TSTP Solution File: LAT238-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT238-1 : TPTP v8.1.0. Released v3.1.0.
% 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 06:49:42 EDT 2022
% Result : Unsatisfiable 89.27s 89.49s
% Output : Refutation 89.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 41 ( 37 unt; 0 nHn; 41 RR)
% Number of literals : 47 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 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(v,meet(w,join(v,join(x,meet(u,w)))))),meet(u,join(v,meet(w,join(u,x))))),
file('LAT238-1.p',unknown),
[] ).
cnf(2,axiom,
equal(meet(b,a),a),
file('LAT238-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(join(complement(b),complement(a)),complement(a)),
file('LAT238-1.p',unknown),
[] ).
cnf(5,axiom,
equal(join(u,u),u),
file('LAT238-1.p',unknown),
[] ).
cnf(6,axiom,
equal(meet(u,join(u,v)),u),
file('LAT238-1.p',unknown),
[] ).
cnf(7,axiom,
equal(join(u,meet(u,v)),u),
file('LAT238-1.p',unknown),
[] ).
cnf(8,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT238-1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(u,v),join(v,u)),
file('LAT238-1.p',unknown),
[] ).
cnf(10,axiom,
equal(meet(meet(u,v),w),meet(u,meet(v,w))),
file('LAT238-1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('LAT238-1.p',unknown),
[] ).
cnf(12,axiom,
equal(join(u,complement(u)),one),
file('LAT238-1.p',unknown),
[] ).
cnf(13,axiom,
equal(meet(u,complement(u)),zero),
file('LAT238-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(join(u,v),one)
| ~ equal(meet(u,v),zero)
| equal(complement(u),v) ),
file('LAT238-1.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(66,plain,
equal(join(u,meet(v,u)),u),
inference(spr,[status(thm),theory(equality)],[8,7]),
[iquote('0:SpR:8.0,7.0')] ).
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(167,plain,
equal(join(u,join(v,meet(w,join(u,v)))),join(u,v)),
inference(spr,[status(thm),theory(equality)],[11,66]),
[iquote('0:SpR:11.0,66.0')] ).
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(454,plain,
equal(meet(u,join(join(v,meet(u,w)),meet(w,join(v,meet(u,w))))),meet(u,join(join(v,meet(u,w)),meet(w,join(u,v))))),
inference(spr,[status(thm),theory(equality)],[5,1]),
[iquote('0:SpR:5.0,1.0')] ).
cnf(514,plain,
equal(meet(u,join(v,join(meet(u,w),meet(w,join(v,meet(u,w)))))),meet(u,join(v,join(meet(u,w),meet(w,join(u,v)))))),
inference(rew,[status(thm),theory(equality)],[11,454]),
[iquote('0:Rew:11.0,454.0,11.0,454.0')] ).
cnf(515,plain,
equal(meet(u,join(v,join(meet(u,w),meet(w,join(u,v))))),meet(u,join(v,meet(u,w)))),
inference(rew,[status(thm),theory(equality)],[167,514]),
[iquote('0:Rew:167.0,514.0')] ).
cnf(560,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(597,plain,
equal(meet(a,complement(b)),zero),
inference(spr,[status(thm),theory(equality)],[560,282]),
[iquote('0:SpR:560.0,282.0')] ).
cnf(6730,plain,
equal(meet(u,join(complement(u),join(meet(u,v),meet(v,one)))),meet(u,join(complement(u),meet(u,v)))),
inference(spr,[status(thm),theory(equality)],[12,515]),
[iquote('0:SpR:12.0,515.0')] ).
cnf(6927,plain,
equal(meet(u,join(complement(u),meet(u,v))),meet(u,join(complement(u),v))),
inference(rew,[status(thm),theory(equality)],[66,6730,9,31]),
[iquote('0:Rew:66.0,6730.0,9.0,6730.0,31.0,6730.0')] ).
cnf(83535,plain,
equal(meet(a,join(complement(a),complement(b))),meet(a,join(complement(a),zero))),
inference(spr,[status(thm),theory(equality)],[597,6927]),
[iquote('0:SpR:597.0,6927.0')] ).
cnf(83677,plain,
equal(meet(a,join(complement(b),complement(a))),zero),
inference(rew,[status(thm),theory(equality)],[9,83535,13,36]),
[iquote('0:Rew:9.0,83535.0,13.0,83535.0,36.0,83535.0,9.0,83535.0')] ).
cnf(84000,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)],[83677,14]),
[iquote('0:SpL:83677.0,14.1')] ).
cnf(84112,plain,
( ~ equal(join(a,join(complement(b),complement(a))),one)
| equal(join(complement(b),complement(a)),complement(a)) ),
inference(obv,[status(thm),theory(equality)],[84000]),
[iquote('0:Obv:84000.1')] ).
cnf(84113,plain,
( ~ equal(one,one)
| equal(join(complement(b),complement(a)),complement(a)) ),
inference(rew,[status(thm),theory(equality)],[212,84112]),
[iquote('0:Rew:212.0,84112.0')] ).
cnf(84114,plain,
equal(join(complement(b),complement(a)),complement(a)),
inference(obv,[status(thm),theory(equality)],[84113]),
[iquote('0:Obv:84113.0')] ).
cnf(84115,plain,
$false,
inference(mrr,[status(thm)],[84114,3]),
[iquote('0:MRR:84114.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT238-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.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 16:39:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 89.27/89.49
% 89.27/89.49 SPASS V 3.9
% 89.27/89.49 SPASS beiseite: Proof found.
% 89.27/89.49 % SZS status Theorem
% 89.27/89.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 89.27/89.49 SPASS derived 54249 clauses, backtracked 0 clauses, performed 0 splits and kept 6385 clauses.
% 89.27/89.49 SPASS allocated 146135 KBytes.
% 89.27/89.49 SPASS spent 0:1:27.76 on the problem.
% 89.27/89.49 0:00:00.04 for the input.
% 89.27/89.49 0:00:00.00 for the FLOTTER CNF translation.
% 89.27/89.49 0:00:00.38 for inferences.
% 89.27/89.49 0:00:00.00 for the backtracking.
% 89.27/89.49 0:1:27.27 for the reduction.
% 89.27/89.49
% 89.27/89.49
% 89.27/89.49 Here is a proof with depth 5, length 41 :
% 89.27/89.49 % SZS output start Refutation
% See solution above
% 89.27/89.49 Formulae used in the proof : equation_H42 prove_distributivity_hypothesis prove_distributivity idempotence_of_join absorption1 absorption2 commutativity_of_meet commutativity_of_join associativity_of_meet associativity_of_join complement_join complement_meet meet_join_complement
% 89.27/89.49
%------------------------------------------------------------------------------