%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP166-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 11:46:01 EDT 2022
% Result : Unsatisfiable 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 16 RR)
% Number of literals : 16 ( 0 equ; 1 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(2,axiom,
equal(greatest_lower_bound(b,identity),identity),
file('GRP166-2.p',unknown),
[] ).
cnf(3,axiom,
~ equal(greatest_lower_bound(a,multiply(a,b)),a),
file('GRP166-2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(identity,u),u),
file('GRP166-2.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP166-2.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP166-2.p',unknown),
[] ).
cnf(7,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP166-2.p',unknown),
[] ).
cnf(16,axiom,
equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
file('GRP166-2.p',unknown),
[] ).
cnf(19,plain,
equal(greatest_lower_bound(identity,b),identity),
inference(rew,[status(thm),theory(equality)],[7,2]),
[iquote('0:Rew:7.0,2.0')] ).
cnf(344,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[5,6]),
[iquote('0:SpR:5.0,6.0')] ).
cnf(345,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[4,344]),
[iquote('0:Rew:4.0,344.0')] ).
cnf(348,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[345]),
[iquote('0:SpR:345.0,345.0')] ).
cnf(351,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[5,345]),
[iquote('0:SpR:5.0,345.0')] ).
cnf(353,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[348,351]),
[iquote('0:Rew:348.0,351.0')] ).
cnf(610,plain,
equal(greatest_lower_bound(multiply(u,identity),multiply(u,b)),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[19,16]),
[iquote('0:SpR:19.0,16.0')] ).
cnf(628,plain,
equal(greatest_lower_bound(u,multiply(u,b)),u),
inference(rew,[status(thm),theory(equality)],[353,610]),
[iquote('0:Rew:353.0,610.0')] ).
cnf(629,plain,
$false,
inference(unc,[status(thm)],[628,3]),
[iquote('0:UnC:628.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP166-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.14 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n018.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jun 13 19:23:43 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.21/0.47
% 0.21/0.47 SPASS V 3.9
% 0.21/0.47 SPASS beiseite: Proof found.
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.47 SPASS derived 471 clauses, backtracked 0 clauses, performed 0 splits and kept 125 clauses.
% 0.21/0.47 SPASS allocated 63732 KBytes.
% 0.21/0.47 SPASS spent 0:00:00.10 on the problem.
% 0.21/0.47 0:00:00.04 for the input.
% 0.21/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.47 0:00:00.01 for inferences.
% 0.21/0.47 0:00:00.00 for the backtracking.
% 0.21/0.47 0:00:00.04 for the reduction.
% 0.21/0.47
% 0.21/0.47
% 0.21/0.47 Here is a proof with depth 2, length 16 :
% 0.21/0.47 % SZS output start Refutation
% See solution above
% 0.21/0.47 Formulae used in the proof : lat2b_2 prove_lat2b left_identity left_inverse associativity symmetry_of_glb monotony_glb1
% 0.21/0.47
%------------------------------------------------------------------------------