%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : FLD005-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 : Thu Sep 24 08:38:46 AM UTC 2026
% Result : Unsatisfiable 227.94s 228.51s
% Output : Proof 227.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 18 unt; 0 nHn; 30 RR)
% Number of literals : 48 ( 0 equ; 20 neg)
% Maximal clause size : 4 ( 1 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 : 15 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_addition_1,axiom,
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
file('FLD002-0.ax',associativity_addition_1) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('FLD002-0.ax',existence_of_identity_addition) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
file('FLD002-0.ax',existence_of_inverse_addition) ).
cnf(commutativity_addition,axiom,
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('FLD002-0.ax',commutativity_addition) ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X)
| defined(additive_inverse(X)) ),
file('FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(totality_of_addition,axiom,
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
file('FLD002-0.ax',totality_of_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(not_sum_3,negated_conjecture,
~ sum(a,X,b),
file('theBenchmark.p',not_sum_3) ).
cnf(t1,plain,
~ sum(a,add(additive_inverse(a),b),b),
inference(start,[status(thm),parent(0:0)],[not_sum_3]) ).
cnf(t2,plain,
( ~ sum(additive_inverse(a),b,add(additive_inverse(a),b))
| ~ sum(additive_identity,b,b)
| ~ sum(a,additive_inverse(a),additive_identity)
| sum(a,add(additive_inverse(a),b),b) ),
inference(extension,[status(thm),parent(t1:1)],[associativity_addition_1]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ sum(additive_inverse(a),a,additive_identity)
| sum(a,additive_inverse(a),additive_identity) ),
inference(extension,[status(thm),parent(t2:2)],[commutativity_addition]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ defined(a)
| sum(additive_inverse(a),a,additive_identity) ),
inference(extension,[status(thm),parent(t4:2)],[existence_of_inverse_addition]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
defined(a),
inference(extension,[status(thm),parent(t6:2)],[a_is_defined]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ defined(b)
| sum(additive_identity,b,b) ),
inference(extension,[status(thm),parent(t2:3)],[existence_of_identity_addition]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
defined(b),
inference(extension,[status(thm),parent(t10:2)],[b_is_defined]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ defined(b)
| ~ defined(additive_inverse(a))
| sum(additive_inverse(a),b,add(additive_inverse(a),b)) ),
inference(extension,[status(thm),parent(t2:4)],[totality_of_addition]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:4]) ).
cnf(t16,plain,
( ~ defined(a)
| defined(additive_inverse(a)) ),
inference(extension,[status(thm),parent(t14:2)],[well_definedness_of_additive_inverse]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
defined(a),
inference(extension,[status(thm),parent(t16:2)],[a_is_defined]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
defined(b),
inference(extension,[status(thm),parent(t14:3)],[b_is_defined]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t14:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD005-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 20 18:43:57 UTC 2026
% 0.13/0.36 % CPUTime :
% 227.94/228.51 % SZS status Unsatisfiable for theBenchmark
% 227.94/228.51 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------