%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD027-3 : 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 : n016.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 07:11:31 AM UTC 2026
% Result : Unsatisfiable 1.93s 0.91s
% Output : CNFRefutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 20 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 29 ~; 22 |; 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 : 30 ( 0 sgn 11 !; 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(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_sum_4,axiom,
~ sum(additive_identity,b,additive_identity),
file('theBenchmark.p',not_sum_4) ).
cnf(c_30,plain,
~ sum(additive_identity,b,additive_identity),
inference(clausify,[status(thm)],[not_sum_4]) ).
fof(product_5,axiom,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
file('theBenchmark.p',product_5) ).
cnf(c_31,plain,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
inference(clausify,[status(thm)],[product_5]) ).
fof(not_product_6,axiom,
~ product(multiplicative_identity,a,b),
file('theBenchmark.p',not_product_6) ).
cnf(c_32,plain,
~ product(multiplicative_identity,a,b),
inference(clausify,[status(thm)],[not_product_6]) ).
cnf(c_2579,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_27,c_9]) ).
cnf(c_98,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(resolve,[status(thm)],[c_29,c_2579]) ).
cnf(c_2580,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_28,c_9]) ).
cnf(c_114,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(resolve,[status(thm)],[c_30,c_2580]) ).
cnf(c_115,plain,
product(multiplicative_identity,b,b),
inference(resolve,[status(thm)],[c_28,c_8]) ).
cnf(c_129,plain,
( ~ product(C,multiplicative_inverse(b),B)
| ~ product(C,multiplicative_identity,A)
| product(A,multiplicative_inverse(a),B) ),
inference(resolve,[status(thm)],[c_31,c_7]) ).
cnf(c_378,plain,
product(b,multiplicative_identity,b),
inference(resolve,[status(thm)],[c_115,c_10]) ).
cnf(c_2581,plain,
( ~ product(A,C,b)
| ~ product(B,a,C)
| ~ product(A,B,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_7,c_32]) ).
cnf(c_2582,plain,
( ~ product(A,multiplicative_identity,b)
| ~ product(A,multiplicative_inverse(a),multiplicative_identity) ),
inference(resolve,[status(thm)],[c_2581,c_98]) ).
cnf(c_963,plain,
~ product(b,multiplicative_inverse(a),multiplicative_identity),
inference(resolve,[status(thm)],[c_2582,c_378]) ).
cnf(c_1158,plain,
product(b,multiplicative_inverse(b),multiplicative_identity),
inference(resolve,[status(thm)],[c_114,c_10]) ).
cnf(c_2583,plain,
( ~ product(A,multiplicative_inverse(b),multiplicative_identity)
| ~ product(A,multiplicative_identity,b) ),
inference(resolve,[status(thm)],[c_129,c_963]) ).
cnf(c_2584,plain,
~ product(b,multiplicative_inverse(b),multiplicative_identity),
inference(resolve,[status(thm)],[c_2583,c_378]) ).
cnf(c_2578,plain,
$false,
inference(resolve,[status(thm)],[c_1158,c_2584]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD027-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.33 % Computer : n016.cluster.edu
% 0.05/0.33 % Model : x86_64 x86_64
% 0.05/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.33 % Memory : 8046.5625MB
% 0.05/0.33 % OS : Linux 6.8.0-71-generic
% 0.05/0.33 % CPULimit : 300
% 0.05/0.33 % WCLimit : 300
% 0.05/0.33 % DateTime : Sun Sep 27 02:29:32 UTC 2026
% 0.05/0.33 % CPUTime :
% 0.05/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/0.34 % Process 2223004 was started by sandbox on n016,
% 0.05/0.34 % Sun Sep 27 02:29:32 2026
% 0.05/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.05/0.34
% 0.05/0.34 % From the command line: assign(max_seconds, 300).
% 1.93/0.91
% 1.93/0.91 % SZS status Unsatisfiable for theBenchmark
% 1.93/0.91
% 1.93/0.91 % Proof 1 at 0.20 (+ 0.04) seconds.
% 1.93/0.91 % Length of proof is 18.
% 1.93/0.91 % Level of proof is 4.
% 1.93/0.91 % Maximum clause weight is 24.000.
% 1.93/0.91 % Given clauses 333.
% 1.93/0.91
% 1.93/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------