%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP185-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 : Sat Jul 16 11:46:12 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 14 RR)
% Number of literals : 14 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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(least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
file('GRP185-1.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(identity,u),u),
file('GRP185-1.p',unknown),
[] ).
cnf(6,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP185-1.p',unknown),
[] ).
cnf(8,axiom,
equal(least_upper_bound(least_upper_bound(u,v),w),least_upper_bound(u,least_upper_bound(v,w))),
file('GRP185-1.p',unknown),
[] ).
cnf(9,axiom,
equal(least_upper_bound(u,u),u),
file('GRP185-1.p',unknown),
[] ).
cnf(13,axiom,
equal(multiply(u,least_upper_bound(v,w)),least_upper_bound(multiply(u,v),multiply(u,w))),
file('GRP185-1.p',unknown),
[] ).
cnf(15,axiom,
equal(multiply(least_upper_bound(u,v),w),least_upper_bound(multiply(u,w),multiply(v,w))),
file('GRP185-1.p',unknown),
[] ).
cnf(17,plain,
~ equal(least_upper_bound(identity,least_upper_bound(multiply(a,b),least_upper_bound(b,least_upper_bound(multiply(a,b),least_upper_bound(identity,multiply(a,identity)))))),least_upper_bound(b,least_upper_bound(multiply(a,b),least_upper_bound(identity,multiply(a,identity))))),
inference(rew,[status(thm),theory(equality)],[8,1,6,2,15,13]),
[iquote('0:Rew:8.0,1.0,6.0,1.0,8.0,1.0,6.0,1.0,2.0,1.0,15.0,1.0,6.0,1.0,2.0,1.0,15.0,1.0,13.0,1.0')] ).
cnf(60,plain,
equal(least_upper_bound(u,least_upper_bound(u,v)),least_upper_bound(u,v)),
inference(spr,[status(thm),theory(equality)],[9,8]),
[iquote('0:SpR:9.0,8.0')] ).
cnf(61,plain,
equal(least_upper_bound(least_upper_bound(u,v),w),least_upper_bound(v,least_upper_bound(u,w))),
inference(spr,[status(thm),theory(equality)],[6,8]),
[iquote('0:SpR:6.0,8.0')] ).
cnf(64,plain,
equal(least_upper_bound(u,least_upper_bound(v,w)),least_upper_bound(v,least_upper_bound(u,w))),
inference(rew,[status(thm),theory(equality)],[8,61]),
[iquote('0:Rew:8.0,61.0')] ).
cnf(65,plain,
~ equal(least_upper_bound(identity,least_upper_bound(b,least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,b),least_upper_bound(identity,multiply(a,identity)))))),least_upper_bound(b,least_upper_bound(multiply(a,b),least_upper_bound(identity,multiply(a,identity))))),
inference(rew,[status(thm),theory(equality)],[64,17]),
[iquote('0:Rew:64.0,17.0')] ).
cnf(68,plain,
~ equal(least_upper_bound(b,least_upper_bound(identity,least_upper_bound(multiply(a,b),multiply(a,identity)))),least_upper_bound(b,least_upper_bound(identity,least_upper_bound(multiply(a,b),multiply(a,identity))))),
inference(rew,[status(thm),theory(equality)],[60,65,64]),
[iquote('0:Rew:60.0,65.0,64.0,65.0,60.0,65.0,64.0,65.0,64.0,65.0')] ).
cnf(69,plain,
$false,
inference(obv,[status(thm),theory(equality)],[68]),
[iquote('0:Obv:68.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP185-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n012.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 14 08:15:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.42
% 0.20/0.42 SPASS V 3.9
% 0.20/0.42 SPASS beiseite: Proof found.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.42 SPASS derived 46 clauses, backtracked 0 clauses, performed 0 splits and kept 28 clauses.
% 0.20/0.42 SPASS allocated 63162 KBytes.
% 0.20/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.42 0:00:00.04 for the input.
% 0.20/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42 0:00:00.00 for inferences.
% 0.20/0.42 0:00:00.00 for the backtracking.
% 0.20/0.42 0:00:00.00 for the reduction.
% 0.20/0.42
% 0.20/0.42
% 0.20/0.42 Here is a proof with depth 1, length 14 :
% 0.20/0.42 % SZS output start Refutation
% See solution above
% 0.20/0.42 Formulae used in the proof : prove_p22a left_identity symmetry_of_lub associativity_of_lub idempotence_of_lub monotony_lub1 monotony_lub2
% 0.20/0.42
%------------------------------------------------------------------------------