%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD030-3 : 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 : n012.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 07:11:32 AM UTC 2026
% Result : Unsatisfiable 0.03s 0.36s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 13 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 43 ( 25 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 12 !; 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(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(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(product_4,axiom,
product(multiplicative_identity,a,d),
file('theBenchmark.p',product_4) ).
cnf(c_30,plain,
product(multiplicative_identity,a,d),
inference(clausify,[status(thm)],[product_4]) ).
fof(not_product_5,axiom,
~ product(d,b,multiply(a,b)),
file('theBenchmark.p',not_product_5) ).
cnf(c_31,plain,
~ product(d,b,multiply(a,b)),
inference(clausify,[status(thm)],[not_product_5]) ).
cnf(c_114,plain,
product(multiplicative_identity,b,b),
inference(resolve,[status(thm)],[c_28,c_8]) ).
cnf(c_140,plain,
product(a,multiplicative_identity,d),
inference(resolve,[status(thm)],[c_30,c_10]) ).
cnf(c_645,plain,
( ~ product(A,C,multiply(a,b))
| ~ product(B,b,C)
| ~ product(A,B,d) ),
inference(resolve,[status(thm)],[c_7,c_31]) ).
cnf(c_646,plain,
( ~ product(a,A,multiply(a,b))
| ~ product(multiplicative_identity,b,A) ),
inference(resolve,[status(thm)],[c_645,c_140]) ).
cnf(c_559,plain,
~ product(a,b,multiply(a,b)),
inference(resolve,[status(thm)],[c_646,c_114]) ).
cnf(c_647,plain,
( ~ defined(b)
| ~ defined(a) ),
inference(resolve,[status(thm)],[c_20,c_559]) ).
cnf(c_648,plain,
~ defined(a),
inference(resolve,[status(thm)],[c_647,c_28]) ).
cnf(c_644,plain,
$false,
inference(resolve,[status(thm)],[c_27,c_648]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : FLD030-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 27 02:24:34 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.31 % Process 1964839 was started by sandbox2 on n012,
% 0.03/0.31 % Sun Sep 27 02:24:34 2026
% 0.03/0.31 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.31
% 0.03/0.31 % From the command line: assign(max_seconds, 300).
% 0.03/0.36
% 0.03/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.03/0.36
% 0.03/0.36 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.03/0.36 % Length of proof is 12.
% 0.03/0.36 % Level of proof is 3.
% 0.03/0.36 % Maximum clause weight is 16.000.
% 0.03/0.36 % Given clauses 99.
% 0.03/0.36
% 0.03/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------