%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT249-1 : TPTP v8.1.0. Released v3.1.0.
% 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 06:49:46 EDT 2022
% Result : Unsatisfiable 0.77s 0.98s
% Output : Refutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of clauses : 35 ( 31 unt; 0 nHn; 35 RR)
% Number of literals : 41 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(meet(u,join(v,meet(u,join(w,meet(u,join(v,meet(u,w))))))),meet(u,join(v,w))),
file('LAT249-1.p',unknown),
[] ).
cnf(2,axiom,
equal(meet(b,a),a),
file('LAT249-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(join(complement(b),complement(a)),complement(a)),
file('LAT249-1.p',unknown),
[] ).
cnf(6,axiom,
equal(meet(u,join(u,v)),u),
file('LAT249-1.p',unknown),
[] ).
cnf(7,axiom,
equal(join(u,meet(u,v)),u),
file('LAT249-1.p',unknown),
[] ).
cnf(8,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT249-1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(u,v),join(v,u)),
file('LAT249-1.p',unknown),
[] ).
cnf(10,axiom,
equal(meet(meet(u,v),w),meet(u,meet(v,w))),
file('LAT249-1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('LAT249-1.p',unknown),
[] ).
cnf(12,axiom,
equal(join(u,complement(u)),one),
file('LAT249-1.p',unknown),
[] ).
cnf(13,axiom,
equal(meet(u,complement(u)),zero),
file('LAT249-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(join(u,v),one)
| ~ equal(meet(u,v),zero)
| equal(complement(u),v) ),
file('LAT249-1.p',unknown),
[] ).
cnf(24,plain,
equal(join(u,zero),u),
inference(spr,[status(thm),theory(equality)],[13,7]),
[iquote('0:SpR:13.0,7.0')] ).
cnf(31,plain,
equal(meet(u,one),u),
inference(spr,[status(thm),theory(equality)],[12,6]),
[iquote('0:SpR:12.0,6.0')] ).
cnf(36,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[9,24]),
[iquote('0:SpR:9.0,24.0')] ).
cnf(50,plain,
equal(meet(zero,u),zero),
inference(spr,[status(thm),theory(equality)],[36,7]),
[iquote('0:SpR:36.0,7.0')] ).
cnf(68,plain,
equal(meet(one,u),u),
inference(spr,[status(thm),theory(equality)],[8,31]),
[iquote('0:SpR:8.0,31.0')] ).
cnf(85,plain,
equal(join(one,u),one),
inference(spr,[status(thm),theory(equality)],[68,7]),
[iquote('0:SpR:68.0,7.0')] ).
cnf(177,plain,
equal(join(u,join(complement(u),v)),join(one,v)),
inference(spr,[status(thm),theory(equality)],[12,11]),
[iquote('0:SpR:12.0,11.0')] ).
cnf(192,plain,
equal(join(u,join(complement(u),v)),one),
inference(rew,[status(thm),theory(equality)],[85,177]),
[iquote('0:Rew:85.0,177.0')] ).
cnf(212,plain,
equal(join(u,join(v,complement(u))),one),
inference(spr,[status(thm),theory(equality)],[9,192]),
[iquote('0:SpR:9.0,192.0')] ).
cnf(282,plain,
equal(meet(b,meet(a,u)),meet(a,u)),
inference(spr,[status(thm),theory(equality)],[2,10]),
[iquote('0:SpR:2.0,10.0')] ).
cnf(284,plain,
equal(meet(u,meet(complement(u),v)),meet(zero,v)),
inference(spr,[status(thm),theory(equality)],[13,10]),
[iquote('0:SpR:13.0,10.0')] ).
cnf(299,plain,
equal(meet(u,meet(complement(u),v)),zero),
inference(rew,[status(thm),theory(equality)],[50,284]),
[iquote('0:Rew:50.0,284.0')] ).
cnf(434,plain,
equal(meet(u,join(v,meet(u,join(complement(u),meet(u,join(v,zero)))))),meet(u,join(v,complement(u)))),
inference(spr,[status(thm),theory(equality)],[13,1]),
[iquote('0:SpR:13.0,1.0')] ).
