TSTP Solution File: LAT043-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT043-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 06:48:46 EDT 2022
% Result : Unsatisfiable 0.76s 0.94s
% Output : Refutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of clauses : 49 ( 49 unt; 0 nHn; 49 RR)
% Number of literals : 49 ( 0 equ; 3 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 : 10 ( 10 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('LAT043-1.p',unknown),
[] ).
cnf(2,axiom,
equal(join(complement(u),u),n1),
file('LAT043-1.p',unknown),
[] ).
cnf(3,axiom,
equal(meet(complement(u),u),n0),
file('LAT043-1.p',unknown),
[] ).
cnf(4,axiom,
equal(complement(complement(u)),u),
file('LAT043-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(meet(complement(c),complement(d)),complement(join(c,d))),
file('LAT043-1.p',unknown),
[] ).
cnf(6,axiom,
equal(meet(u,u),u),
file('LAT043-1.p',unknown),
[] ).
cnf(7,axiom,
equal(join(u,u),u),
file('LAT043-1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(u,meet(u,v)),u),
file('LAT043-1.p',unknown),
[] ).
cnf(10,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT043-1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(u,v),join(v,u)),
file('LAT043-1.p',unknown),
[] ).
cnf(12,axiom,
equal(meet(meet(u,v),w),meet(u,meet(v,w))),
file('LAT043-1.p',unknown),
[] ).
cnf(13,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('LAT043-1.p',unknown),
[] ).
cnf(14,plain,
equal(join(u,complement(u)),n1),
inference(rew,[status(thm),theory(equality)],[11,2]),
[iquote('0:Rew:11.0,2.0')] ).
cnf(15,plain,
equal(meet(u,complement(u)),n0),
inference(rew,[status(thm),theory(equality)],[10,3]),
[iquote('0:Rew:10.0,3.0')] ).
cnf(30,plain,
equal(join(u,n0),u),
inference(spr,[status(thm),theory(equality)],[15,9]),
[iquote('0:SpR:15.0,9.0')] ).
cnf(34,plain,
equal(join(n0,u),u),
inference(spr,[status(thm),theory(equality)],[11,30]),
[iquote('0:SpR:11.0,30.0')] ).
cnf(43,plain,
equal(meet(n0,u),n0),
inference(spr,[status(thm),theory(equality)],[34,9]),
[iquote('0:SpR:34.0,9.0')] ).
cnf(96,plain,
equal(join(u,join(u,v)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[7,13]),
[iquote('0:SpR:7.0,13.0')] ).
cnf(98,plain,
equal(join(u,join(meet(u,v),w)),join(u,w)),
inference(spr,[status(thm),theory(equality)],[9,13]),
[iquote('0:SpR:9.0,13.0')] ).
cnf(116,plain,
equal(join(u,n1),n1),
inference(spr,[status(thm),theory(equality)],[14,96]),
[iquote('0:SpR:14.0,96.0')] ).
cnf(129,plain,
equal(meet(u,meet(v,complement(meet(u,v)))),n0),
inference(spr,[status(thm),theory(equality)],[12,15]),
[iquote('0:SpR:12.0,15.0')] ).
cnf(138,plain,
equal(meet(u,meet(complement(u),v)),meet(n0,v)),
inference(spr,[status(thm),theory(equality)],[15,12]),
[iquote('0:SpR:15.0,12.0')] ).
cnf(146,plain,
equal(meet(u,meet(complement(u),v)),n0),
inference(rew,[status(thm),theory(equality)],[43,138]),
[iquote('0:Rew:43.0,138.0')] ).
cnf(186,plain,
equal(meet(u,meet(v,complement(u))),n0),
inference(spr,[status(thm),theory(equality)],[10,146]),
[iquote('0:SpR:10.0,146.0')] ).
cnf(226,plain,
equal(join(meet(u,v),meet(u,complement(v))),meet(u,n1)),
inference(spr,[status(thm),theory(equality)],[14,1]),
[iquote('0:SpR:14.0,1.0')] ).
cnf(233,plain,
equal(join(meet(u,v),meet(u,n1)),meet(u,n1)),
inference(spr,[status(thm),theory(equality)],[116,1]),
[iquote('0:SpR:116.0,1.0')] ).
cnf(527,plain,
equal(meet(u,meet(v,complement(meet(v,u)))),n0),
inference(spr,[status(thm),theory(equality)],[10,129]),
[iquote('0:SpR:10.0,129.0')] ).
cnf(2541,plain,
equal(join(u,meet(u,n1)),meet(u,n1)),
inference(spr,[status(thm),theory(equality)],[6,233]),
[iquote('0:SpR:6.0,233.0')] ).
cnf(2562,plain,
equal(meet(u,n1),u),
inference(rew,[status(thm),theory(equality)],[9,2541]),
[iquote('0:Rew:9.0,2541.0')] ).
cnf(2565,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[2562,226]),
[iquote('0:Rew:2562.0,226.0')] ).
cnf(2747,plain,
equal(join(meet(u,v),meet(complement(v),u)),u),
inference(spr,[status(thm),theory(equality)],[10,2565]),
[iquote('0:SpR:10.0,2565.0')] ).
