TSTP Solution File: LAT254-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT254-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 06:49:48 EDT 2022
% Result : Unsatisfiable 210.85s 211.22s
% Output : Refutation 210.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of clauses : 38 ( 34 unt; 0 nHn; 38 RR)
% Number of literals : 44 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(meet(u,join(meet(u,join(v,meet(u,w))),meet(w,x))),meet(u,join(v,meet(w,join(u,x))))),
file('LAT254-1.p',unknown),
[] ).
cnf(2,axiom,
equal(meet(b,a),a),
file('LAT254-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(join(complement(b),complement(a)),complement(a)),
file('LAT254-1.p',unknown),
[] ).
cnf(6,axiom,
equal(meet(u,join(u,v)),u),
file('LAT254-1.p',unknown),
[] ).
cnf(7,axiom,
equal(join(u,meet(u,v)),u),
file('LAT254-1.p',unknown),
[] ).
cnf(8,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT254-1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(u,v),join(v,u)),
file('LAT254-1.p',unknown),
[] ).
cnf(10,axiom,
equal(meet(meet(u,v),w),meet(u,meet(v,w))),
file('LAT254-1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('LAT254-1.p',unknown),
[] ).
cnf(12,axiom,
equal(join(u,complement(u)),one),
file('LAT254-1.p',unknown),
[] ).
cnf(13,axiom,
equal(meet(u,complement(u)),zero),
file('LAT254-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(join(u,v),one)
| ~ equal(meet(u,v),zero)
| equal(complement(u),v) ),
file('LAT254-1.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(100,plain,
equal(join(u,one),one),
inference(spr,[status(thm),theory(equality)],[85,9]),
[iquote('0:SpR:85.0,9.0')] ).
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(448,plain,
equal(meet(u,join(meet(u,join(v,zero)),meet(complement(u),w))),meet(u,join(v,meet(complement(u),join(u,w))))),
inference(spr,[status(thm),theory(equality)],[13,1]),
[iquote('0:SpR:13.0,1.0')] ).
cnf(505,plain,
equal(meet(u,join(meet(u,v),meet(complement(u),w))),meet(u,join(v,meet(complement(u),join(u,w))))),
inference(rew,[status(thm),theory(equality)],[24,448]),
[iquote('0:Rew:24.0,448.0')] ).
cnf(568,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(608,plain,
equal(meet(a,complement(b)),zero),
inference(spr,[status(thm),theory(equality)],[568,282]),
[iquote('0:SpR:568.0,282.0')] ).
cnf(7870,plain,
equal(meet(u,join(v,meet(complement(u),join(u,one)))),meet(u,join(meet(u,v),complement(u)))),
inference(spr,[status(thm),theory(equality)],[31,505]),
[iquote('0:SpR:31.0,505.0')] ).
cnf(7957,plain,
equal(meet(u,join(complement(u),meet(u,v))),meet(u,join(v,complement(u)))),
inference(rew,[status(thm),theory(equality)],[68,7870,8,100,9]),
[iquote('0:Rew:68.0,7870.0,8.0,7870.0,100.0,7870.0,9.0,7870.0')] ).
cnf(108650,plain,
equal(meet(a,join(complement(b),complement(a))),meet(a,join(complement(a),zero))),
inference(spr,[status(thm),theory(equality)],[608,7957]),
[iquote('0:SpR:608.0,7957.0')] ).
cnf(108836,plain,
equal(meet(a,join(complement(b),complement(a))),zero),
inference(rew,[status(thm),theory(equality)],[13,108650,36,9]),
[iquote('0:Rew:13.0,108650.0,36.0,108650.0,9.0,108650.0')] ).
cnf(109235,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)],[108836,14]),
[iquote('0:SpL:108836.0,14.1')] ).
cnf(109358,plain,
( ~ equal(join(a,join(complement(b),complement(a))),one)
| equal(join(complement(b),complement(a)),complement(a)) ),
inference(obv,[status(thm),theory(equality)],[109235]),
[iquote('0:Obv:109235.1')] ).
cnf(109359,plain,
( ~ equal(one,one)
| equal(join(complement(b),complement(a)),complement(a)) ),
inference(rew,[status(thm),theory(equality)],[212,109358]),
[iquote('0:Rew:212.0,109358.0')] ).
cnf(109360,plain,
equal(join(complement(b),complement(a)),complement(a)),
inference(obv,[status(thm),theory(equality)],[109359]),
[iquote('0:Obv:109359.0')] ).
cnf(109361,plain,
$false,
inference(mrr,[status(thm)],[109360,3]),
[iquote('0:MRR:109360.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT254-1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 30 15:03:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 210.85/211.22
% 210.85/211.22 SPASS V 3.9
% 210.85/211.22 SPASS beiseite: Proof found.
% 210.85/211.22 % SZS status Theorem
% 210.85/211.22 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 210.85/211.22 SPASS derived 68539 clauses, backtracked 0 clauses, performed 0 splits and kept 7592 clauses.
% 210.85/211.22 SPASS allocated 177796 KBytes.
% 210.85/211.22 SPASS spent 0:3:28.40 on the problem.
% 210.85/211.22 0:00:00.03 for the input.
% 210.85/211.22 0:00:00.00 for the FLOTTER CNF translation.
% 210.85/211.22 0:00:00.60 for inferences.
% 210.85/211.22 0:00:00.00 for the backtracking.
% 210.85/211.22 0:3:27.62 for the reduction.
% 210.85/211.22
% 210.85/211.22
% 210.85/211.22 Here is a proof with depth 5, length 38 :
% 210.85/211.22 % SZS output start Refutation
% See solution above
% 210.85/211.22 Formulae used in the proof : equation_H79 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
% 210.85/211.22
%------------------------------------------------------------------------------