TSTP Solution File: GRP192-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP192-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 11:46:16 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 16 RR)
% Number of literals : 16 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(least_upper_bound(identity,u),u),
file('GRP192-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP192-1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(identity,u),u),
file('GRP192-1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP192-1.p',unknown),
[] ).
cnf(6,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP192-1.p',unknown),
[] ).
cnf(13,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP192-1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP192-1.p',unknown),
[] ).
cnf(25,plain,
equal(greatest_lower_bound(identity,u),identity),
inference(spr,[status(thm),theory(equality)],[1,13]),
[iquote('0:SpR:1.0,13.0')] ).
cnf(49,plain,
equal(greatest_lower_bound(u,identity),identity),
inference(spr,[status(thm),theory(equality)],[6,25]),
[iquote('0:SpR:6.0,25.0')] ).
cnf(381,plain,
equal(greatest_lower_bound(multiply(u,v),multiply(identity,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[49,17]),
[iquote('0:SpR:49.0,17.0')] ).
cnf(388,plain,
equal(greatest_lower_bound(u,multiply(v,u)),u),
inference(rew,[status(thm),theory(equality)],[6,381,3]),
[iquote('0:Rew:6.0,381.0,3.0,381.0')] ).
cnf(426,plain,
equal(greatest_lower_bound(u,identity),u),
inference(spr,[status(thm),theory(equality)],[4,388]),
[iquote('0:SpR:4.0,388.0')] ).
cnf(432,plain,
equal(identity,u),
inference(rew,[status(thm),theory(equality)],[49,426]),
[iquote('0:Rew:49.0,426.0')] ).
cnf(433,plain,
~ equal(multiply(b,identity),multiply(identity,b)),
inference(rew,[status(thm),theory(equality)],[432,2]),
[iquote('0:Rew:432.0,2.0')] ).
cnf(530,plain,
~ equal(identity,identity),
inference(rew,[status(thm),theory(equality)],[432,433]),
[iquote('0:Rew:432.0,433.0,432.0,433.0')] ).
cnf(531,plain,
$false,
inference(obv,[status(thm),theory(equality)],[530]),
[iquote('0:Obv:530.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP192-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n021.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 : Tue Jun 14 06:30:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 395 clauses, backtracked 0 clauses, performed 0 splits and kept 77 clauses.
% 0.20/0.44 SPASS allocated 63502 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.44 0:00:00.04 for the input.
% 0.20/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.00 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.02 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 4, length 16 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.44 Formulae used in the proof : p40a_1 prove_p40a left_identity left_inverse symmetry_of_glb glb_absorbtion monotony_glb2
% 0.20/0.44
%------------------------------------------------------------------------------