%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP034-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 0.19s 0.41s
% Output : Refutation 0.19s
% 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(2,axiom,
product(identity,u,u),
file('GRP034-4.p',unknown),
[] ).
cnf(4,axiom,
product(u,inverse(u),identity),
file('GRP034-4.p',unknown),
[] ).
cnf(7,axiom,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ product(u,inverse(v),w)
| subgroup_member(w) ),
file('GRP034-4.p',unknown),
[] ).
cnf(8,axiom,
subgroup_member(a),
file('GRP034-4.p',unknown),
[] ).
cnf(9,axiom,
~ subgroup_member(inverse(a)),
file('GRP034-4.p',unknown),
[] ).
cnf(10,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ product(u,inverse(v),inverse(a)) ),
inference(res,[status(thm),theory(equality)],[7,9]),
[iquote('0:Res:7.3,9.0')] ).
cnf(13,plain,
( ~ subgroup_member(identity)
| ~ subgroup_member(a) ),
inference(res,[status(thm),theory(equality)],[2,10]),
[iquote('0:Res:2.0,10.2')] ).
cnf(14,plain,
~ subgroup_member(identity),
inference(ssi,[status(thm)],[13,8]),
[iquote('0:SSi:13.1,8.0')] ).
cnf(16,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(u)
| subgroup_member(identity) ),
inference(res,[status(thm),theory(equality)],[4,7]),
[iquote('0:Res:4.0,7.2')] ).
cnf(18,plain,
( ~ subgroup_member(u)
| subgroup_member(identity) ),
inference(obv,[status(thm),theory(equality)],[16]),
[iquote('0:Obv:16.0')] ).
cnf(19,plain,
~ subgroup_member(u),
inference(mrr,[status(thm)],[18,14]),
[iquote('0:MRR:18.1,14.0')] ).
cnf(20,plain,
$false,
inference(unc,[status(thm)],[19,8]),
[iquote('0:UnC:19.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP034-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n007.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 10:07:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.41
% 0.19/0.41 SPASS V 3.9
% 0.19/0.41 SPASS beiseite: Proof found.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 5 clauses, backtracked 0 clauses, performed 0 splits and kept 13 clauses.
% 0.19/0.41 SPASS allocated 75591 KBytes.
% 0.19/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.41 0:00:00.03 for the input.
% 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41 0:00:00.00 for inferences.
% 0.19/0.41 0:00:00.00 for the backtracking.
% 0.19/0.41 0:00:00.00 for the reduction.
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 Here is a proof with depth 2, length 12 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : left_identity right_inverse closure_of_subgroup a_is_in_subgroup prove_inverse_is_in_subgroup
% 0.19/0.41
%------------------------------------------------------------------------------