%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP038-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 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 : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 9 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_9,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_12,plain,
subgroup_member(a),
inference(clausify,[status(thm)],[a_is_in_subgroup]) ).
fof(b_is_in_subgroup,axiom,
subgroup_member(b),
file('theBenchmark.p',b_is_in_subgroup) ).
cnf(c_13,plain,
subgroup_member(b),
inference(clausify,[status(thm)],[b_is_in_subgroup]) ).
fof(a_times_inverse_b_is_c,axiom,
product(a,inverse(b),c),
file('theBenchmark.p',a_times_inverse_b_is_c) ).
cnf(c_14,plain,
product(a,inverse(b),c),
inference(clausify,[status(thm)],[a_times_inverse_b_is_c]) ).
fof(prove_c_is_in_subgroup,axiom,
~ subgroup_member(c),
file('theBenchmark.p',prove_c_is_in_subgroup) ).
cnf(c_15,plain,
~ subgroup_member(c),
inference(clausify,[status(thm)],[prove_c_is_in_subgroup]) ).
cnf(c_43,plain,
( subgroup_member(B)
| ~ product(a,inverse(A),B)
| ~ subgroup_member(A) ),
inference(resolve,[status(thm)],[c_9,c_12]) ).
cnf(c_44,plain,
( subgroup_member(A)
| ~ product(a,inverse(b),A) ),
inference(resolve,[status(thm)],[c_43,c_13]) ).
cnf(c_41,plain,
subgroup_member(c),
inference(resolve,[status(thm)],[c_44,c_14]) ).
cnf(c_42,plain,
$false,
inference(resolve,[status(thm)],[c_41,c_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP038-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:24:40 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3495008 was started by sandbox2 on n001,
% 0.09/0.35 % Fri Sep 25 14:24:40 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.12/0.37 % Length of proof is 7.
% 0.12/0.37 % Level of proof is 2.
% 0.12/0.37 % Maximum clause weight is 11.000.
% 0.12/0.37 % Given clauses 14.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------