%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD010-5 : 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 : n011.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 07:11:26 AM UTC 2026
% Result : Unsatisfiable 0.98s 0.59s
% Output : CNFRefutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 19 unt; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 83 ( 44 ~; 39 |; 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 : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 49 ( 0 sgn 20 !; 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(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(not_sum_1,axiom,
~ sum(additive_identity,multiplicative_identity,additive_identity),
file('theBenchmark.p',not_sum_1) ).
cnf(c_27,plain,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(clausify,[status(thm)],[not_sum_1]) ).
fof(not_sum_2,axiom,
~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file('theBenchmark.p',not_sum_2) ).
cnf(c_28,plain,
~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(clausify,[status(thm)],[not_sum_2]) ).
cnf(c_55,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_1103,plain,
( sum(additive_identity,multiplicative_identity,additive_identity)
| product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_17,c_9]) ).
cnf(c_66,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_27,c_1103]) ).
cnf(c_67,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_17,c_8]) ).
cnf(c_69,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_17,c_3]) ).
cnf(c_1104,plain,
( sum(additive_identity,multiplicative_identity,additive_identity)
| defined(multiplicative_inverse(multiplicative_identity)) ),
inference(resolve,[status(thm)],[c_18,c_17]) ).
cnf(c_70,plain,
defined(multiplicative_inverse(multiplicative_identity)),
inference(resolve,[status(thm)],[c_27,c_1104]) ).
cnf(c_110,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(resolve,[status(thm)],[c_55,c_10]) ).
cnf(c_1105,plain,
( ~ product(B,D,multiplicative_inverse(multiplicative_identity))
| ~ product(A,D,additive_identity)
| ~ product(C,D,multiplicative_identity)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_11,c_28]) ).
cnf(c_1106,plain,
( ~ product(multiplicative_identity,A,multiplicative_inverse(multiplicative_identity))
| ~ product(additive_identity,A,additive_identity)
| ~ product(multiplicative_identity,A,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_1105,c_69]) ).
cnf(c_1107,plain,
( ~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ product(additive_identity,multiplicative_identity,additive_identity) ),
inference(resolve,[status(thm)],[c_1106,c_67]) ).
cnf(c_214,plain,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(resolve,[status(thm)],[c_1107,c_110]) ).
cnf(c_325,plain,
product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)),
inference(resolve,[status(thm)],[c_70,c_8]) ).
cnf(c_374,plain,
product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(resolve,[status(thm)],[c_66,c_10]) ).
cnf(c_1108,plain,
( ~ product(B,C,multiplicative_inverse(multiplicative_identity))
| ~ product(A,C,multiplicative_identity)
| ~ product(multiplicative_identity,A,B) ),
inference(resolve,[status(thm)],[c_6,c_214]) ).
cnf(c_1109,plain,
( ~ product(multiplicative_identity,A,multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_identity,A,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_1108,c_67]) ).
cnf(c_1110,plain,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)),
inference(resolve,[status(thm)],[c_1109,c_374]) ).
cnf(c_1102,plain,
$false,
inference(resolve,[status(thm)],[c_325,c_1110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD010-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n011.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sun Sep 27 02:20:59 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.42 % Process 1989030 was started by sandbox2 on n011,
% 0.17/0.42 % Sun Sep 27 02:20:59 2026
% 0.17/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.43
% 0.17/0.43 % From the command line: assign(max_seconds, 300).
% 0.98/0.59
% 0.98/0.59 % SZS status Unsatisfiable for theBenchmark
% 0.98/0.59
% 0.98/0.59 % Proof 1 at 0.11 (+ 0.04) seconds.
% 0.98/0.59 % Length of proof is 21.
% 0.98/0.59 % Level of proof is 4.
% 0.98/0.59 % Maximum clause weight is 25.000.
% 0.98/0.59 % Given clauses 205.
% 0.98/0.59
% 0.98/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------