%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD043-5 : 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 : n018.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 105.10s 13.83s
% Output : CNFRefutation 105.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 62 ( 26 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 148 ( 79 ~; 69 |; 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; 3 con; 0-2 aty)
% Number of variables : 107 ( 1 sgn 39 !; 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_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(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_multiplication,axiom,
! [VAR_0,VAR_1] :
( ~ defined(VAR_1)
| ~ defined(VAR_0)
| defined(multiply(VAR_0,VAR_1)) ),
file('theBenchmark.p',well_definedness_of_multiplication) ).
cnf(c_16,plain,
( ~ defined(B)
| ~ defined(A)
| defined(multiply(A,B)) ),
inference(clausify,[status(thm)],[well_definedness_of_multiplication]) ).
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(totality_of_multiplication,axiom,
! [VAR_0,VAR_1] :
( ~ defined(VAR_1)
| ~ defined(VAR_0)
| product(VAR_0,VAR_1,multiply(VAR_0,VAR_1)) ),
file('theBenchmark.p',totality_of_multiplication) ).
cnf(c_20,plain,
( ~ defined(B)
| ~ defined(A)
| product(A,B,multiply(A,B)) ),
inference(clausify,[status(thm)],[totality_of_multiplication]) ).
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_product_2,axiom,
~ product(additive_identity,a,additive_identity),
file('theBenchmark.p',not_product_2) ).
cnf(c_28,plain,
~ product(additive_identity,a,additive_identity),
inference(clausify,[status(thm)],[not_product_2]) ).
cnf(c_30,plain,
( ~ sum(C,D,B)
| ~ sum(A,C,C)
| sum(A,B,B) ),
inference(factor,[status(thm)],[c_1]) ).
cnf(c_38,plain,
( ~ product(C,E,A)
| ~ product(D,E,B)
| ~ sum(C,D,D)
| sum(A,B,B) ),
inference(factor,[status(thm)],[c_11]) ).
cnf(c_41,plain,
( ~ sum(E,E,C)
| ~ product(D,B,E)
| ~ sum(D,D,A)
| product(A,B,C) ),
inference(factor,[status(thm)],[c_12]) ).
cnf(c_55,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_57,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_59,plain,
( ~ defined(A)
| defined(multiply(additive_identity,A)) ),
inference(resolve,[status(thm)],[c_16,c_14]) ).
cnf(c_69,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_17,c_3]) ).
cnf(c_76,plain,
( ~ defined(A)
| product(additive_identity,A,multiply(additive_identity,A)) ),
inference(resolve,[status(thm)],[c_20,c_14]) ).
cnf(c_95,plain,
product(multiplicative_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_8]) ).
cnf(c_96,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_131,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(resolve,[status(thm)],[c_55,c_10]) ).
cnf(c_151,plain,
( ~ sum(additive_identity,C,B)
| ~ sum(additive_identity,C,A)
| sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_57,c_1]) ).
cnf(c_232,plain,
( ~ product(B,a,A)
| ~ sum(B,multiplicative_identity,multiplicative_identity)
| sum(A,a,a) ),
inference(resolve,[status(thm)],[c_95,c_38]) ).
cnf(c_243,plain,
product(a,multiplicative_identity,a),
inference(resolve,[status(thm)],[c_95,c_10]) ).
cnf(c_308,plain,
defined(multiply(additive_identity,a)),
inference(resolve,[status(thm)],[c_59,c_27]) ).
cnf(c_760,plain,
sum(additive_identity,multiply(additive_identity,a),multiply(additive_identity,a)),
inference(resolve,[status(thm)],[c_308,c_3]) ).
cnf(c_1067,plain,
sum(a,additive_inverse(a),additive_identity),
inference(resolve,[status(thm)],[c_96,c_5]) ).
cnf(c_1251,plain,
product(additive_identity,a,multiply(additive_identity,a)),
inference(resolve,[status(thm)],[c_76,c_27]) ).
cnf(c_1283,plain,
( ~ sum(A,a,a)
| sum(A,additive_identity,additive_identity) ),
inference(resolve,[status(thm)],[c_1067,c_30]) ).
cnf(c_17167,plain,
( ~ product(B,C,additive_identity)
| ~ product(A,C,a)
| ~ product(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_6,c_28]) ).
cnf(c_17168,plain,
( ~ product(multiply(additive_identity,a),A,additive_identity)
| ~ product(a,A,a) ),
inference(resolve,[status(thm)],[c_17167,c_1251]) ).
cnf(c_2987,plain,
~ product(multiply(additive_identity,a),multiplicative_identity,additive_identity),
inference(resolve,[status(thm)],[c_17168,c_243]) ).
cnf(c_17169,plain,
( ~ sum(B,B,additive_identity)
| ~ product(A,multiplicative_identity,B)
| ~ sum(A,A,multiply(additive_identity,a)) ),
inference(resolve,[status(thm)],[c_41,c_2987]) ).
cnf(c_17170,plain,
( ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,multiply(additive_identity,a)) ),
inference(resolve,[status(thm)],[c_17169,c_131]) ).
cnf(c_8003,plain,
~ sum(additive_identity,additive_identity,multiply(additive_identity,a)),
inference(resolve,[status(thm)],[c_17170,c_57]) ).
cnf(c_17171,plain,
( ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| sum(multiply(additive_identity,a),a,a) ),
inference(resolve,[status(thm)],[c_232,c_1251]) ).
cnf(c_10312,plain,
sum(multiply(additive_identity,a),a,a),
inference(resolve,[status(thm)],[c_69,c_17171]) ).
cnf(c_10450,plain,
sum(multiply(additive_identity,a),additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_10312,c_1283]) ).
cnf(c_11236,plain,
sum(additive_identity,multiply(additive_identity,a),additive_identity),
inference(resolve,[status(thm)],[c_10450,c_5]) ).
cnf(c_17172,plain,
( ~ sum(additive_identity,A,multiply(additive_identity,a))
| ~ sum(additive_identity,A,additive_identity) ),
inference(resolve,[status(thm)],[c_151,c_8003]) ).
cnf(c_17173,plain,
~ sum(additive_identity,multiply(additive_identity,a),multiply(additive_identity,a)),
inference(resolve,[status(thm)],[c_17172,c_11236]) ).
cnf(c_17166,plain,
$false,
inference(resolve,[status(thm)],[c_760,c_17173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD043-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n018.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 02:28:38 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 1921728 was started by sandbox on n018,
% 0.15/0.42 % Sun Sep 27 02:28:38 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.42
% 0.15/0.42 % From the command line: assign(max_seconds, 300).
% 105.10/13.83
% 105.10/13.83 % given #500 (T,wt=10): 3147 product(additive_identity,a,multiply(a,additive_identity)). [resolve(1383,a,10,b)].
% 105.10/13.83
% 105.10/13.83 % given #1000 (F,wt=10): 5366 -product(multiplicative_identity,a,add(additive_identity,multiplicative_identity)). [ur(7,a,2649,a,c,243,a,d,95,a)].
% 105.10/13.83
% 105.10/13.83 % SZS status Unsatisfiable for theBenchmark
% 105.10/13.83
% 105.10/13.83 % Proof 1 at 4.63 (+ 0.71) seconds.
% 105.10/13.83 % Length of proof is 40.
% 105.10/13.83 % Level of proof is 6.
% 105.10/13.83 % Maximum clause weight is 22.000.
% 105.10/13.83 % Given clauses 1128.
% 105.10/13.83
% 105.10/13.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------