%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD059-3 : 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 : n001.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 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 28 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_of_identity_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_identity,VAR_0,VAR_0) ),
file('theBenchmark.p',existence_of_identity_addition) ).
cnf(c_3,plain,
( ~ defined(A)
| sum(additive_identity,A,A) ),
inference(clausify,[status(thm)],[existence_of_identity_addition]) ).
fof(totality_of_addition,axiom,
! [VAR_0,VAR_1] :
( ~ defined(VAR_1)
| ~ defined(VAR_0)
| sum(VAR_0,VAR_1,add(VAR_0,VAR_1)) ),
file('theBenchmark.p',totality_of_addition) ).
cnf(c_19,plain,
( ~ defined(B)
| ~ defined(A)
| sum(A,B,add(A,B)) ),
inference(clausify,[status(thm)],[totality_of_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_22,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,VAR_3,VAR_4] :
( ~ sum(VAR_3,VAR_4,VAR_1)
| ~ sum(VAR_2,VAR_4,VAR_0)
| ~ less_or_equal(VAR_2,VAR_3)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',compatibility_of_order_relation_and_addition) ).
cnf(c_24,plain,
( ~ sum(D,E,B)
| ~ sum(C,E,A)
| ~ less_or_equal(C,D)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
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(less_or_equal_2,axiom,
less_or_equal(additive_identity,a),
file('theBenchmark.p',less_or_equal_2) ).
cnf(c_28,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_29,plain,
~ less_or_equal(additive_identity,add(a,a)),
inference(clausify,[status(thm)],[not_less_or_equal_3]) ).
cnf(c_115,plain,
sum(additive_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_3]) ).
cnf(c_260,plain,
( ~ defined(A)
| sum(a,A,add(a,A)) ),
inference(resolve,[status(thm)],[c_19,c_27]) ).
cnf(c_123,plain,
sum(a,a,add(a,a)),
inference(resolve,[status(thm)],[c_260,c_27]) ).
cnf(c_261,plain,
( ~ less_or_equal(A,add(a,a))
| ~ less_or_equal(additive_identity,A) ),
inference(resolve,[status(thm)],[c_22,c_29]) ).
cnf(c_143,plain,
~ less_or_equal(a,add(a,a)),
inference(resolve,[status(thm)],[c_261,c_28]) ).
cnf(c_262,plain,
( ~ sum(B,C,add(a,a))
| ~ sum(A,C,a)
| ~ less_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_24,c_143]) ).
cnf(c_263,plain,
( ~ sum(a,A,add(a,a))
| ~ sum(additive_identity,A,a) ),
inference(resolve,[status(thm)],[c_262,c_28]) ).
cnf(c_264,plain,
~ sum(a,a,add(a,a)),
inference(resolve,[status(thm)],[c_263,c_115]) ).
cnf(c_259,plain,
$false,
inference(resolve,[status(thm)],[c_123,c_264]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD059-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n001.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 02:38:29 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 3173459 was started by sandbox on n001,
% 0.10/0.38 % Sun Sep 27 02:38:29 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.10/0.41
% 0.10/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.41
% 0.10/0.41 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.10/0.41 % Length of proof is 11.
% 0.10/0.41 % Level of proof is 2.
% 0.10/0.41 % Maximum clause weight is 20.000.
% 0.10/0.41 % Given clauses 69.
% 0.10/0.41
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------