TSTP Solution File: GRP034-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP034-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 11:44:54 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 12 ( 7 unt; 0 nHn; 12 RR)
% Number of literals : 21 ( 0 equ; 14 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subgroup_member(a),
file('GRP034-3.p',unknown),
[] ).
cnf(2,axiom,
~ subgroup_member(inverse(a)),
file('GRP034-3.p',unknown),
[] ).
cnf(3,axiom,
product(identity,u,u),
file('GRP034-3.p',unknown),
[] ).
cnf(6,axiom,
product(u,inverse(u),identity),
file('GRP034-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ product(v,inverse(u),w)
| subgroup_member(w) ),
file('GRP034-3.p',unknown),
[] ).
cnf(12,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ product(v,inverse(u),inverse(a)) ),
inference(res,[status(thm),theory(equality)],[11,2]),
[iquote('0:Res:11.3,2.0')] ).
cnf(13,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(identity) ),
inference(res,[status(thm),theory(equality)],[3,12]),
[iquote('0:Res:3.0,12.2')] ).
cnf(14,plain,
~ subgroup_member(identity),
inference(ssi,[status(thm)],[13,1]),
[iquote('0:SSi:13.0,1.0')] ).
cnf(37,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(u)
| subgroup_member(identity) ),
inference(res,[status(thm),theory(equality)],[6,11]),
[iquote('0:Res:6.0,11.2')] ).
cnf(39,plain,
( ~ subgroup_member(u)
| subgroup_member(identity) ),
inference(obv,[status(thm),theory(equality)],[37]),
[iquote('0:Obv:37.0')] ).
cnf(40,plain,
~ subgroup_member(u),
inference(mrr,[status(thm)],[39,14]),
[iquote('0:MRR:39.1,14.0')] ).
cnf(41,plain,
$false,
inference(unc,[status(thm)],[40,1]),
[iquote('0:UnC:40.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP034-3 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.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 01:40:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.41
% 0.20/0.41 SPASS V 3.9
% 0.20/0.41 SPASS beiseite: Proof found.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.41 SPASS derived 26 clauses, backtracked 0 clauses, performed 0 splits and kept 24 clauses.
% 0.20/0.41 SPASS allocated 75611 KBytes.
% 0.20/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.41 0:00:00.03 for the input.
% 0.20/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41 0:00:00.00 for inferences.
% 0.20/0.41 0:00:00.00 for the backtracking.
% 0.20/0.41 0:00:00.00 for the reduction.
% 0.20/0.41
% 0.20/0.41
% 0.20/0.41 Here is a proof with depth 2, length 12 :
% 0.20/0.41 % SZS output start Refutation
% See solution above
% 0.20/0.41 Formulae used in the proof : a_is_in_subgroup prove_a_inverse_is_in_subgroup left_identity right_inverse closure_of_product_and_inverse
% 0.20/0.41
%------------------------------------------------------------------------------