%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD025-4 : 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 : 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 07:11:30 AM UTC 2026
% Result : Unsatisfiable 0.10s 5.64s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 19 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 26 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 28 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_multiplication_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ product(VAR_4,VAR_5,VAR_2)
| ~ product(VAR_3,VAR_5,VAR_1)
| ~ product(VAR_0,VAR_3,VAR_4)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_multiplication_1) ).
cnf(c_6,plain,
( ~ product(E,F,C)
| ~ product(D,F,B)
| ~ product(A,D,E)
| product(A,B,C) ),
inference(clausify,[status(thm)],[associativity_multiplication_1]) ).
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(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(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(product_6,axiom,
product(multiplicative_identity,a,b),
file('theBenchmark.p',product_6) ).
cnf(c_32,plain,
product(multiplicative_identity,a,b),
inference(clausify,[status(thm)],[product_6]) ).
fof(product_7,axiom,
product(multiplicative_identity,c,d),
file('theBenchmark.p',product_7) ).
cnf(c_33,plain,
product(multiplicative_identity,c,d),
inference(clausify,[status(thm)],[product_7]) ).
fof(product_8,axiom,
product(a,c,u),
file('theBenchmark.p',product_8) ).
cnf(c_34,plain,
product(a,c,u),
inference(clausify,[status(thm)],[product_8]) ).
fof(not_product_9,axiom,
~ product(d,b,u),
file('theBenchmark.p',not_product_9) ).
cnf(c_35,plain,
~ product(d,b,u),
inference(clausify,[status(thm)],[not_product_9]) ).
cnf(c_74,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_17,c_8]) ).
cnf(c_102,plain,
product(multiplicative_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_8]) ).
cnf(c_194,plain,
~ product(b,d,u),
inference(resolve,[status(thm)],[c_10,c_35]) ).
cnf(c_456,plain,
( ~ product(B,C,u)
| ~ product(A,C,d)
| ~ product(b,A,B) ),
inference(resolve,[status(thm)],[c_6,c_194]) ).
cnf(c_457,plain,
( ~ product(A,c,u)
| ~ product(b,multiplicative_identity,A) ),
inference(resolve,[status(thm)],[c_456,c_33]) ).
cnf(c_235,plain,
~ product(b,multiplicative_identity,a),
inference(resolve,[status(thm)],[c_457,c_34]) ).
cnf(c_236,plain,
~ product(multiplicative_identity,b,a),
inference(resolve,[status(thm)],[c_10,c_235]) ).
cnf(c_458,plain,
( ~ product(B,C,a)
| ~ product(A,C,b)
| ~ product(multiplicative_identity,A,B) ),
inference(resolve,[status(thm)],[c_6,c_236]) ).
cnf(c_459,plain,
( ~ product(multiplicative_identity,A,a)
| ~ product(multiplicative_identity,A,b) ),
inference(resolve,[status(thm)],[c_458,c_74]) ).
cnf(c_460,plain,
~ product(multiplicative_identity,a,a),
inference(resolve,[status(thm)],[c_459,c_32]) ).
cnf(c_455,plain,
$false,
inference(resolve,[status(thm)],[c_102,c_460]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD025-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.60 % Computer : n013.cluster.edu
% 0.10/5.60 % Model : x86_64 x86_64
% 0.10/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.60 % Memory : 8046.5625MB
% 0.10/5.60 % OS : Linux 6.8.0-71-generic
% 0.10/5.60 % CPULimit : 300
% 0.10/5.60 % WCLimit : 300
% 0.10/5.60 % DateTime : Sun Sep 27 02:23:11 UTC 2026
% 0.10/5.61 % CPUTime :
% 0.10/5.61 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.61 % Process 4008490 was started by sandbox on n013,
% 0.10/5.61 % Sun Sep 27 02:23:11 2026
% 0.10/5.61 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.61
% 0.10/5.61 % From the command line: assign(max_seconds, 300).
% 0.10/5.64
% 0.10/5.64 % SZS status Unsatisfiable for theBenchmark
% 0.10/5.64
% 0.10/5.64 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.10/5.64 % Length of proof is 15.
% 0.10/5.64 % Level of proof is 4.
% 0.10/5.64 % Maximum clause weight is 16.000.
% 0.10/5.64 % Given clauses 81.
% 0.10/5.64
% 0.10/5.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------