cnf(2754,plain,
equal(join(meet(u,v),meet(v,complement(u))),v),
inference(spr,[status(thm),theory(equality)],[10,2565]),
[iquote('0:SpR:10.0,2565.0')] ).
cnf(2758,plain,
equal(join(n0,meet(u,complement(meet(v,complement(u))))),u),
inference(spr,[status(thm),theory(equality)],[186,2565]),
[iquote('0:SpR:186.0,2565.0')] ).
cnf(2764,plain,
equal(join(n0,meet(u,complement(meet(complement(u),v)))),u),
inference(spr,[status(thm),theory(equality)],[146,2565]),
[iquote('0:SpR:146.0,2565.0')] ).
cnf(2787,plain,
equal(meet(u,complement(meet(v,complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[34,2758]),
[iquote('0:Rew:34.0,2758.0')] ).
cnf(2788,plain,
equal(meet(u,complement(meet(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[34,2764]),
[iquote('0:Rew:34.0,2764.0')] ).
cnf(2989,plain,
equal(meet(complement(u),complement(meet(v,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[4,2787]),
[iquote('0:SpR:4.0,2787.0')] ).
cnf(3458,plain,
equal(join(meet(u,v),meet(complement(u),v)),v),
inference(spr,[status(thm),theory(equality)],[10,2747]),
[iquote('0:SpR:10.0,2747.0')] ).
cnf(3556,plain,
equal(join(u,meet(complement(meet(complement(u),v)),complement(u))),complement(meet(complement(u),v))),
inference(spr,[status(thm),theory(equality)],[2788,2754]),
[iquote('0:SpR:2788.0,2754.0')] ).
cnf(3563,plain,
equal(join(n0,meet(meet(u,complement(meet(u,v))),complement(v))),meet(u,complement(meet(u,v)))),
inference(spr,[status(thm),theory(equality)],[527,2754]),
[iquote('0:SpR:527.0,2754.0')] ).
cnf(3605,plain,
equal(join(u,meet(complement(u),complement(meet(complement(u),v)))),complement(meet(complement(u),v))),
inference(rew,[status(thm),theory(equality)],[10,3556]),
[iquote('0:Rew:10.0,3556.0')] ).
cnf(3620,plain,
equal(meet(u,complement(meet(u,v))),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[34,3563,2989,10,12]),
[iquote('0:Rew:34.0,3563.0,2989.0,3563.0,10.0,3563.0,12.0,3563.0')] ).
cnf(3622,plain,
equal(join(u,meet(complement(u),complement(v))),complement(meet(complement(u),v))),
inference(rew,[status(thm),theory(equality)],[3620,3605]),
[iquote('0:Rew:3620.0,3605.0')] ).
cnf(4482,plain,
equal(join(u,meet(complement(u),v)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[3458,98]),
[iquote('0:SpR:3458.0,98.0')] ).
cnf(4545,plain,
equal(complement(meet(complement(u),v)),join(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[4482,3622]),
[iquote('0:Rew:4482.0,3622.0')] ).
cnf(4856,plain,
equal(meet(complement(u),v),complement(join(u,complement(v)))),
inference(spr,[status(thm),theory(equality)],[4545,4]),
[iquote('0:SpR:4545.0,4.0')] ).
cnf(4930,plain,
~ equal(complement(join(c,complement(complement(d)))),complement(join(c,d))),
inference(rew,[status(thm),theory(equality)],[4856,5]),
[iquote('0:Rew:4856.0,5.0')] ).
cnf(5126,plain,
~ equal(complement(join(c,d)),complement(join(c,d))),
inference(rew,[status(thm),theory(equality)],[4,4930]),
[iquote('0:Rew:4.0,4930.0')] ).
cnf(5127,plain,
$false,
inference(obv,[status(thm),theory(equality)],[5126]),
[iquote('0:Obv:5126.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : LAT043-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.10 % Command : run_spass %d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Wed Jun 29 01:31:42 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.76/0.94
% 0.76/0.94 SPASS V 3.9
% 0.76/0.94 SPASS beiseite: Proof found.
% 0.76/0.94 % SZS status Theorem
% 0.76/0.94 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.76/0.94 SPASS derived 3419 clauses, backtracked 0 clauses, performed 0 splits and kept 575 clauses.
% 0.76/0.94 SPASS allocated 67744 KBytes.
% 0.76/0.94 SPASS spent 0:00:00.61 on the problem.
% 0.76/0.94 0:00:00.02 for the input.
% 0.76/0.94 0:00:00.00 for the FLOTTER CNF translation.
% 0.76/0.94 0:00:00.02 for inferences.
% 0.76/0.94 0:00:00.00 for the backtracking.
% 0.76/0.94 0:00:00.54 for the reduction.
% 0.76/0.94
% 0.76/0.94
% 0.76/0.94 Here is a proof with depth 4, length 49 :
% 0.76/0.94 % SZS output start Refutation
% See solution above
% 0.76/0.94 Formulae used in the proof : distributivity invertability1 invertability2 invertability3 prove_compatability_law idempotence_of_meet idempotence_of_join absorption2 commutativity_of_meet commutativity_of_join associativity_of_meet associativity_of_join
% 0.76/0.94
%------------------------------------------------------------------------------