%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD071-3 : 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 : n005.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 07:11:43 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 13 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 35 ( 21 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(compatibility_of_order_relation_and_multiplication,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ product(VAR_1,VAR_2,VAR_0)
| ~ less_or_equal(additive_identity,VAR_2)
| ~ less_or_equal(additive_identity,VAR_1)
| less_or_equal(additive_identity,VAR_0) ),
file('theBenchmark.p',compatibility_of_order_relation_and_multiplication) ).
cnf(c_25,plain,
( ~ product(B,C,A)
| ~ less_or_equal(additive_identity,C)
| ~ less_or_equal(additive_identity,B)
| less_or_equal(additive_identity,A) ),
inference(clausify,[status(thm)],[compatibility_of_order_relation_and_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(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(less_or_equal_3,axiom,
less_or_equal(additive_identity,a),
file('theBenchmark.p',less_or_equal_3) ).
cnf(c_29,plain,
less_or_equal(additive_identity,a),
inference(clausify,[status(thm)],[less_or_equal_3]) ).
fof(less_or_equal_4,axiom,
less_or_equal(additive_identity,b),
file('theBenchmark.p',less_or_equal_4) ).
cnf(c_30,plain,
less_or_equal(additive_identity,b),
inference(clausify,[status(thm)],[less_or_equal_4]) ).
fof(not_less_or_equal_5,axiom,
~ less_or_equal(additive_identity,multiply(a,b)),
file('theBenchmark.p',not_less_or_equal_5) ).
cnf(c_31,plain,
~ less_or_equal(additive_identity,multiply(a,b)),
inference(clausify,[status(thm)],[not_less_or_equal_5]) ).
cnf(c_260,plain,
( ~ product(A,B,multiply(a,b))
| ~ less_or_equal(additive_identity,B)
| ~ less_or_equal(additive_identity,A) ),
inference(resolve,[status(thm)],[c_25,c_31]) ).
cnf(c_261,plain,
( ~ product(a,A,multiply(a,b))
| ~ less_or_equal(additive_identity,A) ),
inference(resolve,[status(thm)],[c_260,c_29]) ).
cnf(c_128,plain,
~ product(a,b,multiply(a,b)),
inference(resolve,[status(thm)],[c_261,c_30]) ).
cnf(c_262,plain,
( ~ defined(b)
| ~ defined(a) ),
inference(resolve,[status(thm)],[c_20,c_128]) ).
cnf(c_263,plain,
~ defined(a),
inference(resolve,[status(thm)],[c_262,c_28]) ).
cnf(c_259,plain,
$false,
inference(resolve,[status(thm)],[c_27,c_263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD071-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n005.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sun Sep 27 02:34:46 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 3608567 was started by sandbox on n005,
% 0.18/0.44 % Sun Sep 27 02:34:46 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.47
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47
% 0.18/0.47 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.18/0.47 % Length of proof is 9.
% 0.18/0.47 % Level of proof is 2.
% 0.18/0.47 % Maximum clause weight is 20.000.
% 0.18/0.47 % Given clauses 73.
% 0.18/0.47
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------