TSTP Solution File: LAT021-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT021-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 06:48:37 EDT 2022
% Result : Unsatisfiable 3.73s 3.89s
% Output : Refutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of clauses : 70 ( 70 unt; 0 nHn; 70 RR)
% Number of literals : 70 ( 0 equ; 5 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(join(join(u,meet(v,w)),meet(join(u,v),w)),join(u,meet(v,w))),
file('LAT021-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(join(meet(a,b),meet(a,c)),meet(a,join(b,c))),
file('LAT021-1.p',unknown),
[] ).
cnf(3,axiom,
equal(meet(u,u),u),
file('LAT021-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(u,u),u),
file('LAT021-1.p',unknown),
[] ).
cnf(5,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT021-1.p',unknown),
[] ).
cnf(6,axiom,
equal(join(u,v),join(v,u)),
file('LAT021-1.p',unknown),
[] ).
cnf(7,axiom,
equal(meet(meet(u,v),w),meet(u,meet(v,w))),
file('LAT021-1.p',unknown),
[] ).
cnf(8,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('LAT021-1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(meet(u,join(v,w)),meet(u,v)),meet(u,join(v,w))),
file('LAT021-1.p',unknown),
[] ).
cnf(10,axiom,
equal(meet(join(u,meet(v,w)),join(u,v)),join(u,meet(v,w))),
file('LAT021-1.p',unknown),
[] ).
cnf(11,plain,
equal(meet(join(u,v),join(u,meet(v,w))),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[5,10]),
[iquote('0:Rew:5.0,10.0')] ).
cnf(12,plain,
equal(join(meet(u,v),meet(u,join(v,w))),meet(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[6,9]),
[iquote('0:Rew:6.0,9.0')] ).
cnf(13,plain,
equal(join(u,join(meet(v,w),meet(join(u,v),w))),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[8,1]),
[iquote('0:Rew:8.0,1.0')] ).
cnf(29,plain,
equal(join(u,join(v,w)),join(v,join(w,u))),
inference(spr,[status(thm),theory(equality)],[8,6]),
[iquote('0:SpR:8.0,6.0')] ).
cnf(34,plain,
equal(join(join(u,v),w),join(v,join(u,w))),
inference(spr,[status(thm),theory(equality)],[6,8]),
[iquote('0:SpR:6.0,8.0')] ).
cnf(36,plain,
equal(join(u,join(v,w)),join(v,join(u,w))),
inference(rew,[status(thm),theory(equality)],[8,34]),
[iquote('0:Rew:8.0,34.0')] ).
cnf(66,plain,
equal(meet(u,meet(v,w)),meet(v,meet(w,u))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(70,plain,
equal(meet(u,meet(u,v)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(81,plain,
equal(meet(u,meet(v,u)),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[5,70]),
[iquote('0:SpR:5.0,70.0')] ).
cnf(129,plain,
equal(join(u,join(v,w)),join(w,join(v,u))),
inference(spr,[status(thm),theory(equality)],[6,29]),
[iquote('0:SpR:6.0,29.0')] ).
cnf(267,plain,
equal(meet(u,meet(v,w)),meet(w,meet(v,u))),
inference(spr,[status(thm),theory(equality)],[5,66]),
[iquote('0:SpR:5.0,66.0')] ).
cnf(319,plain,
equal(meet(join(meet(u,v),u),meet(u,v)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[4,11]),
[iquote('0:SpR:4.0,11.0')] ).
cnf(323,plain,
equal(meet(u,join(u,meet(u,v))),join(u,meet(u,v))),
inference(spr,[status(thm),theory(equality)],[4,11]),
[iquote('0:SpR:4.0,11.0')] ).
cnf(333,plain,
equal(meet(u,meet(v,join(v,meet(v,u)))),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[5,319,66,6]),
[iquote('0:Rew:5.0,319.0,66.0,319.0,6.0,319.0')] ).
cnf(334,plain,
equal(meet(u,join(v,meet(v,u))),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[323,333]),
[iquote('0:Rew:323.0,333.0')] ).
