TSTP Solution File: GRP186-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP186-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 11:46:13 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% 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 : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(multiply(a,least_upper_bound(inverse(a),b)),least_upper_bound(multiply(a,b),identity)),
file('GRP186-3.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(identity,u),u),
file('GRP186-3.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP186-3.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP186-3.p',unknown),
[] ).
cnf(6,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP186-3.p',unknown),
[] ).
cnf(13,axiom,
equal(multiply(u,least_upper_bound(v,w)),least_upper_bound(multiply(u,v),multiply(u,w))),
file('GRP186-3.p',unknown),
[] ).
cnf(17,plain,
~ equal(least_upper_bound(multiply(a,b),multiply(a,inverse(a))),least_upper_bound(identity,multiply(a,b))),
inference(rew,[status(thm),theory(equality)],[13,1,6]),
[iquote('0:Rew:13.0,1.0,6.0,1.0,6.0,1.0')] ).
cnf(267,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(268,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[2,267]),
[iquote('0:Rew:2.0,267.0')] ).
cnf(271,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[268]),
[iquote('0:SpR:268.0,268.0')] ).
cnf(291,plain,
equal(multiply(u,inverse(u)),identity),
inference(spr,[status(thm),theory(equality)],[271,3]),
[iquote('0:SpR:271.0,3.0')] ).
cnf(298,plain,
~ equal(least_upper_bound(multiply(a,b),identity),least_upper_bound(identity,multiply(a,b))),
inference(rew,[status(thm),theory(equality)],[291,17]),
[iquote('0:Rew:291.0,17.0')] ).
cnf(303,plain,
~ equal(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,multiply(a,b))),
inference(rew,[status(thm),theory(equality)],[6,298]),
[iquote('0:Rew:6.0,298.0')] ).
cnf(304,plain,
$false,
inference(obv,[status(thm),theory(equality)],[303]),
[iquote('0:Obv:303.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP186-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 04:13:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.43
% 0.20/0.43 SPASS V 3.9
% 0.20/0.43 SPASS beiseite: Proof found.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.43 SPASS derived 228 clauses, backtracked 0 clauses, performed 0 splits and kept 72 clauses.
% 0.20/0.43 SPASS allocated 63363 KBytes.
% 0.20/0.43 SPASS spent 0:00:00.07 on the problem.
% 0.20/0.43 0:00:00.03 for the input.
% 0.20/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43 0:00:00.00 for inferences.
% 0.20/0.43 0:00:00.00 for the backtracking.
% 0.20/0.43 0:00:00.01 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 3, length 14 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : prove_p23x left_identity left_inverse associativity symmetry_of_lub monotony_lub1
% 0.20/0.43
%------------------------------------------------------------------------------