95.0')] ).
cnf(5270,plain,
equal(join(join(u,v),join(v,meet(w,u))),join(u,v)),
inference(spr,[status(thm),theory(equality)],[153,95]),
[iquote('0:SpR:153.0,95.0')] ).
cnf(5745,plain,
equal(meet(join(u,v),join(join(v,u),w)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[2541,50]),
[iquote('0:SpR:2541.0,50.0')] ).
cnf(5758,plain,
equal(join(meet(join(u,v),w),join(v,u)),join(v,u)),
inference(spr,[status(thm),theory(equality)],[2541,2200]),
[iquote('0:SpR:2541.0,2200.0')] ).
cnf(5899,plain,
equal(join(join(u,v),meet(join(v,u),w)),join(u,v)),
inference(rew,[status(thm),theory(equality)],[6,5758]),
[iquote('0:Rew:6.0,5758.0')] ).
cnf(7297,plain,
equal(meet(meet(u,v),meet(v,join(w,u))),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[468,213]),
[iquote('0:SpR:468.0,213.0')] ).
cnf(7305,plain,
equal(meet(meet(meet(u,v),w),meet(w,v)),meet(meet(u,v),w)),
inference(spr,[status(thm),theory(equality)],[1141,213]),
[iquote('0:SpR:1141.0,213.0')] ).
cnf(7374,plain,
equal(meet(meet(u,v),meet(meet(w,v),u)),meet(meet(w,v),u)),
inference(rew,[status(thm),theory(equality)],[5,7305]),
[iquote('0:Rew:5.0,7305.0')] ).
cnf(7792,plain,
equal(join(u,join(meet(v,meet(u,w)),meet(u,x))),u),
inference(spr,[status(thm),theory(equality)],[458,318]),
[iquote('0:SpR:458.0,318.0')] ).
cnf(50528,plain,
equal(join(meet(join(join(u,v),w),join(u,w)),join(w,u)),meet(join(join(u,v),w),join(u,w))),
inference(spr,[status(thm),theory(equality)],[4411,217]),
[iquote('0:SpR:4411.0,217.0')] ).
cnf(50969,plain,
equal(join(join(u,v),meet(join(v,u),join(join(v,w),u))),meet(join(v,u),join(join(v,w),u))),
inference(rew,[status(thm),theory(equality)],[6,50528,5]),
[iquote('0:Rew:6.0,50528.0,5.0,50528.0')] ).
cnf(50970,plain,
equal(meet(join(u,v),join(join(u,w),v)),join(v,u)),
inference(rew,[status(thm),theory(equality)],[5899,50969]),
[iquote('0:Rew:5899.0,50969.0')] ).
cnf(62738,plain,
equal(meet(join(meet(meet(u,v),w),meet(w,u)),meet(w,u)),join(meet(meet(u,v),w),meet(w,u))),
inference(spr,[status(thm),theory(equality)],[5256,348]),
[iquote('0:SpR:5256.0,348.0')] ).
cnf(63217,plain,
equal(join(meet(u,v),meet(meet(v,w),u)),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[30,62738,5,6]),
[iquote('0:Rew:30.0,62738.0,5.0,62738.0,6.0,62738.0')] ).
cnf(70112,plain,
equal(meet(join(u,v),join(u,join(v,w))),join(u,v)),
inference(spr,[status(thm),theory(equality)],[1003,5745]),
[iquote('0:SpR:1003.0,5745.0')] ).
cnf(86333,plain,
equal(meet(join(meet(u,meet(v,w)),meet(v,u)),meet(u,v)),join(meet(u,meet(v,w)),meet(v,u))),
inference(spr,[status(thm),theory(equality)],[7792,416]),
[iquote('0:SpR:7792.0,416.0')] ).
cnf(86879,plain,
equal(join(meet(u,v),meet(v,meet(u,w))),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[4309,86333,5,6]),
[iquote('0:Rew:4309.0,86333.0,5.0,86333.0,6.0,86333.0')] ).
cnf(97011,plain,
equal(meet(join(u,join(v,meet(w,u))),join(u,v)),join(join(v,meet(w,u)),u)),
inference(spr,[status(thm),theory(equality)],[5270,50970]),
[iquote('0:SpR:5270.0,50970.0')] ).
cnf(97349,plain,
equal(meet(join(u,v),join(u,join(v,meet(w,u)))),join(u,join(v,meet(w,u)))),
inference(rew,[status(thm),theory(equality)],[5,97011,6]),
[iquote('0:Rew:5.0,97011.0,6.0,97011.0')] ).
