%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD070-3 : 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 : n013.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 0.17s 0.53s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 15 unt; 0 def)
% Number of atoms : 48 ( 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 : 4 ( 4 usr; 3 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(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,add(a,b)),
file('theBenchmark.p',not_less_or_equal_5) ).
cnf(c_31,plain,
~ less_or_equal(additive_identity,add(a,b)),
inference(clausify,[status(thm)],[not_less_or_equal_5]) ).
cnf(c_154,plain,
sum(additive_identity,b,b),
inference(resolve,[status(thm)],[c_28,c_3]) ).
cnf(c_358,plain,
( ~ defined(A)
| sum(a,A,add(a,A)) ),
inference(resolve,[status(thm)],[c_19,c_27]) ).
cnf(c_166,plain,
sum(a,b,add(a,b)),
inference(resolve,[status(thm)],[c_358,c_28]) ).
cnf(c_359,plain,
( ~ less_or_equal(A,add(a,b))
| ~ less_or_equal(additive_identity,A) ),
inference(resolve,[status(thm)],[c_22,c_31]) ).
cnf(c_198,plain,
~ less_or_equal(b,add(a,b)),
inference(resolve,[status(thm)],[c_359,c_30]) ).
cnf(c_360,plain,
( ~ sum(B,C,add(a,b))
| ~ sum(A,C,b)
| ~ less_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_24,c_198]) ).
cnf(c_361,plain,
( ~ sum(a,A,add(a,b))
| ~ sum(additive_identity,A,b) ),
inference(resolve,[status(thm)],[c_360,c_29]) ).
cnf(c_362,plain,
~ sum(a,b,add(a,b)),
inference(resolve,[status(thm)],[c_361,c_154]) ).
cnf(c_357,plain,
$false,
inference(resolve,[status(thm)],[c_166,c_362]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD070-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n013.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sun Sep 27 02:34:06 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 4035120 was started by sandbox on n013,
% 0.17/0.45 % Sun Sep 27 02:34:06 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.17/0.53
% 0.17/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.53
% 0.17/0.53 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.17/0.53 % Length of proof is 13.
% 0.17/0.53 % Level of proof is 2.
% 0.17/0.53 % Maximum clause weight is 20.000.
% 0.17/0.53 % Given clauses 76.
% 0.17/0.53
% 0.17/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------