%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD059-1 : 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 : n016.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 07:11:39 AM UTC 2026
% Result : Unsatisfiable 0.69s 0.50s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 25 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_of_identity_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| equalish(add(additive_identity,VAR_0),VAR_0) ),
file('theBenchmark.p',existence_of_identity_addition) ).
cnf(c_2,plain,
( ~ defined(A)
| equalish(add(additive_identity,A),A) ),
inference(clausify,[status(thm)],[existence_of_identity_addition]) ).
fof(transitivity_of_order_relation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ less_or_equal(VAR_2,VAR_1)
| ~ less_or_equal(VAR_0,VAR_2)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_order_relation) ).
cnf(c_17,plain,
( ~ less_or_equal(C,B)
| ~ less_or_equal(A,C)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_order_relation]) ).
fof(compatibility_of_order_relation_and_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ less_or_equal(VAR_0,VAR_2)
| ~ defined(VAR_1)
| less_or_equal(add(VAR_0,VAR_1),add(VAR_2,VAR_1)) ),
file('theBenchmark.p',compatibility_of_order_relation_and_addition) ).
cnf(c_19,plain,
( ~ less_or_equal(A,C)
| ~ defined(B)
| less_or_equal(add(A,B),add(C,B)) ),
inference(clausify,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
fof(compatibility_of_equality_and_order_relation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ equalish(VAR_2,VAR_0)
| ~ less_or_equal(VAR_2,VAR_1)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',compatibility_of_equality_and_order_relation) ).
cnf(c_26,plain,
( ~ equalish(C,A)
| ~ less_or_equal(C,B)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[compatibility_of_equality_and_order_relation]) ).
fof(a_is_defined,axiom,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(c_28,plain,
defined(a),
inference(clausify,[status(thm)],[a_is_defined]) ).
fof(less_or_equal_2,axiom,
less_or_equal(additive_identity,a),
file('theBenchmark.p',less_or_equal_2) ).
cnf(c_29,plain,
less_or_equal(additive_identity,a),
inference(clausify,[status(thm)],[less_or_equal_2]) ).
fof(not_less_or_equal_3,axiom,
~ less_or_equal(additive_identity,add(a,a)),
file('theBenchmark.p',not_less_or_equal_3) ).
cnf(c_30,plain,
~ less_or_equal(additive_identity,add(a,a)),
inference(clausify,[status(thm)],[not_less_or_equal_3]) ).
cnf(c_144,plain,
equalish(add(additive_identity,a),a),
inference(resolve,[status(thm)],[c_28,c_2]) ).
cnf(c_1667,plain,
( ~ less_or_equal(A,add(a,a))
| ~ less_or_equal(additive_identity,A) ),
inference(resolve,[status(thm)],[c_17,c_30]) ).
cnf(c_166,plain,
~ less_or_equal(a,add(a,a)),
inference(resolve,[status(thm)],[c_1667,c_29]) ).
cnf(c_1668,plain,
( ~ equalish(A,a)
| ~ less_or_equal(A,add(a,a)) ),
inference(resolve,[status(thm)],[c_26,c_166]) ).
cnf(c_1489,plain,
~ less_or_equal(add(additive_identity,a),add(a,a)),
inference(resolve,[status(thm)],[c_1668,c_144]) ).
cnf(c_1669,plain,
( ~ less_or_equal(additive_identity,a)
| ~ defined(a) ),
inference(resolve,[status(thm)],[c_19,c_1489]) ).
cnf(c_1670,plain,
~ defined(a),
inference(resolve,[status(thm)],[c_1669,c_29]) ).
cnf(c_1666,plain,
$false,
inference(resolve,[status(thm)],[c_28,c_1670]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD059-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 02:37:15 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 2236165 was started by sandbox on n016,
% 0.10/0.37 % Sun Sep 27 02:37:15 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).
% 0.69/0.50
% 0.69/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.69/0.50
% 0.69/0.50 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.69/0.50 % Length of proof is 11.
% 0.69/0.50 % Level of proof is 3.
% 0.69/0.50 % Maximum clause weight is 22.000.
% 0.69/0.50 % Given clauses 172.
% 0.69/0.50
% 0.69/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------