%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD010-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 07:11:26 AM UTC 2026
% Result : Unsatisfiable 0.15s 5.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 9 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 8 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_of_inverse_multiplication,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_identity,VAR_0,additive_identity)
| product(multiplicative_inverse(VAR_0),VAR_0,multiplicative_identity) ),
file('theBenchmark.p',existence_of_inverse_multiplication) ).
cnf(c_9,plain,
( ~ defined(A)
| sum(additive_identity,A,additive_identity)
| product(multiplicative_inverse(A),A,multiplicative_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_multiplication]) ).
fof(commutativity_multiplication,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ product(VAR_1,VAR_0,VAR_2)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_multiplication) ).
cnf(c_10,plain,
( ~ product(B,A,C)
| product(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_multiplication]) ).
fof(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('theBenchmark.p',well_definedness_of_multiplicative_identity) ).
cnf(c_17,plain,
defined(multiplicative_identity),
inference(clausify,[status(thm)],[well_definedness_of_multiplicative_identity]) ).
fof(not_sum_1,axiom,
~ sum(additive_identity,multiplicative_identity,additive_identity),
file('theBenchmark.p',not_sum_1) ).
cnf(c_27,plain,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(clausify,[status(thm)],[not_sum_1]) ).
fof(not_product_2,axiom,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file('theBenchmark.p',not_product_2) ).
cnf(c_28,plain,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(clausify,[status(thm)],[not_product_2]) ).
cnf(c_85,plain,
( sum(additive_identity,multiplicative_identity,additive_identity)
| product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_17,c_9]) ).
cnf(c_66,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_27,c_85]) ).
cnf(c_86,plain,
~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_10,c_28]) ).
cnf(c_84,plain,
$false,
inference(resolve,[status(thm)],[c_66,c_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD010-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n007.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sun Sep 27 02:19:15 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 1001468 was started by sandbox on n007,
% 0.09/5.38 % Sun Sep 27 02:19:15 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.39
% 0.09/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.40
% 0.15/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.40
% 0.15/5.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/5.40 % Length of proof is 7.
% 0.15/5.40 % Level of proof is 2.
% 0.15/5.40 % Maximum clause weight is 11.000.
% 0.15/5.40 % Given clauses 28.
% 0.15/5.40
% 0.15/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------