%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP033-3 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 18 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 17 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : product(identity,VAR_0,VAR_0),
file('theBenchmark.p',left_identity) ).
cnf(c_11,plain,
product(identity,A,A),
inference(clausify,[status(thm)],[left_identity]) ).
fof(right_identity,axiom,
! [VAR_0] : product(VAR_0,identity,VAR_0),
file('theBenchmark.p',right_identity) ).
cnf(c_12,plain,
product(A,identity,A),
inference(clausify,[status(thm)],[right_identity]) ).
fof(right_inverse,axiom,
! [VAR_0] : product(VAR_0,inverse(VAR_0),identity),
file('theBenchmark.p',right_inverse) ).
cnf(c_14,plain,
product(A,inverse(A),identity),
inference(clausify,[status(thm)],[right_inverse]) ).
fof(closure_of_product_and_inverse,axiom,
! [VAR_0,VAR_1,VAR_2] :
( subgroup_member(VAR_2)
| ~ product(VAR_0,inverse(VAR_1),VAR_2)
| ~ subgroup_member(VAR_1)
| ~ subgroup_member(VAR_0) ),
file('theBenchmark.p',closure_of_product_and_inverse) ).
cnf(c_19,plain,
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(clausify,[status(thm)],[closure_of_product_and_inverse]) ).
fof(a_is_in_subgroup,axiom,
subgroup_member(a),
file('theBenchmark.p',a_is_in_subgroup) ).
cnf(c_20,plain,
subgroup_member(a),
inference(clausify,[status(thm)],[a_is_in_subgroup]) ).
fof(prove_subgr2,axiom,
! [VAR_0] :
( ~ subgroup_member(VAR_0)
| ~ product(VAR_0,j(VAR_0),j(VAR_0))
| ~ product(j(VAR_0),VAR_0,j(VAR_0)) ),
file('theBenchmark.p',prove_subgr2) ).
cnf(c_22,plain,
( ~ subgroup_member(A)
| ~ product(A,j(A),j(A))
| ~ product(j(A),A,j(A)) ),
inference(clausify,[status(thm)],[prove_subgr2]) ).
cnf(c_110,plain,
( subgroup_member(B)
| ~ product(a,inverse(A),B)
| ~ subgroup_member(A) ),
inference(resolve,[status(thm)],[c_19,c_20]) ).
cnf(c_111,plain,
( subgroup_member(A)
| ~ product(a,inverse(a),A) ),
inference(resolve,[status(thm)],[c_110,c_20]) ).
cnf(c_105,plain,
subgroup_member(identity),
inference(resolve,[status(thm)],[c_111,c_14]) ).
cnf(c_112,plain,
( ~ subgroup_member(identity)
| ~ product(identity,j(identity),j(identity)) ),
inference(resolve,[status(thm)],[c_22,c_12]) ).
cnf(c_113,plain,
~ subgroup_member(identity),
inference(resolve,[status(thm)],[c_11,c_112]) ).
cnf(c_109,plain,
$false,
inference(resolve,[status(thm)],[c_105,c_113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP033-3 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:18:28 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2194525 was started by sandbox2 on n011,
% 0.08/0.35 % Fri Sep 25 14:18:28 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.08/0.38 % Length of proof is 8.
% 0.08/0.38 % Level of proof is 2.
% 0.08/0.38 % Maximum clause weight is 14.000.
% 0.08/0.38 % Given clauses 22.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------