TSTP Solution File: LAT019-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT019-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 0.70s 0.87s
% Output : Refutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 45 RR)
% Number of literals : 45 ( 0 equ; 4 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(meet(u,join(v,w)),join(meet(u,v),meet(u,w))),
file('LAT019-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(meet(join(a,b),join(a,c)),join(a,meet(b,c))),
file('LAT019-1.p',unknown),
[] ).
cnf(3,axiom,
equal(meet(u,u),u),
file('LAT019-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(u,u),u),
file('LAT019-1.p',unknown),
[] ).
cnf(5,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT019-1.p',unknown),
[] ).
cnf(6,axiom,
equal(join(u,v),join(v,u)),
file('LAT019-1.p',unknown),
[] ).
cnf(7,axiom,
equal(meet(meet(u,v),w),meet(u,meet(v,w))),
file('LAT019-1.p',unknown),
[] ).
cnf(8,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('LAT019-1.p',unknown),
[] ).
cnf(10,axiom,
equal(meet(join(u,meet(v,w)),join(u,v)),join(u,meet(v,w))),
file('LAT019-1.p',unknown),
[] ).
cnf(11,plain,
~ equal(join(a,join(meet(a,b),join(meet(a,c),meet(b,c)))),join(a,meet(b,c))),
inference(rew,[status(thm),theory(equality)],[8,2,3,1,5]),
[iquote('0:Rew:8.0,2.0,3.0,2.0,1.0,2.0,5.0,2.0,5.0,2.0,5.0,2.0,1.0,2.0,5.0,2.0,1.0,2.0')] ).
cnf(12,plain,
equal(join(u,join(meet(u,meet(v,w)),join(meet(v,u),meet(v,meet(v,w))))),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[8,10,3,1,5]),
[iquote('0:Rew:8.0,10.0,3.0,10.0,1.0,10.0,5.0,10.0,1.0,10.0,5.0,10.0,1.0,10.0')] ).
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(33,plain,
equal(join(u,join(u,v)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[4,8]),
[iquote('0:SpR:4.0,8.0')] ).
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(44,plain,
equal(join(u,join(v,u)),join(v,u)),
inference(spr,[status(thm),theory(equality)],[6,33]),
[iquote('0:SpR:6.0,33.0')] ).
cnf(53,plain,
equal(join(u,join(join(v,u),w)),join(join(v,u),w)),
inference(spr,[status(thm),theory(equality)],[44,8]),
[iquote('0:SpR:44.0,8.0')] ).
cnf(63,plain,
equal(join(u,join(v,join(u,w))),join(v,join(u,w))),
inference(rew,[status(thm),theory(equality)],[8,53]),
[iquote('0:Rew:8.0,53.0')] ).
cnf(71,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(72,plain,
equal(meet(meet(u,v),w),meet(v,meet(u,w))),
inference(spr,[status(thm),theory(equality)],[5,7]),
[iquote('0:SpR:5.0,7.0')] ).
cnf(74,plain,
equal(join(u,join(meet(u,meet(v,w)),join(meet(v,u),meet(v,w)))),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[71,12]),
[iquote('0:Rew:71.0,12.0')] ).
cnf(75,plain,
equal(meet(u,meet(v,w)),meet(v,meet(u,w))),
inference(rew,[status(thm),theory(equality)],[7,72]),
[iquote('0:Rew:7.0,72.0')] ).
cnf(78,plain,
equal(join(u,join(meet(v,w),join(meet(u,meet(v,w)),meet(v,u)))),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[29,74]),
[iquote('0:Rew:29.0,74.0')] ).
cnf(84,plain,
equal(meet(u,meet(v,u)),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[5,71]),
[iquote('0:SpR:5.0,71.0')] ).
cnf(92,plain,
equal(meet(join(u,v),w),join(meet(w,u),meet(w,v))),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(114,plain,
equal(meet(u,meet(meet(v,u),w)),meet(meet(v,u),w)),
inference(spr,[status(thm),theory(equality)],[84,7]),
[iquote('0:SpR:84.0,7.0')] ).
cnf(125,plain,
equal(meet(u,meet(v,meet(u,w))),meet(v,meet(u,w))),
inference(rew,[status(thm),theory(equality)],[7,114]),
[iquote('0:Rew:7.0,114.0')] ).
cnf(769,plain,
equal(join(u,join(meet(v,w),join(meet(u,meet(v,w)),meet(u,v)))),join(u,meet(v,w))),
inference(spr,[status(thm),theory(equality)],[5,78]),
[iquote('0:SpR:5.0,78.0')] ).
cnf(773,plain,
equal(join(meet(u,v),join(meet(v,w),join(meet(meet(u,v),meet(v,w)),meet(u,v)))),join(meet(u,v),meet(v,w))),
inference(spr,[status(thm),theory(equality)],[84,78]),
[iquote('0:SpR:84.0,78.0')] ).
cnf(839,plain,
equal(join(u,join(meet(v,w),join(meet(u,v),meet(u,meet(v,w))))),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[6,769]),
[iquote('0:Rew:6.0,769.0')] ).