cnf(503,plain,
equal(meet(u,join(v,meet(u,join(complement(u),meet(u,v))))),meet(u,join(v,complement(u)))),
inference(rew,[status(thm),theory(equality)],[24,434]),
[iquote('0:Rew:24.0,434.0')] ).
cnf(618,plain,
equal(meet(u,meet(v,complement(u))),zero),
inference(spr,[status(thm),theory(equality)],[8,299]),
[iquote('0:SpR:8.0,299.0')] ).
cnf(689,plain,
equal(meet(a,complement(b)),zero),
inference(spr,[status(thm),theory(equality)],[282,618]),
[iquote('0:SpR:282.0,618.0')] ).
cnf(6784,plain,
equal(meet(a,join(complement(b),meet(a,join(complement(a),zero)))),meet(a,join(complement(b),complement(a)))),
inference(spr,[status(thm),theory(equality)],[689,503]),
[iquote('0:SpR:689.0,503.0')] ).
cnf(6845,plain,
equal(meet(a,join(complement(b),complement(a))),zero),
inference(rew,[status(thm),theory(equality)],[689,6784,36,9,13]),
[iquote('0:Rew:689.0,6784.0,36.0,6784.0,9.0,6784.0,13.0,6784.0,36.0,6784.0,9.0,6784.0')] ).
cnf(6947,plain,
( ~ equal(join(a,join(complement(b),complement(a))),one)
| ~ equal(zero,zero)
| equal(join(complement(b),complement(a)),complement(a)) ),
inference(spl,[status(thm),theory(equality)],[6845,14]),
[iquote('0:SpL:6845.0,14.1')] ).
cnf(6976,plain,
( ~ equal(join(a,join(complement(b),complement(a))),one)
| equal(join(complement(b),complement(a)),complement(a)) ),
inference(obv,[status(thm),theory(equality)],[6947]),
[iquote('0:Obv:6947.1')] ).
cnf(6977,plain,
( ~ equal(one,one)
| equal(join(complement(b),complement(a)),complement(a)) ),
inference(rew,[status(thm),theory(equality)],[212,6976]),
[iquote('0:Rew:212.0,6976.0')] ).
cnf(6978,plain,
equal(join(complement(b),complement(a)),complement(a)),
inference(obv,[status(thm),theory(equality)],[6977]),
[iquote('0:Obv:6977.0')] ).
cnf(6979,plain,
$false,
inference(mrr,[status(thm)],[6978,3]),
[iquote('0:MRR:6978.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT249-1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 29 16:29:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.77/0.98
% 0.77/0.98 SPASS V 3.9
% 0.77/0.98 SPASS beiseite: Proof found.
% 0.77/0.98 % SZS status Theorem
% 0.77/0.98 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.77/0.98 SPASS derived 4933 clauses, backtracked 0 clauses, performed 0 splits and kept 534 clauses.
% 0.77/0.98 SPASS allocated 68295 KBytes.
% 0.77/0.98 SPASS spent 0:00:00.61 on the problem.
% 0.77/0.98 0:00:00.04 for the input.
% 0.77/0.98 0:00:00.00 for the FLOTTER CNF translation.
% 0.77/0.98 0:00:00.04 for inferences.
% 0.77/0.98 0:00:00.00 for the backtracking.
% 0.77/0.98 0:00:00.51 for the reduction.
% 0.77/0.98
% 0.77/0.98
% 0.77/0.98 Here is a proof with depth 5, length 35 :
% 0.77/0.98 % SZS output start Refutation
% See solution above
% 0.77/0.98 Formulae used in the proof : equation_H64 prove_distributivity_hypothesis prove_distributivity absorption1 absorption2 commutativity_of_meet commutativity_of_join associativity_of_meet associativity_of_join complement_join complement_meet meet_join_complement
% 0.77/0.98
%------------------------------------------------------------------------------