%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD025-5 : 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 : n010.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 0.21s 5.70s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 29 ( 17 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 31 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 40 ( 0 sgn 16 !; 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(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(u_is_defined,axiom,
defined(u),
file('theBenchmark.p',u_is_defined) ).
cnf(c_31,plain,
defined(u),
inference(clausify,[status(thm)],[u_is_defined]) ).
fof(product_7,axiom,
product(multiplicative_identity,a,b),
file('theBenchmark.p',product_7) ).
cnf(c_33,plain,
product(multiplicative_identity,a,b),
inference(clausify,[status(thm)],[product_7]) ).
fof(product_8,axiom,
product(multiplicative_identity,c,d),
file('theBenchmark.p',product_8) ).
cnf(c_34,plain,
product(multiplicative_identity,c,d),
inference(clausify,[status(thm)],[product_8]) ).
fof(product_9,axiom,
product(a,c,u),
file('theBenchmark.p',product_9) ).
cnf(c_35,plain,
product(a,c,u),
inference(clausify,[status(thm)],[product_9]) ).
fof(product_10,axiom,
product(d,b,v),
file('theBenchmark.p',product_10) ).
cnf(c_36,plain,
product(d,b,v),
inference(clausify,[status(thm)],[product_10]) ).
fof(not_product_11,axiom,
~ product(multiplicative_identity,u,v),
file('theBenchmark.p',not_product_11) ).
cnf(c_37,plain,
~ product(multiplicative_identity,u,v),
inference(clausify,[status(thm)],[not_product_11]) ).
cnf(c_168,plain,
product(multiplicative_identity,u,u),
inference(resolve,[status(thm)],[c_31,c_8]) ).
cnf(c_325,plain,
( ~ product(B,C,v)
| ~ product(A,C,u)
| ~ product(multiplicative_identity,A,B) ),
inference(resolve,[status(thm)],[c_6,c_37]) ).
cnf(c_326,plain,
( ~ product(d,A,v)
| ~ product(c,A,u) ),
inference(resolve,[status(thm)],[c_325,c_34]) ).
cnf(c_253,plain,
~ product(c,b,u),
inference(resolve,[status(thm)],[c_326,c_36]) ).
cnf(c_322,plain,
~ product(b,c,u),
inference(resolve,[status(thm)],[c_10,c_253]) ).
cnf(c_327,plain,
( ~ product(A,C,u)
| ~ product(B,c,C)
| ~ product(A,B,b) ),
inference(resolve,[status(thm)],[c_7,c_322]) ).
cnf(c_328,plain,
( ~ product(multiplicative_identity,A,u)
| ~ product(a,c,A) ),
inference(resolve,[status(thm)],[c_327,c_33]) ).
cnf(c_329,plain,
~ product(multiplicative_identity,u,u),
inference(resolve,[status(thm)],[c_328,c_35]) ).
cnf(c_324,plain,
$false,
inference(resolve,[status(thm)],[c_168,c_329]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD025-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.66 % Computer : n010.cluster.edu
% 0.17/5.66 % Model : x86_64 x86_64
% 0.17/5.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.66 % Memory : 8046.5625MB
% 0.17/5.66 % OS : Linux 6.8.0-71-generic
% 0.17/5.66 % CPULimit : 300
% 0.17/5.66 % WCLimit : 300
% 0.17/5.66 % DateTime : Sun Sep 27 02:24:06 UTC 2026
% 0.17/5.66 % CPUTime :
% 0.17/5.67 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.67 % Process 531516 was started by sandbox2 on n010,
% 0.17/5.67 % Sun Sep 27 02:24:06 2026
% 0.17/5.67 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.67
% 0.17/5.67 % From the command line: assign(max_seconds, 300).
% 0.21/5.70
% 0.21/5.70 % SZS status Unsatisfiable for theBenchmark
% 0.21/5.70
% 0.21/5.70 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.21/5.70 % Length of proof is 14.
% 0.21/5.70 % Level of proof is 3.
% 0.21/5.70 % Maximum clause weight is 21.000.
% 0.21/5.70 % Given clauses 65.
% 0.21/5.70
% 0.21/5.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------