cnf(759,plain,
equal(join(meet(u,v),meet(u,join(w,v))),meet(u,join(w,v))),
inference(spr,[status(thm),theory(equality)],[6,12]),
[iquote('0:SpR:6.0,12.0')] ).
cnf(772,plain,
equal(join(meet(join(u,v),u),join(u,v)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[3,12]),
[iquote('0:SpR:3.0,12.0')] ).
cnf(773,plain,
equal(join(meet(u,v),meet(join(v,w),u)),meet(join(v,w),u)),
inference(spr,[status(thm),theory(equality)],[5,12]),
[iquote('0:SpR:5.0,12.0')] ).
cnf(777,plain,
equal(join(u,meet(u,join(u,v))),meet(u,join(u,v))),
inference(spr,[status(thm),theory(equality)],[3,12]),
[iquote('0:SpR:3.0,12.0')] ).
cnf(778,plain,
equal(join(meet(u,v),meet(v,join(u,w))),meet(v,join(u,w))),
inference(spr,[status(thm),theory(equality)],[5,12]),
[iquote('0:SpR:5.0,12.0')] ).
cnf(783,plain,
equal(join(meet(u,v),meet(v,join(meet(u,v),w))),meet(v,join(meet(u,v),w))),
inference(spr,[status(thm),theory(equality)],[81,12]),
[iquote('0:SpR:81.0,12.0')] ).
cnf(784,plain,
equal(join(meet(u,v),meet(u,join(meet(u,v),w))),meet(u,join(meet(u,v),w))),
inference(spr,[status(thm),theory(equality)],[70,12]),
[iquote('0:SpR:70.0,12.0')] ).
cnf(790,plain,
equal(join(u,join(v,meet(v,join(v,u)))),join(v,u)),
inference(rew,[status(thm),theory(equality)],[129,772,5]),
[iquote('0:Rew:129.0,772.0,5.0,772.0')] ).
cnf(791,plain,
equal(join(u,meet(v,join(v,u))),join(v,u)),
inference(rew,[status(thm),theory(equality)],[777,790]),
[iquote('0:Rew:777.0,790.0')] ).
cnf(809,plain,
equal(join(meet(u,v),meet(v,u)),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[334,12]),
[iquote('0:SpR:334.0,12.0')] ).
cnf(979,plain,
equal(meet(join(u,v),join(v,u)),join(v,u)),
inference(spr,[status(thm),theory(equality)],[791,11]),
[iquote('0:SpR:791.0,11.0')] ).
cnf(1031,plain,
equal(join(meet(u,v),join(meet(v,u),w)),join(w,meet(u,v))),
inference(spr,[status(thm),theory(equality)],[809,129]),
[iquote('0:SpR:809.0,129.0')] ).
cnf(1035,plain,
equal(join(meet(u,v),join(meet(v,u),w)),join(meet(v,u),w)),
inference(spr,[status(thm),theory(equality)],[809,8]),
[iquote('0:SpR:809.0,8.0')] ).
cnf(1039,plain,
equal(join(meet(u,v),join(meet(v,u),w)),join(w,meet(v,u))),
inference(spr,[status(thm),theory(equality)],[809,29]),
[iquote('0:SpR:809.0,29.0')] ).
cnf(1088,plain,
equal(join(u,meet(v,w)),join(meet(w,v),u)),
inference(rew,[status(thm),theory(equality)],[1031,1035]),
[iquote('0:Rew:1031.0,1035.0')] ).
cnf(1089,plain,
equal(join(u,meet(v,w)),join(u,meet(w,v))),
inference(rew,[status(thm),theory(equality)],[1031,1039]),
[iquote('0:Rew:1031.0,1039.0')] ).
cnf(1169,plain,
equal(join(u,join(meet(v,w),meet(join(u,w),v))),join(u,meet(v,w))),
inference(spr,[status(thm),theory(equality)],[5,13]),
[iquote('0:SpR:5.0,13.0')] ).
