%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD037-3 : 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 : n026.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 07:11:34 AM UTC 2026
% Result : Unsatisfiable 0.10s 5.63s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 16 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 23 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 26 ( 0 sgn 11 !; 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(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(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(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(product_4,axiom,
product(multiplicative_identity,a,b),
file('theBenchmark.p',product_4) ).
cnf(c_30,plain,
product(multiplicative_identity,a,b),
inference(clausify,[status(thm)],[product_4]) ).
fof(not_product_5,axiom,
~ product(b,multiplicative_inverse(a),multiplicative_identity),
file('theBenchmark.p',not_product_5) ).
cnf(c_31,plain,
~ product(b,multiplicative_inverse(a),multiplicative_identity),
inference(clausify,[status(thm)],[not_product_5]) ).
cnf(c_70,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_17,c_8]) ).
cnf(c_389,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_27,c_9]) ).
cnf(c_97,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(resolve,[status(thm)],[c_29,c_389]) ).
cnf(c_125,plain,
product(a,multiplicative_identity,b),
inference(resolve,[status(thm)],[c_30,c_10]) ).
cnf(c_135,plain,
~ product(multiplicative_inverse(a),b,multiplicative_identity),
inference(resolve,[status(thm)],[c_10,c_31]) ).
cnf(c_390,plain,
( ~ product(B,C,multiplicative_identity)
| ~ product(A,C,b)
| ~ product(multiplicative_inverse(a),A,B) ),
inference(resolve,[status(thm)],[c_6,c_135]) ).
cnf(c_391,plain,
( ~ product(A,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_inverse(a),a,A) ),
inference(resolve,[status(thm)],[c_390,c_125]) ).
cnf(c_392,plain,
~ product(multiplicative_inverse(a),a,multiplicative_identity),
inference(resolve,[status(thm)],[c_391,c_70]) ).
cnf(c_388,plain,
$false,
inference(resolve,[status(thm)],[c_97,c_392]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD037-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.60 % Computer : n026.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 02:28:33 UTC 2026
% 0.10/5.60 % CPUTime :
% 0.10/5.60 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.60 % Process 2433889 was started by sandbox2 on n026,
% 0.10/5.60 % Sun Sep 27 02:28:33 2026
% 0.10/5.60 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.61
% 0.10/5.61 % From the command line: assign(max_seconds, 300).
% 0.10/5.63
% 0.10/5.63 % SZS status Unsatisfiable for theBenchmark
% 0.10/5.63
% 0.10/5.63 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.10/5.63 % Length of proof is 14.
% 0.10/5.63 % Level of proof is 2.
% 0.10/5.63 % Maximum clause weight is 21.000.
% 0.10/5.63 % Given clauses 83.
% 0.10/5.63
% 0.10/5.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------