%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP006-1 : 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 : n016.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 07:26:09 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.56s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% 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_1,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_3,plain,
product(A,inverse(A),identity),
inference(clausify,[status(thm)],[right_inverse]) ).
fof(condition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( an_element(VAR_2)
| ~ product(VAR_0,inverse(VAR_1),VAR_2)
| ~ an_element(VAR_1)
| ~ an_element(VAR_0) ),
file('theBenchmark.p',condition) ).
cnf(c_5,plain,
( an_element(C)
| ~ product(A,inverse(B),C)
| ~ an_element(B)
| ~ an_element(A) ),
inference(clausify,[status(thm)],[condition]) ).
fof(element_of_set,axiom,
an_element(the_element),
file('theBenchmark.p',element_of_set) ).
cnf(c_8,plain,
an_element(the_element),
inference(clausify,[status(thm)],[element_of_set]) ).
fof(prove_b_inverse_is_in_set,axiom,
~ an_element(inverse(the_element)),
file('theBenchmark.p',prove_b_inverse_is_in_set) ).
cnf(c_9,plain,
~ an_element(inverse(the_element)),
inference(clausify,[status(thm)],[prove_b_inverse_is_in_set]) ).
cnf(c_33,plain,
( an_element(B)
| ~ product(the_element,inverse(A),B)
| ~ an_element(A) ),
inference(resolve,[status(thm)],[c_5,c_8]) ).
cnf(c_34,plain,
( an_element(A)
| ~ product(the_element,inverse(the_element),A) ),
inference(resolve,[status(thm)],[c_33,c_8]) ).
cnf(c_22,plain,
an_element(identity),
inference(resolve,[status(thm)],[c_34,c_3]) ).
cnf(c_35,plain,
( an_element(B)
| ~ product(identity,inverse(A),B)
| ~ an_element(A) ),
inference(resolve,[status(thm)],[c_5,c_22]) ).
cnf(c_36,plain,
( an_element(A)
| ~ product(identity,inverse(the_element),A) ),
inference(resolve,[status(thm)],[c_35,c_8]) ).
cnf(c_31,plain,
an_element(inverse(the_element)),
inference(resolve,[status(thm)],[c_36,c_1]) ).
cnf(c_32,plain,
$false,
inference(resolve,[status(thm)],[c_31,c_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.54 % Computer : n016.cluster.edu
% 0.08/0.54 % Model : x86_64 x86_64
% 0.08/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.54 % Memory : 8046.5625MB
% 0.08/0.54 % OS : Linux 6.8.0-71-generic
% 0.08/0.54 % CPULimit : 300
% 0.08/0.54 % WCLimit : 300
% 0.08/0.54 % DateTime : Fri Sep 25 14:20:45 UTC 2026
% 0.08/0.54 % CPUTime :
% 0.08/0.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.54 % Process 2570715 was started by sandbox on n016,
% 0.08/0.54 % Fri Sep 25 14:20:45 2026
% 0.08/0.54 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.55
% 0.08/0.55 % From the command line: assign(max_seconds, 300).
% 0.12/0.56
% 0.12/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.56
% 0.12/0.56 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.56 % Length of proof is 8.
% 0.12/0.56 % Level of proof is 3.
% 0.12/0.56 % Maximum clause weight is 11.000.
% 0.12/0.56 % Given clauses 11.
% 0.12/0.56
% 0.12/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------