%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD026-3 : 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 : n008.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 11.36s 1.94s
% Output : CNFRefutation 11.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 61 ( 32 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 123 ( 66 ~; 57 |; 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 : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 74 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(distributivity_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( ~ sum(VAR_5,VAR_6,VAR_2)
| ~ product(VAR_4,VAR_1,VAR_6)
| ~ product(VAR_3,VAR_1,VAR_5)
| ~ sum(VAR_3,VAR_4,VAR_0)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity_2) ).
cnf(c_12,plain,
( ~ sum(F,V6,C)
| ~ product(E,B,V6)
| ~ product(D,B,F)
| ~ sum(D,E,A)
| product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity_2]) ).
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(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(well_definedness_of_multiplicative_inverse,axiom,
! [VAR_0] :
( sum(additive_identity,VAR_0,additive_identity)
| ~ defined(VAR_0)
| defined(multiplicative_inverse(VAR_0)) ),
file('theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
cnf(c_18,plain,
( sum(additive_identity,A,additive_identity)
| ~ defined(A)
| defined(multiplicative_inverse(A)) ),
inference(clausify,[status(thm)],[well_definedness_of_multiplicative_inverse]) ).
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(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(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
file('theBenchmark.p',not_product_5) ).
cnf(c_31,plain,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
inference(clausify,[status(thm)],[not_product_5]) ).
cnf(c_58,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_72,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_17,c_8]) ).
cnf(c_10734,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_27,c_9]) ).
cnf(c_114,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(resolve,[status(thm)],[c_29,c_10734]) ).
cnf(c_115,plain,
product(multiplicative_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_8]) ).
cnf(c_117,plain,
sum(additive_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_3]) ).
cnf(c_146,plain,
( sum(additive_identity,b,additive_identity)
| defined(multiplicative_inverse(b)) ),
inference(resolve,[status(thm)],[c_28,c_18]) ).
cnf(c_152,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_28,c_9]) ).
cnf(c_195,plain,
product(a,multiplicative_identity,b),
inference(resolve,[status(thm)],[c_30,c_10]) ).
cnf(c_205,plain,
~ product(multiplicative_inverse(a),multiplicative_identity,multiplicative_inverse(b)),
inference(resolve,[status(thm)],[c_10,c_31]) ).
cnf(c_228,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(resolve,[status(thm)],[c_58,c_10]) ).
cnf(c_305,plain,
product(a,multiplicative_identity,a),
inference(resolve,[status(thm)],[c_115,c_10]) ).
cnf(c_10735,plain,
( ~ product(B,D,a)
| ~ product(A,D,additive_identity)
| ~ product(C,D,additive_identity)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_11,c_29]) ).
cnf(c_10736,plain,
( ~ product(a,A,a)
| ~ product(additive_identity,A,additive_identity)
| ~ product(a,A,additive_identity) ),
inference(resolve,[status(thm)],[c_10735,c_117]) ).
cnf(c_10737,plain,
( ~ product(a,multiplicative_identity,a)
| ~ product(a,multiplicative_identity,additive_identity) ),
inference(resolve,[status(thm)],[c_10736,c_228]) ).
cnf(c_478,plain,
~ product(a,multiplicative_identity,additive_identity),
inference(resolve,[status(thm)],[c_10737,c_305]) ).
cnf(c_10738,plain,
( ~ sum(C,D,additive_identity)
| ~ product(B,multiplicative_identity,D)
| ~ product(A,multiplicative_identity,C)
| ~ sum(A,B,a) ),
inference(resolve,[status(thm)],[c_12,c_478]) ).
cnf(c_10739,plain,
( ~ sum(A,B,additive_identity)
| ~ product(a,multiplicative_identity,B)
| ~ product(additive_identity,multiplicative_identity,A) ),
inference(resolve,[status(thm)],[c_10738,c_117]) ).
cnf(c_10740,plain,
( ~ sum(additive_identity,A,additive_identity)
| ~ product(a,multiplicative_identity,A) ),
inference(resolve,[status(thm)],[c_10739,c_228]) ).
cnf(c_577,plain,
~ sum(additive_identity,b,additive_identity),
inference(resolve,[status(thm)],[c_10740,c_195]) ).
cnf(c_580,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(resolve,[status(thm)],[c_577,c_152]) ).
cnf(c_581,plain,
defined(multiplicative_inverse(b)),
inference(resolve,[status(thm)],[c_577,c_146]) ).
cnf(c_2182,plain,
product(multiplicative_identity,multiplicative_inverse(b),multiplicative_inverse(b)),
inference(resolve,[status(thm)],[c_581,c_8]) ).
cnf(c_10741,plain,
( ~ product(multiplicative_identity,C,B)
| ~ product(a,C,A)
| product(multiplicative_inverse(a),A,B) ),
inference(resolve,[status(thm)],[c_6,c_114]) ).
cnf(c_10742,plain,
( ~ product(multiplicative_identity,multiplicative_identity,A)
| product(multiplicative_inverse(a),b,A) ),
inference(resolve,[status(thm)],[c_10741,c_195]) ).
cnf(c_9396,plain,
product(multiplicative_inverse(a),b,multiplicative_identity),
inference(resolve,[status(thm)],[c_10742,c_72]) ).
cnf(c_9933,plain,
product(b,multiplicative_inverse(b),multiplicative_identity),
inference(resolve,[status(thm)],[c_580,c_10]) ).
cnf(c_10743,plain,
( ~ product(B,C,multiplicative_inverse(b))
| ~ product(A,C,multiplicative_identity)
| ~ product(multiplicative_inverse(a),A,B) ),
inference(resolve,[status(thm)],[c_6,c_205]) ).
cnf(c_10744,plain,
( ~ product(multiplicative_identity,A,multiplicative_inverse(b))
| ~ product(b,A,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_10743,c_9396]) ).
cnf(c_10745,plain,
~ product(multiplicative_identity,multiplicative_inverse(b),multiplicative_inverse(b)),
inference(resolve,[status(thm)],[c_10744,c_9933]) ).
cnf(c_10733,plain,
$false,
inference(resolve,[status(thm)],[c_2182,c_10745]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD026-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n008.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sun Sep 27 02:24:54 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 824042 was started by sandbox on n008,
% 0.15/0.43 % Sun Sep 27 02:24:54 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 11.36/1.94
% 11.36/1.94 % given #500 (W,wt=15): 9533 -sum(b,additive_inverse(b),b). [ur(2,a,9463,a,c,154,a,d,351,a)].
% 11.36/1.94
% 11.36/1.94 % SZS status Unsatisfiable for theBenchmark
% 11.36/1.94
% 11.36/1.94 % Proof 1 at 1.10 (+ 0.37) seconds.
% 11.36/1.94 % Length of proof is 34.
% 11.36/1.94 % Level of proof is 7.
% 11.36/1.94 % Maximum clause weight is 25.000.
% 11.36/1.94 % Given clauses 509.
% 11.36/1.94
% 11.36/1.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------