TSTP Solution File: LAT040-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT040-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 06:48:44 EDT 2022
% Result : Unsatisfiable 0.13s 0.47s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 40 RR)
% Number of literals : 40 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(meet(join(u,v),join(u,w)),join(u,meet(v,w))),
file('LAT040-1.p',unknown),
[] ).
cnf(2,axiom,
equal(join(meet(u,v),meet(u,w)),meet(u,join(v,w))),
file('LAT040-1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(xx,zz),join(xx,yy)),
file('LAT040-1.p',unknown),
[] ).
cnf(4,axiom,
equal(meet(xx,zz),meet(xx,yy)),
file('LAT040-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(zz,yy),
file('LAT040-1.p',unknown),
[] ).
cnf(7,axiom,
equal(join(u,u),u),
file('LAT040-1.p',unknown),
[] ).
cnf(8,axiom,
equal(meet(u,join(u,v)),u),
file('LAT040-1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(u,meet(u,v)),u),
file('LAT040-1.p',unknown),
[] ).
cnf(10,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT040-1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(u,v),join(v,u)),
file('LAT040-1.p',unknown),
[] ).
cnf(12,axiom,
equal(meet(meet(u,v),w),meet(u,meet(v,w))),
file('LAT040-1.p',unknown),
[] ).
cnf(13,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('LAT040-1.p',unknown),
[] ).
cnf(27,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[11,8]),
[iquote('0:SpR:11.0,8.0')] ).
cnf(35,plain,
equal(join(u,meet(v,u)),u),
inference(spr,[status(thm),theory(equality)],[10,9]),
[iquote('0:SpR:10.0,9.0')] ).
cnf(52,plain,
equal(join(join(xx,yy),u),join(xx,join(zz,u))),
inference(spr,[status(thm),theory(equality)],[3,13]),
[iquote('0:SpR:3.0,13.0')] ).
cnf(55,plain,
equal(join(xx,join(zz,u)),join(xx,join(yy,u))),
inference(rew,[status(thm),theory(equality)],[13,52]),
[iquote('0:Rew:13.0,52.0')] ).
cnf(66,plain,
equal(meet(zz,join(xx,yy)),zz),
inference(spr,[status(thm),theory(equality)],[3,27]),
[iquote('0:SpR:3.0,27.0')] ).
cnf(68,plain,
equal(meet(u,join(v,join(w,u))),u),
inference(spr,[status(thm),theory(equality)],[13,27]),
[iquote('0:SpR:13.0,27.0')] ).
cnf(84,plain,
equal(join(join(xx,yy),zz),join(xx,yy)),
inference(spr,[status(thm),theory(equality)],[66,35]),
[iquote('0:SpR:66.0,35.0')] ).
cnf(89,plain,
equal(join(xx,join(yy,zz)),join(xx,yy)),
inference(rew,[status(thm),theory(equality)],[13,84]),
[iquote('0:Rew:13.0,84.0')] ).
cnf(108,plain,
equal(meet(meet(xx,yy),u),meet(xx,meet(zz,u))),
inference(spr,[status(thm),theory(equality)],[4,12]),
[iquote('0:SpR:4.0,12.0')] ).
cnf(115,plain,
equal(meet(xx,meet(zz,u)),meet(xx,meet(yy,u))),
inference(rew,[status(thm),theory(equality)],[12,108]),
[iquote('0:Rew:12.0,108.0')] ).
cnf(123,plain,
equal(meet(join(yy,zz),join(xx,yy)),join(yy,zz)),
inference(spr,[status(thm),theory(equality)],[89,27]),
[iquote('0:SpR:89.0,27.0')] ).
cnf(124,plain,
equal(meet(join(xx,yy),join(yy,zz)),join(yy,zz)),
inference(rew,[status(thm),theory(equality)],[10,123]),
[iquote('0:Rew:10.0,123.0')] ).
cnf(173,plain,
equal(meet(u,join(v,join(u,w))),u),
inference(spr,[status(thm),theory(equality)],[11,68]),
[iquote('0:SpR:11.0,68.0')] ).
cnf(213,plain,
equal(join(meet(u,v),meet(v,w)),meet(v,join(u,w))),
inference(spr,[status(thm),theory(equality)],[10,2]),
[iquote('0:SpR:10.0,2.0')] ).
