%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD029-3 : 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 : n001.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 11.00s 1.87s
% Output : CNFRefutation 11.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 63 ( 31 unt; 0 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 127 ( 68 ~; 59 |; 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 : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 93 ( 4 sgn 32 !; 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(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(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(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_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(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(u_is_defined,axiom,
defined(u),
file('theBenchmark.p',u_is_defined) ).
cnf(c_29,plain,
defined(u),
inference(clausify,[status(thm)],[u_is_defined]) ).
fof(v_is_defined,axiom,
defined(v),
file('theBenchmark.p',v_is_defined) ).
cnf(c_30,plain,
defined(v),
inference(clausify,[status(thm)],[v_is_defined]) ).
fof(not_sum_5,axiom,
~ sum(additive_identity,b,additive_identity),
file('theBenchmark.p',not_sum_5) ).
cnf(c_31,plain,
~ sum(additive_identity,b,additive_identity),
inference(clausify,[status(thm)],[not_sum_5]) ).
fof(product_6,axiom,
product(a,u,b),
file('theBenchmark.p',product_6) ).
cnf(c_32,plain,
product(a,u,b),
inference(clausify,[status(thm)],[product_6]) ).
fof(product_7,axiom,
product(a,v,b),
file('theBenchmark.p',product_7) ).
cnf(c_33,plain,
product(a,v,b),
inference(clausify,[status(thm)],[product_7]) ).
fof(not_product_8,axiom,
~ product(multiplicative_identity,u,v),
file('theBenchmark.p',not_product_8) ).
cnf(c_34,plain,
~ product(multiplicative_identity,u,v),
inference(clausify,[status(thm)],[not_product_8]) ).
cnf(c_37,plain,
( ~ sum(D,B,D)
| ~ sum(C,D,A)
| sum(A,B,A) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_43,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_56,plain,
( ~ product(B,C,A)
| ~ sum(B,B,B)
| sum(A,A,A) ),
inference(factor,[status(thm)],[c_43]) ).
cnf(c_73,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_17,c_8]) ).
cnf(c_100,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_27,c_9]) ).
cnf(c_103,plain,
sum(additive_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_3]) ).
cnf(c_118,plain,
sum(additive_inverse(b),b,additive_identity),
inference(resolve,[status(thm)],[c_28,c_4]) ).
cnf(c_133,plain,
product(multiplicative_identity,u,u),
inference(resolve,[status(thm)],[c_29,c_8]) ).
cnf(c_149,plain,
product(multiplicative_identity,v,v),
inference(resolve,[status(thm)],[c_30,c_8]) ).
cnf(c_160,plain,
( ~ product(C,u,B)
| ~ product(A,a,C)
| product(A,b,B) ),
inference(resolve,[status(thm)],[c_32,c_6]) ).
cnf(c_165,plain,
( ~ product(C,b,B)
| ~ product(C,a,A)
| product(A,v,B) ),
inference(resolve,[status(thm)],[c_33,c_7]) ).
cnf(c_313,plain,
sum(a,additive_identity,a),
inference(resolve,[status(thm)],[c_103,c_5]) ).
cnf(c_9583,plain,
( ~ product(B,C,v)
| ~ product(A,C,u)
| ~ product(multiplicative_identity,A,B) ),
inference(resolve,[status(thm)],[c_6,c_34]) ).
cnf(c_9584,plain,
( ~ product(multiplicative_identity,A,v)
| ~ product(multiplicative_identity,A,u) ),
inference(resolve,[status(thm)],[c_9583,c_73]) ).
cnf(c_418,plain,
~ product(multiplicative_identity,v,u),
inference(resolve,[status(thm)],[c_9584,c_149]) ).
cnf(c_503,plain,
( ~ sum(additive_identity,A,additive_identity)
| sum(a,A,a) ),
inference(resolve,[status(thm)],[c_313,c_37]) ).
cnf(c_9585,plain,
( ~ sum(B,b,B)
| ~ sum(A,B,additive_identity) ),
inference(resolve,[status(thm)],[c_37,c_31]) ).
cnf(c_1510,plain,
~ sum(b,b,b),
inference(resolve,[status(thm)],[c_9585,c_118]) ).
cnf(c_9586,plain,
( ~ product(A,B,b)
| ~ sum(A,A,A) ),
inference(resolve,[status(thm)],[c_56,c_1510]) ).
cnf(c_1583,plain,
~ sum(a,a,a),
inference(resolve,[status(thm)],[c_9586,c_33]) ).
cnf(c_9587,plain,
( product(multiplicative_inverse(a),a,multiplicative_identity)
| sum(a,a,a) ),
inference(resolve,[status(thm)],[c_503,c_100]) ).
cnf(c_1592,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(resolve,[status(thm)],[c_1583,c_9587]) ).
cnf(c_2304,plain,
( ~ product(A,a,multiplicative_identity)
| product(A,b,u) ),
inference(resolve,[status(thm)],[c_160,c_133]) ).
cnf(c_9562,plain,
product(multiplicative_inverse(a),b,u),
inference(resolve,[status(thm)],[c_1592,c_2304]) ).
cnf(c_9588,plain,
( ~ product(A,b,u)
| ~ product(A,a,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_165,c_418]) ).
cnf(c_9589,plain,
~ product(multiplicative_inverse(a),b,u),
inference(resolve,[status(thm)],[c_9588,c_1592]) ).
cnf(c_9582,plain,
$false,
inference(resolve,[status(thm)],[c_9562,c_9589]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD029-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n001.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 02:30:17 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 3160550 was started by sandbox on n001,
% 0.08/0.37 % Sun Sep 27 02:30:17 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 11.00/1.87
% 11.00/1.87 % given #500 (A,wt=14): 183 defined(multiply(a,a)). [resolve(49,b,27,a)].
% 11.00/1.87
% 11.00/1.87 % given #1000 (T,wt=15): 569 less_or_equal(b,A) | -less_or_equal(b,B) | -sum(B,additive_identity,A). [resolve(373,a,24,c)].
% 11.00/1.87
% 11.00/1.87 % SZS status Unsatisfiable for theBenchmark
% 11.00/1.87
% 11.00/1.87 % Proof 1 at 1.13 (+ 0.25) seconds.
% 11.00/1.87 % Length of proof is 38.
% 11.00/1.87 % Level of proof is 6.
% 11.00/1.87 % Maximum clause weight is 25.000.
% 11.00/1.87 % Given clauses 1071.
% 11.00/1.87
% 11.00/1.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------