TSTP Solution File: GRP190-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP190-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 11:46:15 EDT 2022
% Result : Unsatisfiable 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 21 RR)
% Number of literals : 21 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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(1,axiom,
equal(least_upper_bound(a,b),a),
file('GRP190-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(least_upper_bound(inverse(a),inverse(b)),inverse(b)),
file('GRP190-1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(identity,u),u),
file('GRP190-1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP190-1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP190-1.p',unknown),
[] ).
cnf(7,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP190-1.p',unknown),
[] ).
cnf(14,axiom,
equal(multiply(u,least_upper_bound(v,w)),least_upper_bound(multiply(u,v),multiply(u,w))),
file('GRP190-1.p',unknown),
[] ).
cnf(16,axiom,
equal(multiply(least_upper_bound(u,v),w),least_upper_bound(multiply(u,w),multiply(v,w))),
file('GRP190-1.p',unknown),
[] ).
cnf(247,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[4,5]),
[iquote('0:SpR:4.0,5.0')] ).
cnf(248,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[3,247]),
[iquote('0:Rew:3.0,247.0')] ).
cnf(251,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[248]),
[iquote('0:SpR:248.0,248.0')] ).
cnf(254,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[4,248]),
[iquote('0:SpR:4.0,248.0')] ).
cnf(256,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[251,254]),
[iquote('0:Rew:251.0,254.0')] ).
cnf(271,plain,
equal(multiply(u,inverse(u)),identity),
inference(spr,[status(thm),theory(equality)],[251,4]),
[iquote('0:SpR:251.0,4.0')] ).
cnf(758,plain,
equal(least_upper_bound(multiply(u,a),multiply(u,b)),multiply(u,a)),
inference(spr,[status(thm),theory(equality)],[1,14]),
[iquote('0:SpR:1.0,14.0')] ).
cnf(1160,plain,
equal(least_upper_bound(identity,multiply(inverse(a),b)),identity),
inference(spr,[status(thm),theory(equality)],[4,758]),
[iquote('0:SpR:4.0,758.0')] ).
cnf(1179,plain,
equal(least_upper_bound(multiply(identity,u),multiply(multiply(inverse(a),b),u)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[1160,16]),
[iquote('0:SpR:1160.0,16.0')] ).
cnf(1189,plain,
equal(least_upper_bound(u,multiply(inverse(a),multiply(b,u))),u),
inference(rew,[status(thm),theory(equality)],[5,1179,3]),
[iquote('0:Rew:5.0,1179.0,3.0,1179.0')] ).
cnf(1207,plain,
equal(least_upper_bound(inverse(b),multiply(inverse(a),identity)),inverse(b)),
inference(spr,[status(thm),theory(equality)],[271,1189]),
[iquote('0:SpR:271.0,1189.0')] ).
cnf(1213,plain,
equal(least_upper_bound(inverse(a),inverse(b)),inverse(b)),
inference(rew,[status(thm),theory(equality)],[7,1207,256]),
[iquote('0:Rew:7.0,1207.0,256.0,1207.0')] ).
cnf(1214,plain,
$false,
inference(mrr,[status(thm)],[1213,2]),
[iquote('0:MRR:1213.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP190-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n019.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 : Mon Jun 13 13:00:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.53
% 0.19/0.53 SPASS V 3.9
% 0.19/0.53 SPASS beiseite: Proof found.
% 0.19/0.53 % SZS status Theorem
% 0.19/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.53 SPASS derived 856 clauses, backtracked 0 clauses, performed 0 splits and kept 225 clauses.
% 0.19/0.53 SPASS allocated 64467 KBytes.
% 0.19/0.53 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.53 0:00:00.04 for the input.
% 0.19/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.53 0:00:00.01 for inferences.
% 0.19/0.53 0:00:00.00 for the backtracking.
% 0.19/0.53 0:00:00.09 for the reduction.
% 0.19/0.53
% 0.19/0.53
% 0.19/0.53 Here is a proof with depth 4, length 21 :
% 0.19/0.53 % SZS output start Refutation
% See solution above
% 0.19/0.53 Formulae used in the proof : p39a_1 prove_p39a left_identity left_inverse associativity symmetry_of_lub monotony_lub1 monotony_lub2
% 0.19/0.53
%------------------------------------------------------------------------------