TSTP Solution File: LAT042-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT042-1 : TPTP v8.1.0. Released v2.5.0.
% 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 06:48:45 EDT 2022
% Result : Unsatisfiable 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 11 RR)
% Number of literals : 11 ( 0 equ; 4 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('LAT042-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(meet(join(a,b),join(a,c)),join(a,meet(b,join(a,c)))),
file('LAT042-1.p',unknown),
[] ).
cnf(6,axiom,
equal(meet(u,u),u),
file('LAT042-1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(u,meet(u,v)),u),
file('LAT042-1.p',unknown),
[] ).
cnf(10,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT042-1.p',unknown),
[] ).
cnf(13,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('LAT042-1.p',unknown),
[] ).
cnf(18,plain,
~ equal(join(a,join(meet(a,c),meet(b,c))),join(a,join(meet(a,b),meet(b,c)))),
inference(rew,[status(thm),theory(equality)],[9,5,6,1,10]),
[iquote('0:Rew:9.0,5.0,6.0,5.0,1.0,5.0,10.0,5.0,10.0,5.0,10.0,5.0,1.0,5.0,10.0,5.0,1.0,5.0,10.0,5.0,1.0,5.0')] ).
cnf(83,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(90,plain,
~ equal(join(a,join(meet(a,b),meet(b,c))),join(a,meet(b,c))),
inference(rew,[status(thm),theory(equality)],[83,18]),
[iquote('0:Rew:83.0,18.0')] ).
cnf(94,plain,
~ equal(join(a,meet(b,c)),join(a,meet(b,c))),
inference(rew,[status(thm),theory(equality)],[83,90]),
[iquote('0:Rew:83.0,90.0')] ).
cnf(95,plain,
$false,
inference(obv,[status(thm),theory(equality)],[94]),
[iquote('0:Obv:94.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LAT042-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 28 19:04:52 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.43
% 0.21/0.43 SPASS V 3.9
% 0.21/0.43 SPASS beiseite: Proof found.
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.43 SPASS derived 71 clauses, backtracked 0 clauses, performed 0 splits and kept 32 clauses.
% 0.21/0.43 SPASS allocated 63166 KBytes.
% 0.21/0.43 SPASS spent 0:00:00.07 on the problem.
% 0.21/0.43 0:00:00.04 for the input.
% 0.21/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.43 0:00:00.00 for inferences.
% 0.21/0.43 0:00:00.00 for the backtracking.
% 0.21/0.43 0:00:00.00 for the reduction.
% 0.21/0.43
% 0.21/0.43
% 0.21/0.43 Here is a proof with depth 1, length 11 :
% 0.21/0.43 % SZS output start Refutation
% See solution above
% 0.21/0.43 Formulae used in the proof : distributivity prove_modular_law idempotence_of_meet absorption2 commutativity_of_meet associativity_of_join
% 0.21/0.43
%------------------------------------------------------------------------------