TSTP Solution File: GRP165-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP165-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 11:46:00 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 17 RR)
% Number of literals : 17 ( 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(least_upper_bound(a,identity),a),
file('GRP165-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(least_upper_bound(a,multiply(a,a)),multiply(a,a)),
file('GRP165-1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(identity,u),u),
file('GRP165-1.p',unknown),
[] ).
cnf(6,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP165-1.p',unknown),
[] ).
cnf(7,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP165-1.p',unknown),
[] ).
cnf(12,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP165-1.p',unknown),
[] ).
cnf(13,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP165-1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP165-1.p',unknown),
[] ).
cnf(31,plain,
equal(greatest_lower_bound(u,least_upper_bound(v,u)),u),
inference(spr,[status(thm),theory(equality)],[7,13]),
[iquote('0:SpR:7.0,13.0')] ).
cnf(39,plain,
equal(least_upper_bound(u,greatest_lower_bound(v,u)),u),
inference(spr,[status(thm),theory(equality)],[6,12]),
[iquote('0:SpR:6.0,12.0')] ).
cnf(49,plain,
equal(greatest_lower_bound(identity,a),identity),
inference(spr,[status(thm),theory(equality)],[1,31]),
[iquote('0:SpR:1.0,31.0')] ).
cnf(54,plain,
equal(greatest_lower_bound(a,identity),identity),
inference(rew,[status(thm),theory(equality)],[6,49]),
[iquote('0:Rew:6.0,49.0')] ).
cnf(294,plain,
equal(greatest_lower_bound(multiply(a,u),multiply(identity,u)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[54,17]),
[iquote('0:SpR:54.0,17.0')] ).
cnf(299,plain,
equal(greatest_lower_bound(u,multiply(a,u)),u),
inference(rew,[status(thm),theory(equality)],[6,294,3]),
[iquote('0:Rew:6.0,294.0,3.0,294.0')] ).
cnf(331,plain,
equal(least_upper_bound(multiply(a,u),u),multiply(a,u)),
inference(spr,[status(thm),theory(equality)],[299,39]),
[iquote('0:SpR:299.0,39.0')] ).
cnf(340,plain,
equal(least_upper_bound(u,multiply(a,u)),multiply(a,u)),
inference(rew,[status(thm),theory(equality)],[7,331]),
[iquote('0:Rew:7.0,331.0')] ).
cnf(341,plain,
$false,
inference(unc,[status(thm)],[340,2]),
[iquote('0:UnC:340.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP165-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n009.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 02:34:23 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 261 clauses, backtracked 0 clauses, performed 0 splits and kept 80 clauses.
% 0.20/0.43 SPASS allocated 63419 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 0:00:00.02 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 4, length 17 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : lat1a_1 prove_lat1a left_identity symmetry_of_glb symmetry_of_lub lub_absorbtion glb_absorbtion monotony_glb2
% 0.20/0.43
%------------------------------------------------------------------------------