%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : FLD019-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 08:38:50 AM UTC 2026
% Result : Unsatisfiable 135.22s 150.50s
% Output : Proof 135.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of clauses : 44 ( 27 unt; 0 nHn; 44 RR)
% Number of literals : 69 ( 0 equ; 27 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_identity_addition,axiom,
( ~ defined(X)
| equalish(add(additive_identity,X),X) ),
file('FLD001-0.ax',existence_of_identity_addition) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X)
| equalish(add(X,additive_inverse(X)),additive_identity) ),
file('FLD001-0.ax',existence_of_inverse_addition) ).
cnf(commutativity_addition,axiom,
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ),
file('FLD001-0.ax',commutativity_addition) ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X)
| defined(additive_inverse(X)) ),
file('FLD001-0.ax',well_definedness_of_additive_inverse) ).
cnf(symmetry_of_equality,axiom,
( ~ equalish(Y,X)
| equalish(X,Y) ),
file('FLD001-0.ax',symmetry_of_equality) ).
cnf(transitivity_of_equality,axiom,
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
file('FLD001-0.ax',transitivity_of_equality) ).
cnf(compatibility_of_equality_and_addition,axiom,
( ~ equalish(X,Y)
| ~ defined(Z)
| equalish(add(X,Z),add(Y,Z)) ),
file('FLD001-0.ax',compatibility_of_equality_and_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(additive_inverse_equals_additive_identity_2,negated_conjecture,
equalish(additive_inverse(a),additive_identity),
file('theBenchmark.p',additive_inverse_equals_additive_identity_2) ).
cnf(a_not_equal_to_additive_identity_3,negated_conjecture,
~ equalish(a,additive_identity),
file('theBenchmark.p',a_not_equal_to_additive_identity_3) ).
cnf(t1,plain,
~ equalish(a,additive_identity),
inference(start,[status(thm),parent(0:0)],[a_not_equal_to_additive_identity_3]) ).
cnf(t2,plain,
( ~ equalish(a,add(additive_inverse(a),a))
| ~ equalish(add(additive_inverse(a),a),additive_identity)
| equalish(a,additive_identity) ),
inference(extension,[status(thm),parent(t1:1)],[transitivity_of_equality]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ equalish(add(additive_inverse(a),a),add(a,additive_inverse(a)))
| ~ equalish(add(a,additive_inverse(a)),additive_identity)
| equalish(add(additive_inverse(a),a),additive_identity) ),
inference(extension,[status(thm),parent(t2:2)],[transitivity_of_equality]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ defined(a)
| equalish(add(a,additive_inverse(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(additive_inverse(a))
| ~ defined(a)
| equalish(add(additive_inverse(a),a),add(a,additive_inverse(a))) ),
inference(extension,[status(thm),parent(t4:3)],[commutativity_addition]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:3]) ).
cnf(t12,plain,
defined(a),
inference(extension,[status(thm),parent(t10:2)],[a_is_defined]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(l6,lemma,
defined(a),
inference(lemma,[status(cth),parent(t10:2),below(t4:3)],[t10:2]) ).
cnf(t14,plain,
( ~ defined(a)
| defined(additive_inverse(a)) ),
inference(extension,[status(thm),parent(t10:3)],[well_definedness_of_additive_inverse]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
defined(a),
inference(lemma_extension,[status(thm),parent(t14:2)],[l6:1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ equalish(a,add(additive_identity,a))
| ~ equalish(add(additive_identity,a),add(additive_inverse(a),a))
| equalish(a,add(additive_inverse(a),a)) ),
inference(extension,[status(thm),parent(t2:3)],[transitivity_of_equality]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t2:3]) ).
cnf(t20,plain,
( ~ defined(a)
| ~ equalish(additive_identity,additive_inverse(a))
| equalish(add(additive_identity,a),add(additive_inverse(a),a)) ),
inference(extension,[status(thm),parent(t18:2)],[compatibility_of_equality_and_addition]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( ~ equalish(additive_inverse(a),additive_identity)
| equalish(additive_identity,additive_inverse(a)) ),
inference(extension,[status(thm),parent(t20:2)],[symmetry_of_equality]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
equalish(additive_inverse(a),additive_identity),
inference(extension,[status(thm),parent(t22:2)],[additive_inverse_equals_additive_identity_2]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
defined(a),
inference(extension,[status(thm),parent(t20:3)],[a_is_defined]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t20:3]) ).
cnf(t28,plain,
( ~ equalish(add(additive_identity,a),a)
| equalish(a,add(additive_identity,a)) ),
inference(extension,[status(thm),parent(t18:3)],[symmetry_of_equality]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t18:3]) ).
cnf(t30,plain,
( ~ defined(a)
| equalish(add(additive_identity,a),a) ),
inference(extension,[status(thm),parent(t28:2)],[existence_of_identity_addition]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
defined(a),
inference(extension,[status(thm),parent(t30:2)],[a_is_defined]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD019-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 This is a CNF_UNS_RFO_NEQ_NHN problem
% 0.00/0.05 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/15.42 % Computer : n017.cluster.edu
% 0.14/15.42 % Model : x86_64 x86_64
% 0.14/15.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/15.42 % Memory : 8046.5625MB
% 0.14/15.42 % OS : Linux 6.8.0-71-generic
% 0.14/15.42 % CPULimit : 300
% 0.14/15.42 % WCLimit : 300
% 0.14/15.42 % DateTime : Sun Sep 20 18:43:28 UTC 2026
% 0.14/15.42 % CPUTime :
% 135.22/150.50 % SZS status Unsatisfiable for theBenchmark
% 135.22/150.50 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------