TSTP Solution File: GRP174-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP174-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:46:06 EDT 2022
% Result : Unsatisfiable 0.21s 0.45s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 15 RR)
% Number of literals : 15 ( 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; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(greatest_lower_bound(identity,a),a),
file('GRP174-1.p',unknown),
[] ).
cnf(2,axiom,
equal(greatest_lower_bound(identity,inverse(a)),inverse(a)),
file('GRP174-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(a,identity),
file('GRP174-1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(identity,u),u),
file('GRP174-1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP174-1.p',unknown),
[] ).
cnf(8,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP174-1.p',unknown),
[] ).
cnf(13,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP174-1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(least_upper_bound(u,v),w),least_upper_bound(multiply(u,w),multiply(v,w))),
file('GRP174-1.p',unknown),
[] ).
cnf(29,plain,
equal(least_upper_bound(identity,a),identity),
inference(spr,[status(thm),theory(equality)],[1,13]),
[iquote('0:SpR:1.0,13.0')] ).
cnf(30,plain,
equal(least_upper_bound(identity,inverse(a)),identity),
inference(spr,[status(thm),theory(equality)],[2,13]),
[iquote('0:SpR:2.0,13.0')] ).
cnf(327,plain,
equal(least_upper_bound(multiply(identity,u),multiply(inverse(a),u)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[30,17]),
[iquote('0:SpR:30.0,17.0')] ).
cnf(338,plain,
equal(least_upper_bound(u,multiply(inverse(a),u)),u),
inference(rew,[status(thm),theory(equality)],[4,327]),
[iquote('0:Rew:4.0,327.0')] ).
cnf(361,plain,
equal(least_upper_bound(a,identity),a),
inference(spr,[status(thm),theory(equality)],[5,338]),
[iquote('0:SpR:5.0,338.0')] ).
cnf(364,plain,
equal(a,identity),
inference(rew,[status(thm),theory(equality)],[29,361,8]),
[iquote('0:Rew:29.0,361.0,8.0,361.0')] ).
cnf(365,plain,
$false,
inference(mrr,[status(thm)],[364,3]),
[iquote('0:MRR:364.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP174-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 08:16:25 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.45
% 0.21/0.45 SPASS V 3.9
% 0.21/0.45 SPASS beiseite: Proof found.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.45 SPASS derived 291 clauses, backtracked 0 clauses, performed 0 splits and kept 100 clauses.
% 0.21/0.45 SPASS allocated 63504 KBytes.
% 0.21/0.45 SPASS spent 0:00:00.08 on the problem.
% 0.21/0.45 0:00:00.03 for the input.
% 0.21/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.45 0:00:00.00 for inferences.
% 0.21/0.45 0:00:00.00 for the backtracking.
% 0.21/0.45 0:00:00.02 for the reduction.
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 Here is a proof with depth 3, length 15 :
% 0.21/0.45 % SZS output start Refutation
% See solution above
% 0.21/0.45 Formulae used in the proof : p05b_1 p05b_2 prove_p05b left_identity left_inverse symmetry_of_lub lub_absorbtion monotony_lub2
% 0.21/0.45
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