cnf(1177,plain,
equal(join(u,join(meet(v,w),meet(join(u,w),join(v,meet(v,w))))),join(u,meet(v,w))),
inference(spr,[status(thm),theory(equality)],[334,13]),
[iquote('0:SpR:334.0,13.0')] ).
cnf(1277,plain,
equal(meet(join(u,v),meet(join(v,u),w)),meet(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[979,267]),
[iquote('0:SpR:979.0,267.0')] ).
cnf(1282,plain,
equal(meet(join(u,v),meet(join(v,u),w)),meet(join(v,u),w)),
inference(spr,[status(thm),theory(equality)],[979,7]),
[iquote('0:SpR:979.0,7.0')] ).
cnf(1344,plain,
equal(meet(u,join(v,w)),meet(join(w,v),u)),
inference(rew,[status(thm),theory(equality)],[1277,1282]),
[iquote('0:Rew:1277.0,1282.0')] ).
cnf(1463,plain,
equal(join(u,join(meet(v,w),x)),join(x,join(u,meet(w,v)))),
inference(spr,[status(thm),theory(equality)],[1088,36]),
[iquote('0:SpR:1088.0,36.0')] ).
cnf(1809,plain,
equal(join(meet(u,v),meet(join(w,v),u)),meet(join(w,v),u)),
inference(spr,[status(thm),theory(equality)],[1344,12]),
[iquote('0:SpR:1344.0,12.0')] ).
cnf(1856,plain,
equal(join(u,join(meet(v,w),meet(w,join(v,u)))),join(u,meet(v,w))),
inference(spr,[status(thm),theory(equality)],[1344,13]),
[iquote('0:SpR:1344.0,13.0')] ).
cnf(1921,plain,
equal(join(u,meet(join(u,v),w)),join(u,meet(w,v))),
inference(rew,[status(thm),theory(equality)],[1809,1169]),
[iquote('0:Rew:1809.0,1169.0')] ).
cnf(1961,plain,
equal(join(u,meet(v,join(w,u))),join(u,meet(w,v))),
inference(rew,[status(thm),theory(equality)],[778,1856]),
[iquote('0:Rew:778.0,1856.0')] ).
cnf(1969,plain,
equal(join(u,join(meet(v,w),meet(v,join(u,w)))),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[1961,1177]),
[iquote('0:Rew:1961.0,1177.0')] ).
cnf(1971,plain,
equal(join(u,meet(v,join(u,w))),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[759,1969]),
[iquote('0:Rew:759.0,1969.0')] ).
cnf(1975,plain,
equal(join(meet(u,v),meet(u,w)),meet(u,join(meet(u,v),w))),
inference(rew,[status(thm),theory(equality)],[1971,784]),
[iquote('0:Rew:1971.0,784.0')] ).
cnf(1976,plain,
equal(join(meet(u,v),meet(v,w)),meet(v,join(meet(u,v),w))),
inference(rew,[status(thm),theory(equality)],[1971,783]),
[iquote('0:Rew:1971.0,783.0')] ).
cnf(1981,plain,
equal(join(u,meet(u,v)),meet(u,join(u,v))),
inference(rew,[status(thm),theory(equality)],[1971,777]),
[iquote('0:Rew:1971.0,777.0')] ).
cnf(1998,plain,
~ equal(meet(a,join(meet(a,b),c)),meet(a,join(b,c))),
inference(rew,[status(thm),theory(equality)],[1975,2]),
[iquote('0:Rew:1975.0,2.0')] ).
cnf(2015,plain,
~ equal(meet(a,join(c,meet(a,b))),meet(a,join(b,c))),
inference(rew,[status(thm),theory(equality)],[6,1998]),
[iquote('0:Rew:6.0,1998.0')] ).
cnf(2506,plain,
equal(join(u,meet(v,u)),meet(u,join(u,v))),
inference(spr,[status(thm),theory(equality)],[1981,1089]),
[iquote('0:SpR:1981.0,1089.0')] ).
