%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD005-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 07:11:25 AM UTC 2026
% Result : Unsatisfiable 0.90s 0.55s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 14 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 28 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 5 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_addition_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ sum(VAR_3,VAR_5,VAR_2)
| ~ sum(VAR_4,VAR_1,VAR_5)
| ~ sum(VAR_3,VAR_4,VAR_0)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_addition_2) ).
cnf(c_2,plain,
( ~ sum(D,F,C)
| ~ sum(E,B,F)
| ~ sum(D,E,A)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_addition_2]) ).
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(existence_of_inverse_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_inverse(VAR_0),VAR_0,additive_identity) ),
file('theBenchmark.p',existence_of_inverse_addition) ).
cnf(c_4,plain,
( ~ defined(A)
| sum(additive_inverse(A),A,additive_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_addition]) ).
fof(commutativity_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ sum(VAR_1,VAR_0,VAR_2)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_addition) ).
cnf(c_5,plain,
( ~ sum(B,A,C)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_addition]) ).
fof(well_definedness_of_additive_inverse,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| defined(additive_inverse(VAR_0)) ),
file('theBenchmark.p',well_definedness_of_additive_inverse) ).
cnf(c_15,plain,
( ~ defined(A)
| defined(additive_inverse(A)) ),
inference(clausify,[status(thm)],[well_definedness_of_additive_inverse]) ).
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(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(not_sum_3,axiom,
! [VAR_0] : ~ sum(a,VAR_0,b),
file('theBenchmark.p',not_sum_3) ).
cnf(c_29,plain,
~ sum(a,A,b),
inference(clausify,[status(thm)],[not_sum_3]) ).
cnf(c_92,plain,
defined(additive_inverse(a)),
inference(resolve,[status(thm)],[c_27,c_15]) ).
cnf(c_97,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_104,plain,
( ~ defined(A)
| sum(b,A,add(b,A)) ),
inference(resolve,[status(thm)],[c_28,c_19]) ).
cnf(c_114,plain,
sum(additive_identity,b,b),
inference(resolve,[status(thm)],[c_28,c_3]) ).
cnf(c_116,plain,
~ sum(A,a,b),
inference(resolve,[status(thm)],[c_5,c_29]) ).
cnf(c_316,plain,
sum(b,additive_identity,b),
inference(resolve,[status(thm)],[c_114,c_5]) ).
cnf(c_868,plain,
( ~ sum(A,D,b)
| ~ sum(B,a,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_2,c_116]) ).
cnf(c_869,plain,
( ~ sum(A,additive_identity,b)
| ~ sum(A,additive_inverse(a),B) ),
inference(resolve,[status(thm)],[c_868,c_97]) ).
cnf(c_811,plain,
~ sum(b,additive_inverse(a),A),
inference(resolve,[status(thm)],[c_869,c_316]) ).
cnf(c_870,plain,
sum(b,additive_inverse(a),add(b,additive_inverse(a))),
inference(resolve,[status(thm)],[c_104,c_92]) ).
cnf(c_867,plain,
$false,
inference(resolve,[status(thm)],[c_811,c_870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD005-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.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 02:20:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3100285 was started by sandbox2 on n004,
% 0.10/0.36 % Sun Sep 27 02:20:36 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.90/0.55
% 0.90/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.90/0.55
% 0.90/0.55 % Proof 1 at 0.13 (+ 0.04) seconds.
% 0.90/0.55 % Length of proof is 17.
% 0.90/0.55 % Level of proof is 4.
% 0.90/0.55 % Maximum clause weight is 21.000.
% 0.90/0.55 % Given clauses 191.
% 0.90/0.55
% 0.90/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------