%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP166-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% 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 : 3 ( 1 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(least_upper_bound(b,identity),b),
file('GRP166-3.p',unknown),
[] ).
cnf(3,axiom,
~ equal(least_upper_bound(a,multiply(b,a)),multiply(b,a)),
file('GRP166-3.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(identity,u),u),
file('GRP166-3.p',unknown),
[] ).
cnf(7,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP166-3.p',unknown),
[] ).
cnf(8,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP166-3.p',unknown),
[] ).
cnf(13,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP166-3.p',unknown),
[] ).
cnf(14,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP166-3.p',unknown),
[] ).
cnf(18,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP166-3.p',unknown),
[] ).
cnf(19,plain,
equal(least_upper_bound(identity,b),b),
inference(rew,[status(thm),theory(equality)],[8,2]),
[iquote('0:Rew:8.0,2.0')] ).
cnf(28,plain,
equal(greatest_lower_bound(identity,b),identity),
inference(spr,[status(thm),theory(equality)],[19,14]),
[iquote('0:SpR:19.0,14.0')] ).
cnf(45,plain,
equal(least_upper_bound(u,greatest_lower_bound(v,u)),u),
inference(spr,[status(thm),theory(equality)],[7,13]),
[iquote('0:SpR:7.0,13.0')] ).
cnf(392,plain,
equal(greatest_lower_bound(multiply(identity,u),multiply(b,u)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[28,18]),
[iquote('0:SpR:28.0,18.0')] ).
cnf(401,plain,
equal(greatest_lower_bound(u,multiply(b,u)),u),
inference(rew,[status(thm),theory(equality)],[4,392]),
[iquote('0:Rew:4.0,392.0')] ).
cnf(425,plain,
equal(least_upper_bound(multiply(b,u),u),multiply(b,u)),
inference(spr,[status(thm),theory(equality)],[401,45]),
[iquote('0:SpR:401.0,45.0')] ).
cnf(432,plain,
equal(least_upper_bound(u,multiply(b,u)),multiply(b,u)),
inference(rew,[status(thm),theory(equality)],[8,425]),
[iquote('0:Rew:8.0,425.0')] ).
cnf(433,plain,
$false,
inference(unc,[status(thm)],[432,3]),
[iquote('0:UnC:432.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP166-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 01:49:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 329 clauses, backtracked 0 clauses, performed 0 splits and kept 86 clauses.
% 0.20/0.45 SPASS allocated 63480 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.45 0:00:00.04 for the input.
% 0.20/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.02 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 3, length 16 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : lat3a_2 prove_lat3a left_identity symmetry_of_glb symmetry_of_lub lub_absorbtion glb_absorbtion monotony_glb2
% 0.20/0.45
%------------------------------------------------------------------------------