cnf(2732,plain,
equal(join(meet(u,v),join(v,w)),join(w,meet(v,join(v,u)))),
inference(spr,[status(thm),theory(equality)],[2506,129]),
[iquote('0:SpR:2506.0,129.0')] ).
cnf(2782,plain,
equal(join(u,join(meet(v,u),w)),join(w,meet(u,join(u,v)))),
inference(rew,[status(thm),theory(equality)],[36,2732]),
[iquote('0:Rew:36.0,2732.0')] ).
cnf(3407,plain,
equal(join(meet(join(u,v),w),join(x,u)),join(x,join(u,meet(w,v)))),
inference(spr,[status(thm),theory(equality)],[1921,29]),
[iquote('0:SpR:1921.0,29.0')] ).
cnf(3502,plain,
equal(join(u,join(v,meet(join(u,w),x))),join(v,join(u,meet(x,w)))),
inference(rew,[status(thm),theory(equality)],[129,3407]),
[iquote('0:Rew:129.0,3407.0')] ).
cnf(10355,plain,
equal(join(meet(meet(u,join(v,w)),v),meet(u,join(v,w))),meet(u,join(v,w))),
inference(spr,[status(thm),theory(equality)],[81,773]),
[iquote('0:SpR:81.0,773.0')] ).
cnf(10462,plain,
equal(join(meet(join(u,v),w),meet(w,meet(u,join(u,v)))),meet(w,join(u,v))),
inference(rew,[status(thm),theory(equality)],[1088,10355,5,7]),
[iquote('0:Rew:1088.0,10355.0,5.0,10355.0,7.0,10355.0')] ).
cnf(10463,plain,
equal(meet(u,join(v,meet(w,join(meet(w,u),v)))),meet(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[1975,10462,1463,3502,2782,1976]),
[iquote('0:Rew:1975.0,10462.0,1463.0,10462.0,3502.0,10462.0,2782.0,10462.0,1976.0,10462.0')] ).
cnf(10464,plain,
equal(meet(u,join(v,meet(u,w))),meet(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[81,10463,7,1961]),
[iquote('0:Rew:81.0,10463.0,7.0,10463.0,1961.0,10463.0')] ).
cnf(10465,plain,
~ equal(meet(a,join(c,b)),meet(a,join(b,c))),
inference(rew,[status(thm),theory(equality)],[10464,2015]),
[iquote('0:Rew:10464.0,2015.0')] ).
cnf(10469,plain,
~ equal(meet(a,join(b,c)),meet(a,join(b,c))),
inference(rew,[status(thm),theory(equality)],[6,10465]),
[iquote('0:Rew:6.0,10465.0')] ).
cnf(10470,plain,
$false,
inference(obv,[status(thm),theory(equality)],[10469]),
[iquote('0:Obv:10469.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT021-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.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 03:12:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.73/3.89
% 3.73/3.89 SPASS V 3.9
% 3.73/3.89 SPASS beiseite: Proof found.
% 3.73/3.89 % SZS status Theorem
% 3.73/3.89 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.73/3.89 SPASS derived 6373 clauses, backtracked 0 clauses, performed 0 splits and kept 1275 clauses.
% 3.73/3.89 SPASS allocated 72334 KBytes.
% 3.73/3.89 SPASS spent 0:00:03.50 on the problem.
% 3.73/3.89 0:00:00.04 for the input.
% 3.73/3.89 0:00:00.00 for the FLOTTER CNF translation.
% 3.73/3.89 0:00:00.06 for inferences.
% 3.73/3.89 0:00:00.00 for the backtracking.
% 3.73/3.89 0:00:03.38 for the reduction.
% 3.73/3.89
% 3.73/3.89
% 3.73/3.89 Here is a proof with depth 5, length 70 :
% 3.73/3.89 % SZS output start Refutation
% See solution above
% 3.73/3.89 Formulae used in the proof : bowden prove_distributivity idempotence_of_meet idempotence_of_join commutativity_of_meet commutativity_of_join associativity_of_meet associativity_of_join quasi_lattice1 quasi_lattice2
% 3.73/3.89
%------------------------------------------------------------------------------