%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD071-4 : 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 : n011.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 07:11:44 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 6 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(less_or_equal_4,axiom,
less_or_equal(additive_identity,a),
file('theBenchmark.p',less_or_equal_4) ).
cnf(c_30,plain,
less_or_equal(additive_identity,a),
inference(clausify,[status(thm)],[less_or_equal_4]) ).
fof(less_or_equal_5,axiom,
less_or_equal(additive_identity,b),
file('theBenchmark.p',less_or_equal_5) ).
cnf(c_31,plain,
less_or_equal(additive_identity,b),
inference(clausify,[status(thm)],[less_or_equal_5]) ).
fof(product_6,axiom,
product(a,b,u),
file('theBenchmark.p',product_6) ).
cnf(c_32,plain,
product(a,b,u),
inference(clausify,[status(thm)],[product_6]) ).
fof(not_less_or_equal_7,axiom,
~ less_or_equal(additive_identity,u),
file('theBenchmark.p',not_less_or_equal_7) ).
cnf(c_33,plain,
~ less_or_equal(additive_identity,u),
inference(clausify,[status(thm)],[not_less_or_equal_7]) ).
cnf(c_145,plain,
( ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(additive_identity,u) ),
inference(resolve,[status(thm)],[c_32,c_25]) ).
cnf(c_146,plain,
( ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ),
inference(resolve,[status(thm)],[c_33,c_145]) ).
cnf(c_147,plain,
~ less_or_equal(additive_identity,b),
inference(resolve,[status(thm)],[c_30,c_146]) ).
cnf(c_144,plain,
$false,
inference(resolve,[status(thm)],[c_31,c_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD071-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 02:34:59 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2019227 was started by sandbox on n011,
% 0.10/0.37 % Sun Sep 27 02:34:59 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.40
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.40
% 0.14/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/0.40 % Length of proof is 6.
% 0.14/0.40 % Level of proof is 1.
% 0.14/0.40 % Maximum clause weight is 13.000.
% 0.14/0.40 % Given clauses 32.
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------