%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP037-3 : 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 : n004.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 0.16s 5.61s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 15 unt; 0 def)
% Number of atoms : 39 ( 10 equ)
% Maximal formula atoms : 3 ( 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 : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 28 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(right_identity,axiom,
! [VAR_0] : product(VAR_0,identity,VAR_0),
file('theBenchmark.p',right_identity) ).
cnf(c_2,plain,
product(A,identity,A),
inference(clausify,[status(thm)],[right_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : product(inverse(VAR_0),VAR_0,identity),
file('theBenchmark.p',left_inverse) ).
cnf(c_3,plain,
product(inverse(A),A,identity),
inference(clausify,[status(thm)],[left_inverse]) ).
fof(another_right_identity,axiom,
! [VAR_0] :
( product(VAR_0,another_identity,VAR_0)
| ~ subgroup_member(VAR_0) ),
file('theBenchmark.p',another_right_identity) ).
cnf(c_11,plain,
( product(A,another_identity,A)
| ~ subgroup_member(A) ),
inference(clausify,[status(thm)],[another_right_identity]) ).
fof(another_left_inverse,axiom,
! [VAR_0] :
( product(another_inverse(VAR_0),VAR_0,another_identity)
| ~ subgroup_member(VAR_0) ),
file('theBenchmark.p',another_left_inverse) ).
cnf(c_13,plain,
( product(another_inverse(A),A,another_identity)
| ~ subgroup_member(A) ),
inference(clausify,[status(thm)],[another_left_inverse]) ).
fof(product_right_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_1
| ~ product(VAR_0,VAR_3,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_right_cancellation) ).
cnf(c_15,plain,
( D = B
| ~ product(A,D,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_right_cancellation]) ).
fof(product_left_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_0
| ~ product(VAR_3,VAR_1,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_left_cancellation) ).
cnf(c_16,plain,
( D = A
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_left_cancellation]) ).
fof(a_is_in_subgroup,axiom,
subgroup_member(a),
file('theBenchmark.p',a_is_in_subgroup) ).
cnf(c_17,plain,
subgroup_member(a),
inference(clausify,[status(thm)],[a_is_in_subgroup]) ).
fof(prove_two_inverses_are_equal,axiom,
inverse(a) != another_inverse(a),
file('theBenchmark.p',prove_two_inverses_are_equal) ).
cnf(c_19,plain,
inverse(a) != another_inverse(a),
inference(clausify,[status(thm)],[prove_two_inverses_are_equal]) ).
cnf(c_105,plain,
product(another_inverse(a),a,another_identity),
inference(resolve,[status(thm)],[c_13,c_17]) ).
cnf(c_107,plain,
product(a,another_identity,a),
inference(resolve,[status(thm)],[c_11,c_17]) ).
cnf(c_218,plain,
( inverse(B) = A
| ~ product(A,B,identity) ),
inference(resolve,[status(thm)],[c_16,c_3]) ).
cnf(c_120,plain,
~ product(another_inverse(a),a,identity),
inference(resolve,[status(thm)],[c_218,c_19]) ).
cnf(c_219,plain,
( B = identity
| ~ product(A,B,A) ),
inference(resolve,[status(thm)],[c_15,c_2]) ).
cnf(c_220,plain,
another_identity = identity,
inference(resolve,[status(thm)],[c_219,c_107]) ).
cnf(c_182,plain,
identity = another_identity,
inference(copy,[status(thm)],[c_220]) ).
cnf(c_221,plain,
~ product(another_inverse(a),a,another_identity),
inference(paramod,[status(thm)],[c_182,c_120]) ).
cnf(c_217,plain,
$false,
inference(resolve,[status(thm)],[c_105,c_221]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.58 % Computer : n004.cluster.edu
% 0.09/5.58 % Model : x86_64 x86_64
% 0.09/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.58 % Memory : 8046.5625MB
% 0.09/5.58 % OS : Linux 6.8.0-71-generic
% 0.09/5.58 % CPULimit : 300
% 0.09/5.58 % WCLimit : 300
% 0.09/5.58 % DateTime : Fri Sep 25 14:18:58 UTC 2026
% 0.09/5.58 % CPUTime :
% 0.09/5.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.59 % Process 3347364 was started by sandbox2 on n004,
% 0.09/5.59 % Fri Sep 25 14:18:58 2026
% 0.09/5.59 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.59
% 0.09/5.59 % From the command line: assign(max_seconds, 300).
% 0.16/5.61
% 0.16/5.61 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.61
% 0.16/5.61 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/5.61 % Length of proof is 13.
% 0.16/5.61 % Level of proof is 3.
% 0.16/5.61 % Maximum clause weight is 17.000.
% 0.16/5.61 % Given clauses 36.
% 0.16/5.61
% 0.16/5.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------