%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD002-3 : 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 : n010.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 07:11:25 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 21 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 67 ( 38 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 45 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_addition_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ sum(VAR_4,VAR_5,VAR_2)
| ~ sum(VAR_3,VAR_5,VAR_1)
| ~ sum(VAR_0,VAR_3,VAR_4)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_addition_1) ).
cnf(c_1,plain,
( ~ sum(E,F,C)
| ~ sum(D,F,B)
| ~ sum(A,D,E)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_addition_1]) ).
fof(existence_of_identity_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_identity,VAR_0,VAR_0) ),
file('theBenchmark.p',existence_of_identity_addition) ).
cnf(c_3,plain,
( ~ defined(A)
| sum(additive_identity,A,A) ),
inference(clausify,[status(thm)],[existence_of_identity_addition]) ).
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(distributivity_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( ~ product(VAR_4,VAR_6,VAR_1)
| ~ product(VAR_3,VAR_6,VAR_0)
| ~ product(VAR_5,VAR_6,VAR_2)
| ~ sum(VAR_3,VAR_4,VAR_5)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity_1) ).
cnf(c_11,plain,
( ~ product(E,V6,B)
| ~ product(D,V6,A)
| ~ product(F,V6,C)
| ~ sum(D,E,F)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[distributivity_1]) ).
fof(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('theBenchmark.p',well_definedness_of_additive_identity) ).
cnf(c_14,plain,
defined(additive_identity),
inference(clausify,[status(thm)],[well_definedness_of_additive_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(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_3,axiom,
product(multiplicative_identity,a,b),
file('theBenchmark.p',product_3) ).
cnf(c_29,plain,
product(multiplicative_identity,a,b),
inference(clausify,[status(thm)],[product_3]) ).
fof(not_sum_4,axiom,
~ sum(additive_identity,a,b),
file('theBenchmark.p',not_sum_4) ).
cnf(c_30,plain,
~ sum(additive_identity,a,b),
inference(clausify,[status(thm)],[not_sum_4]) ).
cnf(c_57,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_59,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_97,plain,
product(multiplicative_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_8]) ).
cnf(c_99,plain,
sum(additive_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_3]) ).
cnf(c_115,plain,
sum(additive_identity,b,b),
inference(resolve,[status(thm)],[c_28,c_3]) ).
cnf(c_123,plain,
product(a,multiplicative_identity,b),
inference(resolve,[status(thm)],[c_29,c_10]) ).
cnf(c_178,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(resolve,[status(thm)],[c_57,c_10]) ).
cnf(c_292,plain,
product(a,multiplicative_identity,a),
inference(resolve,[status(thm)],[c_97,c_10]) ).
cnf(c_417,plain,
( ~ sum(B,C,b)
| ~ sum(A,C,a)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_1,c_30]) ).
cnf(c_418,plain,
( ~ sum(additive_identity,A,b)
| ~ sum(additive_identity,A,a) ),
inference(resolve,[status(thm)],[c_417,c_59]) ).
cnf(c_346,plain,
~ sum(additive_identity,b,a),
inference(resolve,[status(thm)],[c_418,c_115]) ).
cnf(c_419,plain,
( ~ product(B,D,b)
| ~ product(A,D,additive_identity)
| ~ product(C,D,a)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_11,c_346]) ).
cnf(c_420,plain,
( ~ product(a,A,b)
| ~ product(additive_identity,A,additive_identity)
| ~ product(a,A,a) ),
inference(resolve,[status(thm)],[c_419,c_99]) ).
cnf(c_421,plain,
( ~ product(a,multiplicative_identity,b)
| ~ product(a,multiplicative_identity,a) ),
inference(resolve,[status(thm)],[c_420,c_178]) ).
cnf(c_422,plain,
~ product(a,multiplicative_identity,a),
inference(resolve,[status(thm)],[c_421,c_123]) ).
cnf(c_416,plain,
$false,
inference(resolve,[status(thm)],[c_292,c_422]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD002-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 02:21:15 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 526258 was started by sandbox2 on n010,
% 0.09/0.36 % Sun Sep 27 02:21:15 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.45
% 0.14/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.45
% 0.14/0.45 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.14/0.45 % Length of proof is 20.
% 0.14/0.45 % Level of proof is 3.
% 0.14/0.45 % Maximum clause weight is 25.000.
% 0.14/0.45 % Given clauses 82.
% 0.14/0.45
% 0.14/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------