%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD041-3 : 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 07:11:35 AM UTC 2026
% Result : Unsatisfiable 0.82s 0.50s
% Output : CNFRefutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 46 ( 22 unt; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 98 ( 53 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 76 ( 8 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_addition_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ sum(VAR_3,VAR_5,VAR_2)
| ~ sum(VAR_4,VAR_1,VAR_5)
| ~ sum(VAR_3,VAR_4,VAR_0)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_addition_2) ).
cnf(c_2,plain,
( ~ sum(D,F,C)
| ~ sum(E,B,F)
| ~ sum(D,E,A)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_addition_2]) ).
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_inverse_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_inverse(VAR_0),VAR_0,additive_identity) ),
file('theBenchmark.p',existence_of_inverse_addition) ).
cnf(c_4,plain,
( ~ defined(A)
| sum(additive_inverse(A),A,additive_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_addition]) ).
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(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(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(a,b,additive_identity),
file('theBenchmark.p',product_5) ).
cnf(c_31,plain,
product(a,b,additive_identity),
inference(clausify,[status(thm)],[product_5]) ).
cnf(c_34,plain,
( ~ sum(D,B,D)
| ~ sum(C,D,A)
| sum(A,B,A) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_40,plain,
( ~ product(D,E,B)
| ~ product(C,E,A)
| ~ sum(C,D,C)
| sum(A,B,A) ),
inference(factor,[status(thm)],[c_11]) ).
cnf(c_53,plain,
( ~ product(B,C,A)
| ~ sum(B,B,B)
| sum(A,A,A) ),
inference(factor,[status(thm)],[c_40]) ).
cnf(c_60,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_98,plain,
product(multiplicative_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_8]) ).
cnf(c_99,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_1295,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_28,c_9]) ).
cnf(c_113,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(resolve,[status(thm)],[c_30,c_1295]) ).
cnf(c_306,plain,
product(a,multiplicative_identity,a),
inference(resolve,[status(thm)],[c_98,c_10]) ).
cnf(c_1296,plain,
( ~ sum(B,a,B)
| ~ sum(A,B,additive_identity) ),
inference(resolve,[status(thm)],[c_34,c_29]) ).
cnf(c_992,plain,
~ sum(a,a,a),
inference(resolve,[status(thm)],[c_1296,c_99]) ).
cnf(c_1297,plain,
( ~ product(A,B,a)
| ~ sum(A,A,A) ),
inference(resolve,[status(thm)],[c_53,c_992]) ).
cnf(c_1156,plain,
~ product(additive_identity,A,a),
inference(resolve,[status(thm)],[c_1297,c_60]) ).
cnf(c_1176,plain,
product(b,multiplicative_inverse(b),multiplicative_identity),
inference(resolve,[status(thm)],[c_113,c_10]) ).
cnf(c_1298,plain,
( ~ product(A,D,a)
| ~ product(B,C,D)
| ~ product(A,B,additive_identity) ),
inference(resolve,[status(thm)],[c_7,c_1156]) ).
cnf(c_1299,plain,
( ~ product(a,B,a)
| ~ product(b,A,B) ),
inference(resolve,[status(thm)],[c_1298,c_31]) ).
cnf(c_1293,plain,
~ product(b,A,multiplicative_identity),
inference(resolve,[status(thm)],[c_1299,c_306]) ).
cnf(c_1294,plain,
$false,
inference(resolve,[status(thm)],[c_1293,c_1176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD041-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n026.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 02:29:25 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2435328 was started by sandbox2 on n026,
% 0.08/0.36 % Sun Sep 27 02:29:25 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.82/0.50
% 0.82/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.82/0.50
% 0.82/0.50 % Proof 1 at 0.09 (+ 0.03) seconds.
% 0.82/0.50 % Length of proof is 27.
% 0.82/0.50 % Level of proof is 5.
% 0.82/0.50 % Maximum clause weight is 25.000.
% 0.82/0.50 % Given clauses 238.
% 0.82/0.50
% 0.82/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------