cnf(368,plain,
equal(meet(join(u,v),join(v,w)),join(v,meet(u,w))),
inference(spr,[status(thm),theory(equality)],[11,1]),
[iquote('0:SpR:11.0,1.0')] ).
cnf(391,plain,
equal(join(yy,meet(xx,zz)),join(yy,zz)),
inference(rew,[status(thm),theory(equality)],[368,124]),
[iquote('0:Rew:368.0,124.0')] ).
cnf(392,plain,
equal(join(yy,zz),yy),
inference(rew,[status(thm),theory(equality)],[35,391,4]),
[iquote('0:Rew:35.0,391.0,4.0,391.0')] ).
cnf(419,plain,
equal(meet(zz,yy),zz),
inference(spr,[status(thm),theory(equality)],[392,27]),
[iquote('0:SpR:392.0,27.0')] ).
cnf(423,plain,
equal(meet(yy,zz),zz),
inference(rew,[status(thm),theory(equality)],[10,419]),
[iquote('0:Rew:10.0,419.0')] ).
cnf(775,plain,
equal(meet(xx,meet(yy,join(zz,u))),meet(xx,zz)),
inference(spr,[status(thm),theory(equality)],[8,115]),
[iquote('0:SpR:8.0,115.0')] ).
cnf(787,plain,
equal(meet(xx,meet(yy,join(zz,u))),meet(xx,yy)),
inference(rew,[status(thm),theory(equality)],[4,775]),
[iquote('0:Rew:4.0,775.0')] ).
cnf(1292,plain,
equal(join(meet(yy,join(zz,u)),meet(xx,yy)),meet(yy,join(zz,u))),
inference(spr,[status(thm),theory(equality)],[787,35]),
[iquote('0:SpR:787.0,35.0')] ).
cnf(1325,plain,
equal(join(meet(xx,yy),meet(yy,join(zz,u))),meet(yy,join(zz,u))),
inference(rew,[status(thm),theory(equality)],[11,1292]),
[iquote('0:Rew:11.0,1292.0')] ).
cnf(1326,plain,
equal(meet(yy,join(xx,join(zz,u))),meet(yy,join(zz,u))),
inference(rew,[status(thm),theory(equality)],[213,1325]),
[iquote('0:Rew:213.0,1325.0')] ).
cnf(1327,plain,
equal(meet(yy,join(zz,u)),yy),
inference(rew,[status(thm),theory(equality)],[173,1326,55]),
[iquote('0:Rew:173.0,1326.0,55.0,1326.0')] ).
cnf(1350,plain,
equal(meet(yy,zz),yy),
inference(spr,[status(thm),theory(equality)],[7,1327]),
[iquote('0:SpR:7.0,1327.0')] ).
cnf(1363,plain,
equal(zz,yy),
inference(rew,[status(thm),theory(equality)],[423,1350]),
[iquote('0:Rew:423.0,1350.0')] ).
cnf(1364,plain,
$false,
inference(mrr,[status(thm)],[1363,5]),
[iquote('0:MRR:1363.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : LAT040-1 : TPTP v8.1.0. Released v2.4.0.
% 0.00/0.09 % Command : run_spass %d %s
% 0.08/0.28 % Computer : n011.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Wed Jun 29 17:32:47 EDT 2022
% 0.08/0.28 % CPUTime :
% 0.13/0.47
% 0.13/0.47 SPASS V 3.9
% 0.13/0.47 SPASS beiseite: Proof found.
% 0.13/0.47 % SZS status Theorem
% 0.13/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.47 SPASS derived 1023 clauses, backtracked 0 clauses, performed 0 splits and kept 229 clauses.
% 0.13/0.47 SPASS allocated 64304 KBytes.
% 0.13/0.47 SPASS spent 0:00:00.17 on the problem.
% 0.13/0.47 0:00:00.03 for the input.
% 0.13/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.47 0:00:00.01 for inferences.
% 0.13/0.47 0:00:00.00 for the backtracking.
% 0.13/0.47 0:00:00.11 for the reduction.
% 0.13/0.47
% 0.13/0.47
% 0.13/0.47 Here is a proof with depth 5, length 40 :
% 0.13/0.47 % SZS output start Refutation
% See solution above
% 0.13/0.47 Formulae used in the proof : dist_join dist_meet lhs1 lhs2 rhs idempotence_of_join absorption1 absorption2 commutativity_of_meet commutativity_of_join associativity_of_meet associativity_of_join
% 0.13/0.47
%------------------------------------------------------------------------------