%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD011-3 : 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 : n006.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 0.89s 0.71s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of formulae : 66 ( 29 unt; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 147 ( 81 ~; 66 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 100 ( 2 sgn 36 !; 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(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(commutativity_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ sum(VAR_1,VAR_0,VAR_2)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_addition) ).
cnf(c_5,plain,
( ~ sum(B,A,C)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_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(different_identities,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('theBenchmark.p',different_identities) ).
cnf(c_26,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(clausify,[status(thm)],[different_identities]) ).
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(not_sum_2,axiom,
~ sum(additive_identity,a,additive_identity),
file('theBenchmark.p',not_sum_2) ).
cnf(c_28,plain,
~ sum(additive_identity,a,additive_identity),
inference(clausify,[status(thm)],[not_sum_2]) ).
fof(not_product_3,axiom,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a)),a),
file('theBenchmark.p',not_product_3) ).
cnf(c_29,plain,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a)),a),
inference(clausify,[status(thm)],[not_product_3]) ).
cnf(c_32,plain,
( ~ sum(D,B,D)
| ~ sum(C,D,A)
| sum(A,B,A) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_38,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_57,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_4]) ).
cnf(c_58,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_70,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_17,c_3]) ).
cnf(c_1952,plain,
( sum(additive_identity,a,additive_identity)
| defined(multiplicative_inverse(a)) ),
inference(resolve,[status(thm)],[c_27,c_18]) ).
cnf(c_89,plain,
defined(multiplicative_inverse(a)),
inference(resolve,[status(thm)],[c_28,c_1952]) ).
cnf(c_1953,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_27,c_9]) ).
cnf(c_95,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(resolve,[status(thm)],[c_28,c_1953]) ).
cnf(c_96,plain,
product(multiplicative_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_8]) ).
cnf(c_97,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_101,plain,
~ product(multiplicative_inverse(multiplicative_inverse(a)),multiplicative_identity,a),
inference(resolve,[status(thm)],[c_10,c_29]) ).
cnf(c_1954,plain,
( ~ sum(A,C,multiplicative_identity)
| ~ sum(B,additive_identity,C)
| ~ sum(A,B,additive_identity) ),
inference(resolve,[status(thm)],[c_2,c_26]) ).
cnf(c_1955,plain,
( ~ sum(additive_inverse(additive_identity),A,multiplicative_identity)
| ~ sum(additive_identity,additive_identity,A) ),
inference(resolve,[status(thm)],[c_1954,c_57]) ).
cnf(c_194,plain,
~ sum(additive_inverse(additive_identity),additive_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_1955,c_58]) ).
cnf(c_223,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_70,c_5]) ).
cnf(c_1956,plain,
( ~ sum(B,C,multiplicative_identity)
| ~ sum(A,C,additive_identity)
| ~ sum(additive_inverse(additive_identity),A,B) ),
inference(resolve,[status(thm)],[c_1,c_194]) ).
cnf(c_1957,plain,
( ~ sum(additive_identity,A,multiplicative_identity)
| ~ sum(additive_identity,A,additive_identity) ),
inference(resolve,[status(thm)],[c_1956,c_57]) ).
cnf(c_231,plain,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(resolve,[status(thm)],[c_1957,c_70]) ).
cnf(c_301,plain,
( ~ sum(additive_identity,A,additive_identity)
| sum(multiplicative_identity,A,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_223,c_32]) ).
cnf(c_446,plain,
( sum(additive_identity,multiplicative_inverse(a),additive_identity)
| product(multiplicative_inverse(multiplicative_inverse(a)),multiplicative_inverse(a),multiplicative_identity) ),
inference(resolve,[status(thm)],[c_89,c_9]) ).
cnf(c_1958,plain,
( ~ product(B,C,a)
| ~ product(A,C,multiplicative_identity)
| ~ product(multiplicative_inverse(multiplicative_inverse(a)),A,B) ),
inference(resolve,[status(thm)],[c_6,c_101]) ).
cnf(c_1959,plain,
( ~ product(A,a,a)
| ~ product(multiplicative_inverse(multiplicative_inverse(a)),multiplicative_inverse(a),A) ),
inference(resolve,[status(thm)],[c_1958,c_95]) ).
cnf(c_1407,plain,
~ product(multiplicative_inverse(multiplicative_inverse(a)),multiplicative_inverse(a),multiplicative_identity),
inference(resolve,[status(thm)],[c_1959,c_96]) ).
cnf(c_1408,plain,
sum(additive_identity,multiplicative_inverse(a),additive_identity),
inference(resolve,[status(thm)],[c_1407,c_446]) ).
cnf(c_1960,plain,
( ~ sum(B,multiplicative_identity,B)
| ~ sum(A,B,additive_identity) ),
inference(resolve,[status(thm)],[c_32,c_231]) ).
cnf(c_1474,plain,
~ sum(a,multiplicative_identity,a),
inference(resolve,[status(thm)],[c_1960,c_97]) ).
cnf(c_1961,plain,
( ~ product(B,C,multiplicative_identity)
| ~ product(A,C,a)
| ~ sum(A,B,A) ),
inference(resolve,[status(thm)],[c_38,c_1474]) ).
cnf(c_1962,plain,
( ~ product(A,a,multiplicative_identity)
| ~ sum(multiplicative_identity,A,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_1961,c_96]) ).
cnf(c_1513,plain,
~ sum(multiplicative_identity,multiplicative_inverse(a),multiplicative_identity),
inference(resolve,[status(thm)],[c_1962,c_95]) ).
cnf(c_1963,plain,
~ sum(additive_identity,multiplicative_inverse(a),additive_identity),
inference(resolve,[status(thm)],[c_301,c_1513]) ).
cnf(c_1951,plain,
$false,
inference(resolve,[status(thm)],[c_1408,c_1963]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD011-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n006.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 27 02:21:40 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 2569412 was started by sandbox2 on n006,
% 0.19/0.45 % Sun Sep 27 02:21:40 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.89/0.71
% 0.89/0.71 % SZS status Unsatisfiable for theBenchmark
% 0.89/0.71
% 0.89/0.71 % Proof 1 at 0.18 (+ 0.05) seconds.
% 0.89/0.71 % Length of proof is 37.
% 0.89/0.71 % Level of proof is 6.
% 0.89/0.71 % Maximum clause weight is 27.000.
% 0.89/0.71 % Given clauses 281.
% 0.89/0.71
% 0.89/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------