TSTP Solution File: LAT031-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT031-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 06:48:41 EDT 2022
% Result : Unsatisfiable 0.18s 0.41s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 9 ( 9 unt; 0 nHn; 9 RR)
% Number of literals : 9 ( 0 equ; 2 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(u,join(v,w)),join(meet(u,v),meet(u,w))),
file('LAT031-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(meet(join(xx,yy),join(xx,zz)),join(xx,meet(yy,zz))),
file('LAT031-1.p',unknown),
[] ).
cnf(3,axiom,
equal(meet(u,u),u),
file('LAT031-1.p',unknown),
[] ).
cnf(6,axiom,
equal(join(u,meet(u,v)),u),
file('LAT031-1.p',unknown),
[] ).
cnf(7,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT031-1.p',unknown),
[] ).
cnf(10,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('LAT031-1.p',unknown),
[] ).
cnf(13,plain,
~ equal(join(xx,join(meet(xx,zz),meet(yy,zz))),join(xx,meet(yy,zz))),
inference(rew,[status(thm),theory(equality)],[6,2,3,1,7]),
[iquote('0:Rew:6.0,2.0,3.0,2.0,1.0,2.0,7.0,2.0,7.0,2.0,7.0,2.0,1.0,2.0,7.0,2.0,1.0,2.0')] ).
cnf(45,plain,
equal(join(u,join(meet(u,v),w)),join(u,w)),
inference(spr,[status(thm),theory(equality)],[6,10]),
[iquote('0:SpR:6.0,10.0')] ).
cnf(49,plain,
$false,
inference(unc,[status(thm)],[45,13]),
[iquote('0:UnC:45.0,13.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT031-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jun 29 01:03:06 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.41
% 0.18/0.41 SPASS V 3.9
% 0.18/0.41 SPASS beiseite: Proof found.
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.41 SPASS derived 36 clauses, backtracked 0 clauses, performed 0 splits and kept 19 clauses.
% 0.18/0.41 SPASS allocated 63138 KBytes.
% 0.18/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.18/0.41 0:00:00.04 for the input.
% 0.18/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41 0:00:00.00 for inferences.
% 0.18/0.41 0:00:00.00 for the backtracking.
% 0.18/0.41 0:00:00.00 for the reduction.
% 0.18/0.41
% 0.18/0.41
% 0.18/0.41 Here is a proof with depth 1, length 9 :
% 0.18/0.41 % SZS output start Refutation
% See solution above
% 0.18/0.41 Formulae used in the proof : dist_meet dist_join idempotence_of_meet absorption2 commutativity_of_meet associativity_of_join
% 0.18/0.41
%------------------------------------------------------------------------------