TSTP Solution File: GRP172-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP172-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 11:46:05 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 18 RR)
% Number of literals : 18 ( 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(1,axiom,
equal(greatest_lower_bound(identity,a),identity),
file('GRP172-2.p',unknown),
[] ).
cnf(2,axiom,
equal(greatest_lower_bound(identity,b),identity),
file('GRP172-2.p',unknown),
[] ).
cnf(3,axiom,
~ equal(least_upper_bound(identity,multiply(a,b)),multiply(a,b)),
file('GRP172-2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(identity,u),u),
file('GRP172-2.p',unknown),
[] ).
cnf(7,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP172-2.p',unknown),
[] ).
cnf(8,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP172-2.p',unknown),
[] ).
cnf(9,axiom,
equal(greatest_lower_bound(greatest_lower_bound(u,v),w),greatest_lower_bound(u,greatest_lower_bound(v,w))),
file('GRP172-2.p',unknown),
[] ).
cnf(13,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP172-2.p',unknown),
[] ).
cnf(18,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP172-2.p',unknown),
[] ).
cnf(42,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(241,plain,
equal(greatest_lower_bound(identity,greatest_lower_bound(b,u)),greatest_lower_bound(identity,u)),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(386,plain,
equal(greatest_lower_bound(multiply(identity,u),multiply(a,u)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[1,18]),
[iquote('0:SpR:1.0,18.0')] ).
cnf(402,plain,
equal(greatest_lower_bound(u,multiply(a,u)),u),
inference(rew,[status(thm),theory(equality)],[4,386]),
[iquote('0:Rew:4.0,386.0')] ).
cnf(463,plain,
equal(greatest_lower_bound(identity,multiply(a,b)),greatest_lower_bound(identity,b)),
inference(spr,[status(thm),theory(equality)],[402,241]),
[iquote('0:SpR:402.0,241.0')] ).
cnf(469,plain,
equal(greatest_lower_bound(identity,multiply(a,b)),identity),
inference(rew,[status(thm),theory(equality)],[2,463]),
[iquote('0:Rew:2.0,463.0')] ).
cnf(524,plain,
equal(least_upper_bound(multiply(a,b),identity),multiply(a,b)),
inference(spr,[status(thm),theory(equality)],[469,42]),
[iquote('0:SpR:469.0,42.0')] ).
cnf(527,plain,
equal(least_upper_bound(identity,multiply(a,b)),multiply(a,b)),
inference(rew,[status(thm),theory(equality)],[8,524]),
[iquote('0:Rew:8.0,524.0')] ).
cnf(528,plain,
$false,
inference(mrr,[status(thm)],[527,3]),
[iquote('0:MRR:527.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP172-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.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 19:31:50 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 390 clauses, backtracked 0 clauses, performed 0 splits and kept 105 clauses.
% 0.20/0.44 SPASS allocated 63572 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.44 0:00:00.03 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 0:00:00.03 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 3, length 18 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.44 Formulae used in the proof : p04d_1 p04d_2 prove_p04d left_identity symmetry_of_glb symmetry_of_lub associativity_of_glb lub_absorbtion monotony_glb2
% 0.20/0.44
%------------------------------------------------------------------------------