%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP034-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:26:20 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.46s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 16 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : product(identity,VAR_0,VAR_0),
file('theBenchmark.p',left_identity) ).
cnf(c_2,plain,
product(identity,A,A),
inference(clausify,[status(thm)],[left_identity]) ).
fof(right_inverse,axiom,
! [VAR_0] : product(VAR_0,inverse(VAR_0),identity),
file('theBenchmark.p',right_inverse) ).
cnf(c_4,plain,
product(A,inverse(A),identity),
inference(clausify,[status(thm)],[right_inverse]) ).
fof(closure_of_subgroup,axiom,
! [VAR_0,VAR_1,VAR_2] :
( subgroup_member(VAR_2)
| ~ product(VAR_1,inverse(VAR_0),VAR_2)
| ~ subgroup_member(VAR_1)
| ~ subgroup_member(VAR_0) ),
file('theBenchmark.p',closure_of_subgroup) ).
cnf(c_7,plain,
( subgroup_member(C)
| ~ product(B,inverse(A),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(clausify,[status(thm)],[closure_of_subgroup]) ).
fof(a_is_in_subgroup,axiom,
subgroup_member(a),
file('theBenchmark.p',a_is_in_subgroup) ).
cnf(c_8,plain,
subgroup_member(a),
inference(clausify,[status(thm)],[a_is_in_subgroup]) ).
fof(prove_inverse_is_in_subgroup,axiom,
~ subgroup_member(inverse(a)),
file('theBenchmark.p',prove_inverse_is_in_subgroup) ).
cnf(c_9,plain,
~ subgroup_member(inverse(a)),
inference(clausify,[status(thm)],[prove_inverse_is_in_subgroup]) ).
cnf(c_132,plain,
( subgroup_member(B)
| ~ product(A,inverse(a),B)
| ~ subgroup_member(A) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_133,plain,
( subgroup_member(A)
| ~ product(a,inverse(a),A) ),
inference(resolve,[status(thm)],[c_132,c_8]) ).
cnf(c_96,plain,
subgroup_member(identity),
inference(resolve,[status(thm)],[c_133,c_4]) ).
cnf(c_134,plain,
( subgroup_member(B)
| ~ product(A,inverse(a),B)
| ~ subgroup_member(A) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_135,plain,
( subgroup_member(A)
| ~ product(identity,inverse(a),A) ),
inference(resolve,[status(thm)],[c_134,c_96]) ).
cnf(c_136,plain,
subgroup_member(inverse(a)),
inference(resolve,[status(thm)],[c_135,c_2]) ).
cnf(c_131,plain,
$false,
inference(resolve,[status(thm)],[c_9,c_136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP034-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n011.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 14:19:13 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 2196330 was started by sandbox on n011,
% 0.18/0.44 % Fri Sep 25 14:19:13 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.46
% 0.18/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.46
% 0.18/0.46 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.18/0.46 % Length of proof is 7.
% 0.18/0.46 % Level of proof is 2.
% 0.18/0.46 % Maximum clause weight is 21.000.
% 0.18/0.46 % Given clauses 20.
% 0.18/0.46
% 0.18/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------