%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD009-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 0.23s 0.62s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 16 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 30 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 5 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_multiplication_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ product(VAR_3,VAR_5,VAR_2)
| ~ product(VAR_4,VAR_1,VAR_5)
| ~ product(VAR_3,VAR_4,VAR_0)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_multiplication_2) ).
cnf(c_7,plain,
( ~ product(D,F,C)
| ~ product(E,B,F)
| ~ product(D,E,A)
| product(A,B,C) ),
inference(clausify,[status(thm)],[associativity_multiplication_2]) ).
fof(existence_of_identity_multiplication,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| product(multiplicative_identity,VAR_0,VAR_0) ),
file('theBenchmark.p',existence_of_identity_multiplication) ).
cnf(c_8,plain,
( ~ defined(A)
| product(multiplicative_identity,A,A) ),
inference(clausify,[status(thm)],[existence_of_identity_multiplication]) ).
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_inverse,axiom,
! [VAR_0] :
( sum(additive_identity,VAR_0,additive_identity)
| ~ defined(VAR_0)
| defined(multiplicative_inverse(VAR_0)) ),
file('theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
cnf(c_18,plain,
( sum(additive_identity,A,additive_identity)
| ~ defined(A)
| defined(multiplicative_inverse(A)) ),
inference(clausify,[status(thm)],[well_definedness_of_multiplicative_inverse]) ).
fof(totality_of_multiplication,axiom,
! [VAR_0,VAR_1] :
( ~ defined(VAR_1)
| ~ defined(VAR_0)
| product(VAR_0,VAR_1,multiply(VAR_0,VAR_1)) ),
file('theBenchmark.p',totality_of_multiplication) ).
cnf(c_20,plain,
( ~ defined(B)
| ~ defined(A)
| product(A,B,multiply(A,B)) ),
inference(clausify,[status(thm)],[totality_of_multiplication]) ).
fof(a_is_defined,axiom,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(c_27,plain,
defined(a),
inference(clausify,[status(thm)],[a_is_defined]) ).
fof(b_is_defined,axiom,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(c_28,plain,
defined(b),
inference(clausify,[status(thm)],[b_is_defined]) ).
fof(not_sum_3,axiom,
~ sum(additive_identity,a,additive_identity),
file('theBenchmark.p',not_sum_3) ).
cnf(c_29,plain,
~ sum(additive_identity,a,additive_identity),
inference(clausify,[status(thm)],[not_sum_3]) ).
fof(not_product_4,axiom,
! [VAR_0] : ~ product(a,VAR_0,b),
file('theBenchmark.p',not_product_4) ).
cnf(c_30,plain,
~ product(a,A,b),
inference(clausify,[status(thm)],[not_product_4]) ).
cnf(c_977,plain,
( sum(additive_identity,a,additive_identity)
| defined(multiplicative_inverse(a)) ),
inference(resolve,[status(thm)],[c_27,c_18]) ).
cnf(c_90,plain,
defined(multiplicative_inverse(a)),
inference(resolve,[status(thm)],[c_29,c_977]) ).
cnf(c_978,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_27,c_9]) ).
cnf(c_96,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(resolve,[status(thm)],[c_29,c_978]) ).
cnf(c_103,plain,
( ~ defined(A)
| product(b,A,multiply(b,A)) ),
inference(resolve,[status(thm)],[c_28,c_20]) ).
cnf(c_113,plain,
product(multiplicative_identity,b,b),
inference(resolve,[status(thm)],[c_28,c_8]) ).
cnf(c_118,plain,
~ product(A,a,b),
inference(resolve,[status(thm)],[c_10,c_30]) ).
cnf(c_310,plain,
product(b,multiplicative_identity,b),
inference(resolve,[status(thm)],[c_113,c_10]) ).
cnf(c_979,plain,
( ~ product(A,D,b)
| ~ product(B,a,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_118]) ).
cnf(c_980,plain,
( ~ product(A,multiplicative_identity,b)
| ~ product(A,multiplicative_inverse(a),B) ),
inference(resolve,[status(thm)],[c_979,c_96]) ).
cnf(c_907,plain,
~ product(b,multiplicative_inverse(a),A),
inference(resolve,[status(thm)],[c_980,c_310]) ).
cnf(c_981,plain,
product(b,multiplicative_inverse(a),multiply(b,multiplicative_inverse(a))),
inference(resolve,[status(thm)],[c_103,c_90]) ).
cnf(c_976,plain,
$false,
inference(resolve,[status(thm)],[c_907,c_981]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD009-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n011.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sun Sep 27 02:21:15 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.46 % Process 1989425 was started by sandbox2 on n011,
% 0.18/0.46 % Sun Sep 27 02:21:15 2026
% 0.18/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 0.23/0.62
% 0.23/0.62 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.62
% 0.23/0.62 % Proof 1 at 0.10 (+ 0.04) seconds.
% 0.23/0.62 % Length of proof is 18.
% 0.23/0.62 % Level of proof is 4.
% 0.23/0.62 % Maximum clause weight is 21.000.
% 0.23/0.62 % Given clauses 232.
% 0.23/0.62
% 0.23/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------