cnf(97350,plain,
equal(join(u,join(v,meet(w,u))),join(u,v)),
inference(rew,[status(thm),theory(equality)],[70112,97349]),
[iquote('0:Rew:70112.0,97349.0')] ).
cnf(101009,plain,
equal(join(meet(u,v),join(w,meet(v,u))),join(meet(u,v),w)),
inference(spr,[status(thm),theory(equality)],[1442,97350]),
[iquote('0:SpR:1442.0,97350.0')] ).
cnf(101420,plain,
equal(join(u,meet(v,w)),join(meet(w,v),u)),
inference(rew,[status(thm),theory(equality)],[4209,101009]),
[iquote('0:Rew:4209.0,101009.0')] ).
cnf(121731,plain,
equal(join(meet(meet(u,join(v,w)),w),meet(w,u)),meet(meet(u,join(v,w)),w)),
inference(spr,[status(thm),theory(equality)],[7297,63217]),
[iquote('0:SpR:7297.0,63217.0')] ).
cnf(122068,plain,
equal(join(meet(u,v),meet(v,meet(u,join(w,v)))),meet(v,meet(u,join(w,v)))),
inference(rew,[status(thm),theory(equality)],[101420,121731,5]),
[iquote('0:Rew:101420.0,121731.0,5.0,121731.0')] ).
cnf(122069,plain,
equal(meet(u,meet(v,join(w,u))),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[86879,122068]),
[iquote('0:Rew:86879.0,122068.0')] ).
cnf(124306,plain,
equal(meet(meet(u,v),meet(w,v)),meet(meet(u,v),w)),
inference(spr,[status(thm),theory(equality)],[87,122069]),
[iquote('0:SpR:87.0,122069.0')] ).
cnf(124307,plain,
equal(meet(meet(u,v),meet(w,u)),meet(meet(u,v),w)),
inference(spr,[status(thm),theory(equality)],[109,122069]),
[iquote('0:SpR:109.0,122069.0')] ).
cnf(124715,plain,
equal(meet(meet(u,v),meet(w,v)),meet(meet(w,v),u)),
inference(rew,[status(thm),theory(equality)],[124307,7374]),
[iquote('0:Rew:124307.0,7374.0')] ).
cnf(124749,plain,
equal(meet(meet(u,v),w),meet(meet(w,v),u)),
inference(rew,[status(thm),theory(equality)],[124306,124715]),
[iquote('0:Rew:124306.0,124715.0')] ).
cnf(126577,plain,
equal(meet(meet(u,v),w),meet(u,meet(w,v))),
inference(spr,[status(thm),theory(equality)],[124749,5]),
[iquote('0:SpR:124749.0,5.0')] ).
cnf(126980,plain,
equal(meet(meet(u,v),w),meet(meet(w,u),v)),
inference(spr,[status(thm),theory(equality)],[5,124749]),
[iquote('0:SpR:5.0,124749.0')] ).
cnf(130133,plain,
equal(meet(u,meet(v,w)),meet(v,meet(w,u))),
inference(rew,[status(thm),theory(equality)],[126577,126980]),
[iquote('0:Rew:126577.0,126980.0,126577.0,126980.0')] ).
cnf(130134,plain,
$false,
inference(unc,[status(thm)],[130133,11]),
[iquote('0:UnC:130133.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LAT026-1 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 29 17:14:18 EDT 2022
% 0.13/0.35 % CPUTime :
% 294.12/294.37
% 294.12/294.37 SPASS V 3.9
% 294.12/294.37 SPASS beiseite: Proof found.
% 294.12/294.37 % SZS status Theorem
% 294.12/294.37 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 294.12/294.37 SPASS derived 99557 clauses, backtracked 0 clauses, performed 0 splits and kept 17739 clauses.
% 294.12/294.37 SPASS allocated 176177 KBytes.
% 294.12/294.37 SPASS spent 0:4:53.87 on the problem.
% 294.12/294.37 0:00:00.04 for the input.
% 294.12/294.37 0:00:00.00 for the FLOTTER CNF translation.
% 294.12/294.37 0:00:00.65 for inferences.
% 294.12/294.37 0:00:00.00 for the backtracking.
% 294.12/294.37 0:4:53.10 for the reduction.
% 294.12/294.37
% 294.12/294.37
% 294.12/294.37 Here is a proof with depth 9, length 94 :
% 294.12/294.37 % SZS output start Refutation
% See solution above
% 295.69/295.92 Formulae used in the proof : absorbtion prove_associativity_of_meet idempotence_of_meet idempotence_of_join commutativity_of_meet commutativity_of_join wal_1 wal_2
% 295.69/295.92
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