%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP023-2 : 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 : n026.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 07:26:17 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.49s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 8 unt; 0 def)
% Number of atoms : 8 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(right_identity,axiom,
! [VAR_0] : multiply(VAR_0,identity) = VAR_0,
file('theBenchmark.p',right_identity) ).
cnf(c_4,plain,
multiply(A,identity) = A,
inference(clausify,[status(thm)],[right_identity]) ).
fof(prove_inverse_of_id_is_id,axiom,
inverse(identity) != identity,
file('theBenchmark.p',prove_inverse_of_id_is_id) ).
cnf(c_6,plain,
inverse(identity) != identity,
inference(clausify,[status(thm)],[prove_inverse_of_id_is_id]) ).
cnf(c_8,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_9,plain,
$false,
inference(resolve,[status(thm)],[c_8,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP023-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.46 % Computer : n026.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Fri Sep 25 14:19:42 UTC 2026
% 0.21/0.47 % CPUTime :
% 0.21/0.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.21/0.47 % Process 2712458 was started by sandbox on n026,
% 0.21/0.47 % Fri Sep 25 14:19:42 2026
% 0.21/0.47 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.21/0.47
% 0.21/0.47 % From the command line: assign(max_seconds, 300).
% 0.21/0.49
% 0.21/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.49
% 0.21/0.49 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.21/0.49 % Length of proof is 5.
% 0.21/0.49 % Level of proof is 2.
% 0.21/0.49 % Maximum clause weight is 6.000.
% 0.21/0.49 % Given clauses 4.
% 0.21/0.49
% 0.21/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------