%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO011-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 06:55:04 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.81s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_of_add,axiom,
! [VAR_0,VAR_1] : add(VAR_0,VAR_1) = add(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_add) ).
cnf(c_1,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutativity_of_add]) ).
fof(additive_id1,axiom,
! [VAR_0] : add(VAR_0,additive_identity) = VAR_0,
file('theBenchmark.p',additive_id1) ).
cnf(c_6,plain,
add(A,additive_identity) = A,
inference(clausify,[status(thm)],[additive_id1]) ).
fof(additive_inverse1,axiom,
! [VAR_0] : add(VAR_0,inverse(VAR_0)) = multiplicative_identity,
file('theBenchmark.p',additive_inverse1) ).
cnf(c_8,plain,
add(A,inverse(A)) = multiplicative_identity,
inference(clausify,[status(thm)],[additive_inverse1]) ).
fof(prove_inverse_of_1_is_0,axiom,
inverse(additive_identity) != multiplicative_identity,
file('theBenchmark.p',prove_inverse_of_1_is_0) ).
cnf(c_10,plain,
inverse(additive_identity) != multiplicative_identity,
inference(clausify,[status(thm)],[prove_inverse_of_1_is_0]) ).
cnf(c_98,plain,
A = add(additive_identity,A),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_26,plain,
add(additive_identity,A) = A,
inference(copy,[status(thm)],[c_98]) ).
cnf(c_99,plain,
inverse(additive_identity) = multiplicative_identity,
inference(paramod,[status(thm)],[c_26,c_8]) ).
cnf(c_97,plain,
$false,
inference(resolve,[status(thm)],[c_10,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO011-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.79 % Computer : n013.cluster.edu
% 0.12/0.79 % Model : x86_64 x86_64
% 0.12/0.79 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.79 % Memory : 8046.5625MB
% 0.12/0.79 % OS : Linux 6.8.0-71-generic
% 0.12/0.79 % CPULimit : 300
% 0.12/0.79 % WCLimit : 300
% 0.12/0.79 % DateTime : Sat Sep 26 22:34:38 UTC 2026
% 0.12/0.79 % CPUTime :
% 0.12/0.79 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.79 % Process 3708631 was started by sandbox on n013,
% 0.12/0.79 % Sat Sep 26 22:34:38 2026
% 0.12/0.79 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.80
% 0.12/0.80 % From the command line: assign(max_seconds, 300).
% 0.16/0.81
% 0.16/0.81 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.81
% 0.16/0.81 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.81 % Length of proof is 6.
% 0.16/0.81 % Level of proof is 2.
% 0.16/0.81 % Maximum clause weight is 21.000.
% 0.16/0.81 % Given clauses 13.
% 0.16/0.81
% 0.16/0.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------