%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : FLD023-1 : 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 : n003.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 08:38:51 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.53s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 15 unt; 0 nHn; 25 RR)
% Number of literals : 39 ( 0 equ; 16 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(a_equals_b_3,negated_conjecture,
equalish(a,b),
file('theBenchmark.p',a_equals_b_3) ).
cnf(additive_identity_not_equal_to_add_4,negated_conjecture,
~ equalish(additive_identity,add(b,additive_inverse(a))),
file('theBenchmark.p',additive_identity_not_equal_to_add_4) ).
cnf(t1,plain,
~ equalish(additive_identity,add(b,additive_inverse(a))),
inference(start,[status(thm),parent(0:0)],[additive_identity_not_equal_to_add_4]) ).
cnf(t2,plain,
( ~ equalish(additive_identity,add(a,additive_inverse(a)))
| ~ equalish(add(a,additive_inverse(a)),add(b,additive_inverse(a)))
| equalish(additive_identity,add(b,additive_inverse(a))) ),
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,
( ~ defined(additive_inverse(a))
| ~ equalish(a,b)
| equalish(add(a,additive_inverse(a)),add(b,additive_inverse(a))) ),
inference(extension,[status(thm),parent(t2:2)],[compatibility_of_equality_and_addition]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
equalish(a,b),
inference(extension,[status(thm),parent(t4:2)],[a_equals_b_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ defined(a)
| defined(additive_inverse(a)) ),
inference(extension,[status(thm),parent(t4:3)],[well_definedness_of_additive_inverse]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
defined(a),
inference(extension,[status(thm),parent(t8:2)],[a_is_defined]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ equalish(add(a,additive_inverse(a)),additive_identity)
| equalish(additive_identity,add(a,additive_inverse(a))) ),
inference(extension,[status(thm),parent(t2:3)],[symmetry_of_equality]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:3]) ).
cnf(t14,plain,
( ~ defined(a)
| equalish(add(a,additive_inverse(a)),additive_identity) ),
inference(extension,[status(thm),parent(t12:2)],[existence_of_inverse_addition]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
defined(a),
inference(extension,[status(thm),parent(t14:2)],[a_is_defined]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD023-1 : 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
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 20 18:51:31 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.23/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.53 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------