cnf(855,plain,
equal(join(meet(u,v),join(meet(v,w),join(meet(u,v),meet(v,meet(u,meet(v,w)))))),join(meet(u,v),meet(v,w))),
inference(rew,[status(thm),theory(equality)],[6,773,7,75]),
[iquote('0:Rew:6.0,773.0,7.0,773.0,75.0,773.0')] ).
cnf(856,plain,
equal(join(meet(u,v),join(meet(w,u),meet(w,meet(u,v)))),join(meet(w,u),meet(u,v))),
inference(rew,[status(thm),theory(equality)],[63,855,125]),
[iquote('0:Rew:63.0,855.0,125.0,855.0')] ).
cnf(857,plain,
equal(join(u,join(meet(u,v),meet(v,w))),join(u,meet(v,w))),
inference(rew,[status(thm),theory(equality)],[856,839]),
[iquote('0:Rew:856.0,839.0')] ).
cnf(1231,plain,
equal(meet(join(u,v),w),join(meet(w,u),meet(v,w))),
inference(spr,[status(thm),theory(equality)],[5,92]),
[iquote('0:SpR:5.0,92.0')] ).
cnf(2484,plain,
equal(meet(join(u,v),w),join(meet(u,w),meet(v,w))),
inference(spr,[status(thm),theory(equality)],[5,1231]),
[iquote('0:SpR:5.0,1231.0')] ).
cnf(2928,plain,
equal(join(u,join(v,join(meet(u,w),meet(w,x)))),join(v,join(u,meet(w,x)))),
inference(spr,[status(thm),theory(equality)],[857,36]),
[iquote('0:SpR:857.0,36.0')] ).
cnf(2931,plain,
equal(join(u,join(v,join(meet(join(u,v),w),meet(w,x)))),join(join(u,v),meet(w,x))),
inference(spr,[status(thm),theory(equality)],[857,8]),
[iquote('0:SpR:857.0,8.0')] ).
cnf(2942,plain,
equal(join(u,join(meet(u,v),meet(w,v))),join(u,meet(w,v))),
inference(spr,[status(thm),theory(equality)],[5,857]),
[iquote('0:SpR:5.0,857.0')] ).
cnf(3012,plain,
equal(join(u,join(v,join(meet(join(u,v),w),meet(w,x)))),join(u,join(v,meet(w,x)))),
inference(rew,[status(thm),theory(equality)],[8,2931]),
[iquote('0:Rew:8.0,2931.0')] ).
cnf(3013,plain,
equal(join(u,join(v,join(join(meet(u,w),meet(v,w)),meet(w,x)))),join(u,join(v,meet(w,x)))),
inference(rew,[status(thm),theory(equality)],[2484,3012]),
[iquote('0:Rew:2484.0,3012.0')] ).
cnf(3014,plain,
equal(join(u,join(v,join(meet(u,w),join(meet(v,w),meet(w,x))))),join(u,join(v,meet(w,x)))),
inference(rew,[status(thm),theory(equality)],[8,3013]),
[iquote('0:Rew:8.0,3013.0')] ).
cnf(3015,plain,
equal(join(u,join(meet(u,v),join(w,meet(v,x)))),join(u,join(w,meet(v,x)))),
inference(rew,[status(thm),theory(equality)],[2928,3014]),
[iquote('0:Rew:2928.0,3014.0')] ).
cnf(3016,plain,
~ equal(join(a,join(meet(a,c),meet(b,c))),join(a,meet(b,c))),
inference(rew,[status(thm),theory(equality)],[3015,11]),
[iquote('0:Rew:3015.0,11.0')] ).
cnf(3018,plain,
~ equal(join(a,meet(b,c)),join(a,meet(b,c))),
inference(rew,[status(thm),theory(equality)],[2942,3016]),
[iquote('0:Rew:2942.0,3016.0')] ).
cnf(3019,plain,
$false,
inference(obv,[status(thm),theory(equality)],[3018]),
[iquote('0:Obv:3018.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT019-1 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 30 10:35:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.70/0.87
% 0.70/0.87 SPASS V 3.9
% 0.70/0.87 SPASS beiseite: Proof found.
% 0.70/0.87 % SZS status Theorem
% 0.70/0.87 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.70/0.87 SPASS derived 1780 clauses, backtracked 0 clauses, performed 0 splits and kept 437 clauses.
% 0.70/0.87 SPASS allocated 66021 KBytes.
% 0.70/0.87 SPASS spent 0:00:00.51 on the problem.
% 0.70/0.87 0:00:00.04 for the input.
% 0.70/0.87 0:00:00.00 for the FLOTTER CNF translation.
% 0.70/0.87 0:00:00.02 for inferences.
% 0.70/0.87 0:00:00.00 for the backtracking.
% 0.70/0.87 0:00:00.44 for the reduction.
% 0.70/0.87
% 0.70/0.87
% 0.70/0.87 Here is a proof with depth 3, length 45 :
% 0.70/0.87 % SZS output start Refutation
% See solution above
% 0.70/0.87 Formulae used in the proof : distributivity_law prove_distributivity_law_dual idempotence_of_meet idempotence_of_join commutativity_of_meet commutativity_of_join associativity_of_meet associativity_of_join quasi_lattice2
% 0.70/0.87
%------------------------------------------------------------------------------