%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD028-3 : 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 : 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 07:11:31 AM UTC 2026
% Result : Unsatisfiable 1.20s 0.59s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 24 unt; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 66 ( 38 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 40 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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,a,additive_identity),
file('theBenchmark.p',not_sum_5) ).
cnf(c_31,plain,
~ sum(additive_identity,a,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_73,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_17,c_8]) ).
cnf(c_1397,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_27,c_9]) ).
cnf(c_100,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(resolve,[status(thm)],[c_31,c_1397]) ).
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_1398,plain,
( ~ product(B,C,v)
| ~ product(A,C,u)
| ~ product(multiplicative_identity,A,B) ),
inference(resolve,[status(thm)],[c_6,c_34]) ).
cnf(c_1399,plain,
( ~ product(multiplicative_identity,A,v)
| ~ product(multiplicative_identity,A,u) ),
inference(resolve,[status(thm)],[c_1398,c_73]) ).
cnf(c_418,plain,
~ product(multiplicative_identity,v,u),
inference(resolve,[status(thm)],[c_1399,c_149]) ).
cnf(c_1400,plain,
( ~ product(A,C,u)
| ~ product(B,v,C)
| ~ product(A,B,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_7,c_418]) ).
cnf(c_1401,plain,
( ~ product(multiplicative_inverse(a),A,u)
| ~ product(a,v,A) ),
inference(resolve,[status(thm)],[c_1400,c_100]) ).
cnf(c_1201,plain,
~ product(multiplicative_inverse(a),b,u),
inference(resolve,[status(thm)],[c_1401,c_33]) ).
cnf(c_1402,plain,
( ~ product(B,C,u)
| ~ product(A,C,b)
| ~ product(multiplicative_inverse(a),A,B) ),
inference(resolve,[status(thm)],[c_6,c_1201]) ).
cnf(c_1403,plain,
( ~ product(A,u,u)
| ~ product(multiplicative_inverse(a),a,A) ),
inference(resolve,[status(thm)],[c_1402,c_32]) ).
cnf(c_1404,plain,
~ product(multiplicative_inverse(a),a,multiplicative_identity),
inference(resolve,[status(thm)],[c_1403,c_133]) ).
cnf(c_1396,plain,
$false,
inference(resolve,[status(thm)],[c_100,c_1404]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD028-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.39 % Computer : n018.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 02:26:53 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.40 % Process 1919109 was started by sandbox2 on n018,
% 0.14/0.40 % Sun Sep 27 02:26:53 2026
% 0.14/0.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.41
% 0.19/0.41 % From the command line: assign(max_seconds, 300).
% 1.20/0.59
% 1.20/0.59 % SZS status Unsatisfiable for theBenchmark
% 1.20/0.59
% 1.20/0.59 % Proof 1 at 0.12 (+ 0.04) seconds.
% 1.20/0.59 % Length of proof is 19.
% 1.20/0.59 % Level of proof is 4.
% 1.20/0.59 % Maximum clause weight is 21.000.
% 1.20/0.59 % Given clauses 273.
% 1.20/0.59
% 1.20/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------